BacktoBasics/algo_n_ds/intro/python_basics.ipynb

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   "source": [
    "# Chapter 1. Python Primer"
   ]
  },
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   "source": [
    "Python Resource:\n",
    "    https://medium.com/@-TutortAcademy/choosing-the-best-books-for-mastering-python-algorithms-c7d0b5a64057\n",
    "\n",
    "Python Book:\n",
    "    Data Structures and Algorithms in Python by Michael T. Goodrich and Roberto Tamassia\n",
    "    https://nibmehub.com/opac-service/pdf/read/Data%20Structures%20and%20Algorithms%20in%20Python.pdf\n",
    "\n",
    "Chapter 1:\n",
    "    Python is a interpeted and dynamic type language that does not require a compiler\n",
    "    \n",
    "    Class|Description|Immutable?\n",
    "    bool|Boolean value|Yes\n",
    "    int|integer (arbitrary magnitude)|Yes\n",
    "    float|floating-point number| Yes\n",
    "    list|mutable sequence of objects|No\n",
    "    tuple| immutable sequence of objects|Yes\n",
    "    str|character string|Yes\n",
    "    set |unordered set of distinct objects| No\n",
    "    frozenset|immutable form of set class| Yes\n",
    "    dict|associative mapping (aka dictionary)| No\n",
    "\n",
    "    Sequence Types\n",
    "        are list, tuple, and str.\n",
    "        list = []\n",
    "            - list are zero index are similar to an array\n",
    "        Tuple = ()\n",
    "            - tuples are immutable version of a sequence\n",
    "        str = \"\" or '' or \"\"\"\"\"\" or ''''''\n",
    "            - str is specifically designed to represent an immutable sequence of\n",
    "            characters\n",
    "    Set and Frozenset\n",
    "        set = {}\n",
    "            - set class represent the mathamatical notion of a set, namely\n",
    "            a collection of elements, without a duplicate\n",
    "            - No order\n",
    "        frozenset =\n",
    "            - is a immutable form of a set type, so it is legal to have set of frozenset\n",
    "            - frozenset()\n",
    "    Dict\n",
    "        dict represents a dictionary or mapping from a set of dictinct keys to associated values\n",
    "            - key value pair\n",
    "                dictionary = {'k':'V','k1':'V1'}\n",
    "            - access value\n",
    "                dictionary['K'] or dictionary.get('k')\n",
    "    Operators:\n",
    "        Python provides the following bitwise operators for integers:\n",
    "            ∼ bitwise complement (prefix unary operator)\n",
    "            & bitwise and\n",
    "            | bitwise or\n",
    "            ˆ bitwise exclusive-or\n",
    "            << shift bits left, filling in with zeros\n",
    "            >> shift bits right, filling in with sign bit\n",
    "\n",
    "        Each of Python’s built-in sequence types (str, tuple, and list) support the following\n",
    "            operator syntaxes:\n",
    "            s[j] element at index j\n",
    "            s[start:stop] slice including indices [start,stop)\n",
    "            s[start:stop:step] slice including indices start, start + step,\n",
    "            start + 2 step, . . . , up to but not equalling or stop\n",
    "            s+t concatenation of sequences\n",
    "            k s shorthand for s + s + s + ... (k times)\n",
    "            val in s containment check\n",
    "            val not in s non-containment check\n",
    "\n",
    "        Operators for Sets and Dictionaries\n",
    "            Sets and frozensets support the following operators:\n",
    "            key in s containment check\n",
    "            key not in s non-containment check\n",
    "            s1 == s2 s1 is equivalent to s2\n",
    "            s1 != s2 s1 is not equivalent to s2\n",
    "            s1 <= s2 s1 is subset of s2\n",
    "            s1 < s2 s1 is proper subset of s2\n",
    "            s1 >= s2 s1 is superset of s2\n",
    "            s1 > s2 s1 is proper superset of s2\n",
    "            s1 | s2 the union of s1 and s2\n",
    "            s1 & s2 the intersection of s1 and s2\n",
    "            s1 − s2 the set of elements in s1 but not s2\n",
    "            s1 ˆ s2 the set of elements in precisely one of s1 or s2\n",
    "\n",
    "\n",
    "        Control Flow\n",
    "            \n",
    "            if first condition:\n",
    "                first body\n",
    "            elif second condition:\n",
    "                second body\n",
    "            elif third condition:\n",
    "                third body\n",
    "            else:\n",
    "                fourth body\n",
    "\n",
    "\n",
    "        Loops:\n",
    "            while statement:\n",
    "                while condition:\n",
    "                    body\n",
    "            - condition statement needs to be false to exit\n",
    "\n",
    "        Calling Syntax Description\n",
    "            Calling_Syntax Description\n",
    "            abs(x) Return the absolute value of a number.\n",
    "            all(iterable) Return True if bool(e) is True for each element e.\n",
    "            any(iterable) Return True if bool(e) is True for at least one element e.\n",
    "            chr(integer) Return a one-character string with the given Unicode code point.\n",
    "            divmod(x, y) Return (x // y, x % y) as tuple, if x and y are integers.\n",
    "            hash(obj) Return an integer hash value for the object (see Chapter 10).\n",
    "            id(obj) Return the unique integer serving as an “identity” for the object.\n",
    "            input(prompt) Return a string from standard input; the prompt is optional.\n",
    "            isinstance(obj, cls) Determine if obj is an instance of the class (or a subclass).\n",
    "            iter(iterable) Return a new iterator object for the parameter (see Section 1.8).\n",
    "            len(iterable) Return the number of elements in the given iteration.\n",
    "            map(f, iter1, iter2, ...) Return an iterator yielding the result of function calls f(e1, e2, ...)\n",
    "            for respective elements e1 ∈ iter1,e2 ∈ iter2,...\n",
    "            max(iterable) Return the largest element of the given iteration.\n",
    "            max(a, b, c, ...) Return the largest of the arguments.\n",
    "            min(iterable) Return the smallest element of the given iteration.\n",
    "            min(a, b, c, ...) Return the smallest of the arguments.\n",
    "            next(iterator) Return the next element reported by the iterator (see Section 1.8).\n",
    "            open(filename, mode) Open a file with the given name and access mode.\n",
    "            ord(char) Return the Unicode code point of the given character.\n",
    "            pow(x, y) Return the value xy (as an integer if x and y are integers);\n",
    "            equivalent to x y.\n",
    "            pow(x, y, z) Return the value (xy mod z) as an integer.\n",
    "            print(obj1, obj2, ...) Print the arguments, with separating spaces and trailing newline.\n",
    "            range(stop) Construct an iteration of values 0, 1,..., stop−1.\n",
    "            range(start, stop) Construct an iteration of values start, start+1,..., stop−1.\n",
    "            range(start, stop, step) Construct an iteration of values start, start+step, start+2 step,...\n",
    "            reversed(sequence) Return an iteration of the sequence in reverse.\n",
    "            round(x) Return the nearest int value (a tie is broken toward the even value).\n",
    "            round(x, k) Return the value rounded to the nearest 10−k (return-type matches x).\n",
    "            sorted(iterable) Return a list containing elements of the iterable in sorted order.\n",
    "            sum(iterable) Return the sum of the elements in the iterable (must be numeric).\n",
    "            type(obj) Return the class to which the instance obj belongs.\n",
    "\n",
    "        Error Handling\n",
    "            \n",
    "            Class Description\n",
    "            Exception A base class for most error types\n",
    "            AttributeError Raised by syntax obj.foo, if obj has no member named foo\n",
    "            EOFError Raised if “end of file” reached for console or file input\n",
    "            IOError Raised upon failure of I/O operation (e.g., opening file)\n",
    "            IndexError Raised if index to sequence is out of bounds\n",
    "            KeyError Raised if nonexistent key requested for set or dictionary\n",
    "            KeyboardInterrupt Raised if user types ctrl-C while program is executing\n",
    "            NameError Raised if nonexistent identifier used\n",
    "            StopIteration Raised by next(iterator) if no element; see Section 1.8\n",
    "            TypeError Raised when wrong type of parameter is sent to a function\n",
    "            ValueError Raised when parameter has invalid value (e.g., sqrt(−5))\n",
    "            ZeroDivisionError Raised when any division operator used with 0 as divison\n",
    "\n",
    "\n",
    "        Modules\n",
    "            Module Name Description\n",
    "                array Provides compact array storage for primitive types.\n",
    "                collections Defines additional data structures and abstract base classes\n",
    "                involving collections of objects.\n",
    "                copy Defines general functions for making copies of objects.\n",
    "                heapq Provides heap-based priority queue functions (see Section 9.3.7).\n",
    "                math Defines common mathematical constants and functions.\n",
    "                os Provides support for interactions with the operating system.\n",
    "                random Provides random number generation.\n",
    "                re Provides support for processing regular expressions.\n",
    "                sys Provides additional level of interaction with the Python interpreter.\n",
    "                time Provides support for measuring time, or delaying a program.\n",
    "\n",
    "        Generators:\n",
    "            - Generators are most convient ways to create iterators\n",
    "            - A function that uses the yield instead of return keyword\n",
    "            - Yield statement is executed to indicate each element of the series\n",
    "                # list that produces everything\n",
    "                def factor(n):\n",
    "                    results = []\n",
    "                    for k in range(1,n+1):\n",
    "                        if n%k == 0:\n",
    "                            results.append(k)\n",
    "                    return results\n",
    "\n",
    "                # yield implementation\n",
    "                def factor(n):\n",
    "                    for k in range(1,n+1):\n",
    "                        if n%k == 0:\n",
    "                            yield k   "
   ]
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    "### Write a short Python function, is multiple(n, m), that takes two integer\n",
    "### values and returns True if n is a multiple of m, that is, n = mi for some\n",
    "### integer i, and False otherwise.\n"
   ]
  },
  {
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   "execution_count": 123,
   "id": "b1b5f202-3425-4266-9935-40e3d12304fc",
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   "outputs": [],
   "source": [
    "def is_multiple(n,m):\n",
    "    if n%m == 0:\n",
    "        return True\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "4e2fb741-c104-4dd5-b5ee-689b1bbbe4da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_multiple(16,8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "c04e6ee0-58fb-4860-b3aa-3fcb48d71f48",
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_multiple(16,3)"
   ]
  },
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   "id": "8b4ac594-c7a0-4238-abd0-6908d39c2c4f",
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   "source": [
    "### R-1.2 Write a short Python function, is even(k), that takes an integer value and\n",
    "### returns True if k is even, and False otherwise. However, your function\n",
    "### cannot use the multiplication, modulo, or division operators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "ed5dd03b-b2fd-45ce-89aa-7129b5c159df",
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_even(k):\n",
    "    if (k & 1) == 0:\n",
    "        return True\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "ec2a0598-d9f4-4979-8f54-8534123137d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_even(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "4cbf0548-cc4a-4c83-bf80-26d9da4f8ceb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_even(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "264e1a04-e3af-4f7b-ad17-27b3e4d62539",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L1 [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n",
      "l2 [0, 100, 200, 300, 400, 500, 600, 700, 800, 900]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[0, 101, 202, 303, 404, 505, 606, 707, 808, 909]"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Test Map Function\n",
    "\n",
    "def add(a,b):\n",
    "    return a+b\n",
    "\n",
    "def iter_lists(func,list1,list2):\n",
    "    return map(func,list1,list2)\n",
    "\n",
    "l1 = [i for i in range(0,10,)] \n",
    "l2 = [i*100 for i in range(0,10)]\n",
    "\n",
    "print('L1', l1)\n",
    "print('l2',l2)\n",
    "\n",
    "list(iter_lists(add,l1,l2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffdfe873-cd9c-4cdc-96de-25bc70615ad7",
   "metadata": {},
   "source": [
    "### R-1.3 Write a short Python function, minmax(data), that takes a sequence of\n",
    "### one or more numbers, and returns the smallest and largest numbers, in the\n",
    "### form of a tuple of length two. Do not use the built-in functions min or\n",
    "### max in implementing your solution."
   ]
  },
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   "cell_type": "code",
   "execution_count": 130,
   "id": "f29e38d1-af04-4b1b-aa04-f6c942dec0a3",
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   "outputs": [],
   "source": [
    "def minmax(data):\n",
    "    minimum = maximum = data[0]\n",
    "    for i in data[1:]:\n",
    "        if i < minimum:\n",
    "            minimum = i\n",
    "        elif i > maximum:\n",
    "            maximum = i\n",
    "    return (minimum,maximum)        \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "d57c6de6-aa5a-4d93-9aa4-dcd7345a31ee",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[500, 400, 600, 100, 0, 900, 300, 800, 700, 200]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0, 900)"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import random\n",
    "shuffled_list = random.shuffle(l2)\n",
    "print(l2)\n",
    "minmax(l2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b1cbae8-0d85-4880-9a18-9b918dc8144b",
   "metadata": {},
   "source": [
    "### R-1.5\n",
    "### Give a single command that computes the sum from Exercise R-1.4, relying on Python’s comprehension syntax and the built-in sum function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "a52eb96c-5573-4d8e-912d-6507584e5ba8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "900\n"
     ]
    }
   ],
   "source": [
    "l3 = [a for a in minmax(l2)]\n",
    "print(sum(l3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b96bfff2-f8ba-4105-8a98-031034e642d3",
   "metadata": {},
   "source": [
    "### R-1.6 \n",
    "### Write a short Python function that takes a positive integer n and returns the sum of the squares of all the odd positive integers smaller than n\n",
    "\n",
    "### R-1.7 Give a single command that computes the sum from Exercise R-1.6, relying on Python’s comprehension syntax and the built-in sum function.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "05d14cb9-cf9c-49b0-bbf2-ac884b4d43e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def squared_odds(n):\n",
    "    if type(n) == int and n> 0:\n",
    "        return sum([pow(i,2) for i in range(1,n) if i%2 != 0])\n",
    "    else:\n",
    "        print(f'Not greater than 0 or argument is not type of int {n}')\n",
    "            \n",
    "                "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "ad073967-8935-4daf-9eb3-c7866b4dbd3f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Not greater than 0 or argument is not type of int A\n"
     ]
    }
   ],
   "source": [
    "squared_odds('A')\n",
    "assert squared_odds(4) == 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "bf98b1d0-7d5b-4ea1-bca7-72730236434c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "squared_odds(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "090291ab-1de3-45e0-bc90-580261db151d",
   "metadata": {},
   "source": [
    "### R-1.8 \n",
    "### Python allows negative integers to be used as indices into a sequence, such as a string. If string s has length n, and expression s[k] is used for index −n ≤ k < 0, what is the equivalent index j ≥ 0 such that s[j] references the same element?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "d964af08-654c-4edf-8f22-3269926e558b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'o'"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "string = \"Hello\"\n",
    "string[-1]\n",
    "index = len(string)-1\n",
    "string[index]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f24f26d3-86f6-4cd3-a505-997af3678c4a",
   "metadata": {},
   "source": [
    "### R-1.9 What parameters should be sent to the range constructor, to produce a\n",
    "### range with values 50, 60, 70, 80?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "057a5e05-5fd8-449e-8c34-226da6ad23f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[50, 60, 70, 80]"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(range(50,81,10))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89bbec42-d5bb-49ca-89dc-8c75827cdcb6",
   "metadata": {},
   "source": [
    "### R-1.10 \n",
    "### What parameters should be sent to the range constructor, to produce a range with values 8, 6, 4, 2, 0, −2, −4, −6, −8?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "73ec2d7d-9fac-446d-bb50-c928e7840ee9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[8, 6, 4, 2, 0, -2, -4, -6, -8]"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(range(8,-9,-2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "2263996c-1d54-4658-a044-ffaa4ea207b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "### R-1.11 \n",
    "### Demonstrate how to use Python’s list comprehension syntax to produce the list [1, 2, 4, 8, 16, 32, 64, 128, 256].\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "73fda77b-410f-4a85-a438-dd4ef78062bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 4, 8, 16, 32, 64, 128, 256]"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[pow(2,i) for i in range(0,9)] "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23400de6-d7dd-47c5-8bc6-e873ea827909",
   "metadata": {},
   "source": [
    "### R-1.12 \n",
    "### Python’s random module includes a function choice(data) that returns a\n",
    "### random element from a non-empty sequence. The random module includes a more basic function randrange, with parameterization similar to\n",
    "### the built-in range function, that return a random choice from the given\n",
    "### range. Using only the randrange function, implement your own version\n",
    "### of the choice function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "83653a4b-4f5b-44ac-b900-86c40457e182",
   "metadata": {},
   "outputs": [],
   "source": [
    "def choice_rand(start,end):\n",
    "    return random.randrange(start,end)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "927bf1ab-62c5-455a-8b12-50763f8af276",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "choice_rand(1,10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75b516d2-4611-4a11-ada6-5b766f080142",
   "metadata": {},
   "source": [
    "### C-1.13\n",
    "### Write a pseudo-code description of a function that reverses a list of n\n",
    "### integers, so that the numbers are listed in the opposite order than they\n",
    "### were before, and compare this method to an equivalent Python function\n",
    "### for doing the same thing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "92545f70-2184-4147-965d-f9090277ce0a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def reverse_iter(iterable):\n",
    "    return iterable[::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "34bc0ba6-b956-46da-afac-05127b628485",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9, 8, 7, 6, 5, 4, 3, 2, 1, 0]"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reverse_iter(l1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "934f35ae-fe9c-4dea-9cef-b82f0c9583c0",
   "metadata": {},
   "source": [
    "### C-1.14 \n",
    "### Write a short Python function that takes a sequence of integer values and determines if there is a distinct pair of numbers in the sequence whose product is odd."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "26d3f07e-8838-4b60-b106-3ecc8abd93c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def distinct_pair(iterable):\n",
    "    \"\"\"\n",
    "    Used a queue as a strategy here, FIFO\n",
    "    This is O(n^2)\n",
    "    \"\"\"\n",
    "    products = set()\n",
    "    for _ in range(len(iterable)):\n",
    "        head = iterable.pop(0)\n",
    "        for i in iterable:\n",
    "            if (head * i)%2 != 0:\n",
    "                products.add((head,i))\n",
    "    return products"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "b8771e12-bd4f-46df-95ed-d73fb9fefb03",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(1, 3),\n",
       " (1, 5),\n",
       " (1, 7),\n",
       " (1, 9),\n",
       " (3, 5),\n",
       " (3, 7),\n",
       " (3, 9),\n",
       " (5, 7),\n",
       " (5, 9),\n",
       " (7, 9)}"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distinct_pair(l1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "ee696f52-9fb0-41db-a0f9-a7fc85df8eb8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(1, 3), (3, 3)}"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distinct_pair([1,2,3,3,3,3])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97f14817-34e3-433e-9129-2f716cb41f14",
   "metadata": {},
   "source": [
    "### C-1.15\n",
    "### Write a Python function that takes a sequence of numbers and determines if all the numbers are different from each other (that is, they are distinct)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "9b0e43b0-cc26-4b10-9566-9d0c2347f38e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def distinct_numbers(iterable):\n",
    "    if len(iterable) == len(set(iterable)):\n",
    "        return True\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "1dc26c24-e298-4dda-aae8-02e53fb7c412",
   "metadata": {},
   "outputs": [],
   "source": [
    "l1 = [i for i in range(10)]\n",
    "l2 = [2] * 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "5b73317c-3e95-49e0-91ef-cec32329ad68",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "39cd8836-d5ed-471c-83cf-49bc2389d68e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 2, 2, 2]"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "d9927d8c-aa2a-4c11-8460-30185453fe47",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distinct_numbers(l1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "id": "2230be5c-9912-4d74-bf11-acd7e9367080",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distinct_numbers(l2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d2147bf-06b9-4f9f-9dd3-87cb94c8d2b2",
   "metadata": {},
   "source": [
    "### C-1.16\n",
    "### In our implementation of the scale function (page 25), the body of the loop executes the command data[j] = factor. We have discussed that numeric types are immutable, and that use of the = operator in this context causes the creation of a new instance (not the mutation of an existing instance). How is it still possible, then, that our implementation of scale changes the actual parameter sent by the caller?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "id": "513e7829-9307-4beb-863a-41eb0565a05f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "id": "1426d034-966c-4e86-a17a-4df0935784c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = l1.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "aa368a1e-9d19-4308-9555-773bc49705ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "id": "96c391dd-8906-46d5-957c-59237d389a81",
   "metadata": {},
   "outputs": [],
   "source": [
    "def scale(data,factor):\n",
    "    for i in range(len(data)):\n",
    "        data[i] =data[i]*factor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "id": "5e004859-76ee-4bc2-be20-4c321a3a7431",
   "metadata": {},
   "outputs": [],
   "source": [
    "scale(data,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "id": "80960b46-3a13-4e42-a5ba-1e3ae5a48409",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 2, 4, 6, 8, 10, 12, 14, 16, 18]"
      ]
     },
     "execution_count": 159,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "id": "7b580b6e-c2db-4497-9db8-41e63d4b0d8f",
   "metadata": {},
   "outputs": [],
   "source": [
    "immutable_data = set(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "id": "efb36e54-b3b2-4058-a5f1-b33f2f01544a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0, 2, 4, 6, 8, 10, 12, 14, 16, 18}"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "immutable_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "id": "80017977-9909-46d1-b29d-8965a24ff691",
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "'set' object is not subscriptable",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[162], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[43mscale\u001b[49m\u001b[43m(\u001b[49m\u001b[43mimmutable_data\u001b[49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m2\u001b[39;49m\u001b[43m)\u001b[49m\n",
      "Cell \u001b[1;32mIn[157], line 3\u001b[0m, in \u001b[0;36mscale\u001b[1;34m(data, factor)\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mscale\u001b[39m(data,factor):\n\u001b[0;32m      2\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(\u001b[38;5;28mlen\u001b[39m(data)):\n\u001b[1;32m----> 3\u001b[0m         data[i] \u001b[38;5;241m=\u001b[39m\u001b[43mdata\u001b[49m\u001b[43m[\u001b[49m\u001b[43mi\u001b[49m\u001b[43m]\u001b[49m\u001b[38;5;241m*\u001b[39mfactor\n",
      "\u001b[1;31mTypeError\u001b[0m: 'set' object is not subscriptable"
     ]
    }
   ],
   "source": [
    "scale(immutable_data,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c41bf22d-c7c7-4fa7-9332-7501868067ea",
   "metadata": {},
   "source": [
    "### C-1.17 \n",
    "### Had we implemented the scale function (page 25) as follows, does it work properly? \n",
    "### def scale(data, factor):\n",
    "###    for val in data:\n",
    "###        val = factor\n",
    "\n",
    "#### This would not work cause we are only altering the value itself than the index of data. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4efff463-a5f0-43b7-b168-b08d9f1de081",
   "metadata": {},
   "source": [
    "### C-1.18\n",
    "### Demonstrate how to use Python’s list comprehension syntax to producethe list [0, 2, 6, 12, 20, 30, 42, 56, 72, 90]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "id": "e8dcf1bf-a86e-4906-9381-e227587bf8a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 2, 6, 12, 20, 30, 42, 56, 72, 90]"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[i*(i+1) for i in range(10)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d25fe11-4ae1-4d80-bc4d-a1cfb8e85df4",
   "metadata": {},
   "source": [
    "### C-1.19\n",
    "### Demonstrate how to use Python’s list comprehension syntax to produce the list [ a , b , c , ..., z ], but without having to type all 26 such characters literally"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "id": "1d653048-c1a8-42df-9695-aa4fd03a23b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['a',\n",
       " 'b',\n",
       " 'c',\n",
       " 'd',\n",
       " 'e',\n",
       " 'f',\n",
       " 'g',\n",
       " 'h',\n",
       " 'i',\n",
       " 'j',\n",
       " 'k',\n",
       " 'l',\n",
       " 'm',\n",
       " 'n',\n",
       " 'o',\n",
       " 'p',\n",
       " 'q',\n",
       " 'r',\n",
       " 's',\n",
       " 't',\n",
       " 'u',\n",
       " 'v',\n",
       " 'w',\n",
       " 'x',\n",
       " 'y',\n",
       " 'z']"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[chr(i) for i in range(97,123)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9212a17-dcc0-49e5-b4d1-6c9f379fcc60",
   "metadata": {},
   "source": [
    "### C-20 \n",
    "### Python’s random module includes a function shuffle(data) that accepts a list of elements and randomly reorders the elements so that each possible order occurs with equal probability. The random module includes a more basic function randint(a, b) that returns a uniformly random integer from a to b (including both endpoints). Using only the randint function, implement your own version of the shuffle function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "id": "5a92ef7b-7881-436c-8b19-6908128fd8aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "unordered_list = [1,1,4,5,4,6,6,4,7]\n",
    "random.shuffle(unordered_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "id": "84193591-1600-4d11-9157-fd99ebc0bbb3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4, 5, 4, 6, 4, 1, 1, 7, 6]"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unordered_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "id": "4e968c88-9968-4bc4-8019-b6b506bff6bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "def myshuffle(start,end,loops):\n",
    "    return [random.randint(start,end) for _ in range(loops)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "id": "f6d45962-cab1-4117-bb14-c7a5f86aed65",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9, 6, 1, 1, 6, 6, 8, 6, 6, 1]"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "myshuffle(1,10,10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e80ae53e-6fd5-4857-97be-316e0c5177ea",
   "metadata": {},
   "source": [
    "### C-1.22 \n",
    "### Write a short Python program that takes two arrays a and b of length n storing int values, and returns the dot product of a and b. That is, it returns an array c of length n such that c[i] = a[i] · b[i], for i = 0,...,n−1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "id": "7dfef6fe-829c-4b35-b2a1-cde251e3da1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def product_list(a,b):\n",
    "    if len(a) == len(b):\n",
    "        return list(map(lambda x,y: x*y, a,b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "id": "8276f75f-c5ee-4da5-b6b6-4cd8ae9ad9ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 2, 8, 18, 32, 50, 72, 98, 128, 162]"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "product_list([i for i in range(0,10)],[i*2 for i in range(0,10)])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "596e0db2-8a9d-4ca5-b58a-33701be1c439",
   "metadata": {},
   "source": [
    "### C-1.23 Give an example of a Python code fragment that attempts to write an element to a list based on an index that may be out of bounds. If that index is out of bounds, the program should catch the exception that results, and print the following error message: “Don’t try buffer overflow attacks in Python!”"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "id": "cceefde9-ca98-46c6-a4dd-6e01f38f8486",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Don’t try buffer overflow attacks in Python!\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    unordered_list[100]\n",
    "except IndexError as ie:\n",
    "    print('Don’t try buffer overflow attacks in Python!')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "893fe087-7b0c-4a92-99b8-fe71a8acb923",
   "metadata": {},
   "source": [
    "### C-1.24 Write a short Python function that counts the number of vowels in a given character string."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "id": "56c2428b-8d7e-4e63-a329-7c9374799753",
   "metadata": {},
   "outputs": [],
   "source": [
    "def count_vowels(string):\n",
    "    vowels = ['a','e','i','o','u']\n",
    "    count = 0\n",
    "    for char in string.lower():\n",
    "        if char in vowels:\n",
    "            count+=1\n",
    "    return count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "id": "ee1ef3a5-c5f8-4630-a7b8-be46f3966dc2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count_vowels(\"String\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "id": "25a43581-e829-4723-be89-7f130af276b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count_vowels(\"FANNY\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47652b72-a934-4231-8049-47666cb7a7e4",
   "metadata": {},
   "source": [
    "### C-1.25\n",
    "### Write a short Python function that takes a string s, representing a sentence, and returns a copy of the string with all punctuation removed. For example, if given the string \"Let's try, Mike.\", this function would return \"Lets try Mike\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "id": "f9aa9980-0129-47dd-ab05-6fa5cb088933",
   "metadata": {},
   "outputs": [],
   "source": [
    "import re\n",
    "def remove_punctuation(string):\n",
    "    return re.sub(r'[^\\w\\s]','',string)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "id": "f1fcd806-fd9a-4122-819f-57216ed7841e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Lets try Mike'"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "remove_punctuation(\"Let's try, Mike.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "866a67e5-d664-4fda-967e-0626eb3f7638",
   "metadata": {},
   "source": [
    "### C-1.26\n",
    "### Write a short program that takes as input three integers, a, b, and c, from the console and determines if they can be used in a correct arithmetic formula (in the given order), like “a+b = c,” “a = b−c,” or “a ∗ b = c.”"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "id": "63616541-b714-409d-8af7-965c18a65a29",
   "metadata": {},
   "outputs": [],
   "source": [
    "def correct_arithmetic(a,b,c):\n",
    "    for t1,t2,t3 in [(a,b,c),(c,b,a)]:\n",
    "        if t1 + t2 == t3:\n",
    "            print(f'{t1} + {t2} = {t3}')\n",
    "        if t1 - t2 == t3:\n",
    "            print(f'{t1} - {t2} = {t3}')\n",
    "        if t1 * t2 == t3:\n",
    "            print(f'{t1} * {t2} = {t3}')\n",
    "        if t1 / t2 == t3:\n",
    "            print(f'{t1} / {t2} = {t3}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "id": "f34bbfb6-3f00-448a-8a00-21a7a0edcadd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 + 2 = 3\n",
      "3 - 2 = 1\n"
     ]
    }
   ],
   "source": [
    "correct_arithmetic(1,2,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "id": "5111d631-8e43-4e20-ac41-0a66ca60d2d7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 + 2 = 4\n",
      "2 * 2 = 4\n",
      "4 - 2 = 2\n",
      "4 / 2 = 2\n"
     ]
    }
   ],
   "source": [
    "correct_arithmetic(2,2,4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab14281a-54d5-413e-8094-671431067e17",
   "metadata": {},
   "source": [
    "### C-1.27 \n",
    "### In Section 1.8, we provided three different implementations of a generator that computes factors of a given integer. The third of those implementations, from page 41, was the most efficient, but we noted that it did not yield the factors in increasing order. Modify the generator so that it reports factors in increasing order, while maintaining its general performance advantages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "id": "7c4cd89a-0ff5-4c64-bab2-e0a12982ff0f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def factors(n): # generator that computes factors\n",
    "    k=1\n",
    "    while k*k < n: # while k < sqrt(n)\n",
    "        if n % k == 0:\n",
    "            yield k\n",
    "            yield n // k\n",
    "        k += 1\n",
    "    if k *k == n: # special case if n is perfect square\n",
    "        yield k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "id": "30c186b3-dbc5-44cf-b098-51b61c548a93",
   "metadata": {},
   "outputs": [],
   "source": [
    "gen = factors(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "id": "b30f20fd-b8f8-46b5-866d-e7d6fa90a522",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "next(gen)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "id": "b1e5770d-89c4-42df-8d02-fd788c372494",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "next(gen)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "id": "a551e59b-7338-4219-b5e4-8f9d4347505e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 5]"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# list of generator\n",
    "list(gen)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "id": "bfaa7111-cd1e-4880-81d3-b05c0ac3a402",
   "metadata": {},
   "outputs": [
    {
     "ename": "StopIteration",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mStopIteration\u001b[0m                             Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[185], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[38;5;28;43mnext\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mgen\u001b[49m\u001b[43m)\u001b[49m\n",
      "\u001b[1;31mStopIteration\u001b[0m: "
     ]
    }
   ],
   "source": [
    "next(gen)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "id": "2306709e-ac9f-4c31-a553-b1e92f39e15f",
   "metadata": {},
   "outputs": [],
   "source": [
    "gen2 = factors(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "id": "dd45a29f-41f4-4c57-b702-d414b42720d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 100, 2, 50, 4, 25, 5, 20, 10]"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(gen2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "id": "d31178e7-35dc-4b56-82f2-092c35d0a543",
   "metadata": {},
   "outputs": [],
   "source": [
    "gen3 = factors(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "id": "da313dc4-4ebe-4e3a-8369-2101e36e8ce0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 3]"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted(gen3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "id": "af634a28-7d3e-4afd-b395-b9d67d58e9e9",
   "metadata": {},
   "outputs": [
    {
     "ename": "StopIteration",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mStopIteration\u001b[0m                             Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[190], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[38;5;28;43mnext\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mgen3\u001b[49m\u001b[43m)\u001b[49m\n",
      "\u001b[1;31mStopIteration\u001b[0m: "
     ]
    }
   ],
   "source": [
    "next(gen3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "id": "333d5c54-b60c-4681-b296-46e83f1aa1eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sorted_factors(n):\n",
    "    k=1\n",
    "    while k*k  < n:\n",
    "        if n % k == 0:\n",
    "            yield k\n",
    "        k+=1\n",
    "    if k*k == n:\n",
    "        yield k\n",
    "    \n",
    "    while k <= n//2:\n",
    "        k+=1\n",
    "        if n % k == 0:\n",
    "            yield k\n",
    "    yield n\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "id": "0bace045-7a9d-41c9-ba17-f60ad5f0fad3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 4, 5, 10, 20, 25, 50, 100]"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(sorted_factors(100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "id": "14e35d11-398b-459c-8013-affb85027a7f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def loop_iterable(start,end):\n",
    "    for i in range(start,end):\n",
    "        yield i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "id": "72df3a2c-1409-44c9-aaaf-4c7e0844fa20",
   "metadata": {},
   "outputs": [],
   "source": [
    "gene4 = loop_iterable(0,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "id": "35ce3585-0885-4635-b0cf-d6097f2059f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "next(gene4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "id": "e709cb4f-0818-402c-a09d-6f1fa6f1102b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(gene4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "id": "61c0ea1e-dd26-4ee5-b172-041229a3c8c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def loop_2x_iterable(start,end):\n",
    "    for i in range(start,end):\n",
    "        yield i\n",
    "        yield i*2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "id": "0de7f8ab-75ad-4585-a2e8-1f158c5dace2",
   "metadata": {},
   "outputs": [],
   "source": [
    "gene5 = loop_2x_iterable(0,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "id": "fa4aea23-9af4-495d-a085-ba2b6bad44e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "next(gene5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "id": "cb8a0568-136a-45fa-9c09-a83042fa43fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "next(gene5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "id": "e43fa2b8-85e8-4792-951c-7d47aa178217",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "next(gene5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "id": "a49f8dfe-36ef-4a8a-b287-d8e3c8898a84",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "next(gene5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "id": "2dfcf990-913f-4622-adbc-e8b442aeefc1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 4, 3, 6, 4, 8, 5, 10, 6, 12, 7, 14, 8, 16, 9, 18]"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(gene5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec9e41d2-ceb1-49c8-a58c-959733b8d033",
   "metadata": {},
   "source": [
    "### C-1.28 \n",
    "### The p-norm of a vector v = (v1,v2,...,vn) in n-dimensional space is defined as For the special case of p = 2, this results in the traditional Euclidean norm, which represents the length of the vector. For example, the Euclidean norm of a two-dimensional vector with coordinates (4,3) has a Euclidean norm of √ 42 +32 = √16+9 = √ 25 = 5. Give an implementation of a function named norm such that norm(v, p) returns the p-norm value of v and norm(v) returns the Euclidean norm of v. You may assume that v is a list of numbers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "id": "769a78b8-4aa2-4881-9513-e7217518ad21",
   "metadata": {},
   "outputs": [],
   "source": [
    "def norm(v:list, p:int):\n",
    "    return pow(sum([pow(i,p) for i in v]),(1/p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "id": "f31ea04a-e38b-4302-9085-8c504a1874c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm([3,4],2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58a2d035-35b0-4127-8a97-93fc9e2ac01f",
   "metadata": {},
   "source": [
    "### P-1.29 \n",
    "### Write a Python program that outputs all possible strings formed by using the characters c , a , t , d , o , and g exactly once."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "id": "2f8da67e-0c98-4039-a44c-f25f7658c0e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import itertools\n",
    "\n",
    "def get_words(characters):\n",
    "    permutation_set = []\n",
    "    for i in range(2,4): \n",
    "        permutation_set += list(itertools.permutations(characters,i))\n",
    "    return permutation_set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "id": "bfc95271-873e-4f0c-8747-77508562b1bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('c', 'a'),\n",
       " ('c', 't'),\n",
       " ('c', 'd'),\n",
       " ('c', 'o'),\n",
       " ('c', 'g'),\n",
       " ('a', 'c'),\n",
       " ('a', 't'),\n",
       " ('a', 'd'),\n",
       " ('a', 'o'),\n",
       " ('a', 'g'),\n",
       " ('t', 'c'),\n",
       " ('t', 'a'),\n",
       " ('t', 'd'),\n",
       " ('t', 'o'),\n",
       " ('t', 'g'),\n",
       " ('d', 'c'),\n",
       " ('d', 'a'),\n",
       " ('d', 't'),\n",
       " ('d', 'o'),\n",
       " ('d', 'g'),\n",
       " ('o', 'c'),\n",
       " ('o', 'a'),\n",
       " ('o', 't'),\n",
       " ('o', 'd'),\n",
       " ('o', 'g'),\n",
       " ('g', 'c'),\n",
       " ('g', 'a'),\n",
       " ('g', 't'),\n",
       " ('g', 'd'),\n",
       " ('g', 'o'),\n",
       " ('c', 'a', 't'),\n",
       " ('c', 'a', 'd'),\n",
       " ('c', 'a', 'o'),\n",
       " ('c', 'a', 'g'),\n",
       " ('c', 't', 'a'),\n",
       " ('c', 't', 'd'),\n",
       " ('c', 't', 'o'),\n",
       " ('c', 't', 'g'),\n",
       " ('c', 'd', 'a'),\n",
       " ('c', 'd', 't'),\n",
       " ('c', 'd', 'o'),\n",
       " ('c', 'd', 'g'),\n",
       " ('c', 'o', 'a'),\n",
       " ('c', 'o', 't'),\n",
       " ('c', 'o', 'd'),\n",
       " ('c', 'o', 'g'),\n",
       " ('c', 'g', 'a'),\n",
       " ('c', 'g', 't'),\n",
       " ('c', 'g', 'd'),\n",
       " ('c', 'g', 'o'),\n",
       " ('a', 'c', 't'),\n",
       " ('a', 'c', 'd'),\n",
       " ('a', 'c', 'o'),\n",
       " ('a', 'c', 'g'),\n",
       " ('a', 't', 'c'),\n",
       " ('a', 't', 'd'),\n",
       " ('a', 't', 'o'),\n",
       " ('a', 't', 'g'),\n",
       " ('a', 'd', 'c'),\n",
       " ('a', 'd', 't'),\n",
       " ('a', 'd', 'o'),\n",
       " ('a', 'd', 'g'),\n",
       " ('a', 'o', 'c'),\n",
       " ('a', 'o', 't'),\n",
       " ('a', 'o', 'd'),\n",
       " ('a', 'o', 'g'),\n",
       " ('a', 'g', 'c'),\n",
       " ('a', 'g', 't'),\n",
       " ('a', 'g', 'd'),\n",
       " ('a', 'g', 'o'),\n",
       " ('t', 'c', 'a'),\n",
       " ('t', 'c', 'd'),\n",
       " ('t', 'c', 'o'),\n",
       " ('t', 'c', 'g'),\n",
       " ('t', 'a', 'c'),\n",
       " ('t', 'a', 'd'),\n",
       " ('t', 'a', 'o'),\n",
       " ('t', 'a', 'g'),\n",
       " ('t', 'd', 'c'),\n",
       " ('t', 'd', 'a'),\n",
       " ('t', 'd', 'o'),\n",
       " ('t', 'd', 'g'),\n",
       " ('t', 'o', 'c'),\n",
       " ('t', 'o', 'a'),\n",
       " ('t', 'o', 'd'),\n",
       " ('t', 'o', 'g'),\n",
       " ('t', 'g', 'c'),\n",
       " ('t', 'g', 'a'),\n",
       " ('t', 'g', 'd'),\n",
       " ('t', 'g', 'o'),\n",
       " ('d', 'c', 'a'),\n",
       " ('d', 'c', 't'),\n",
       " ('d', 'c', 'o'),\n",
       " ('d', 'c', 'g'),\n",
       " ('d', 'a', 'c'),\n",
       " ('d', 'a', 't'),\n",
       " ('d', 'a', 'o'),\n",
       " ('d', 'a', 'g'),\n",
       " ('d', 't', 'c'),\n",
       " ('d', 't', 'a'),\n",
       " ('d', 't', 'o'),\n",
       " ('d', 't', 'g'),\n",
       " ('d', 'o', 'c'),\n",
       " ('d', 'o', 'a'),\n",
       " ('d', 'o', 't'),\n",
       " ('d', 'o', 'g'),\n",
       " ('d', 'g', 'c'),\n",
       " ('d', 'g', 'a'),\n",
       " ('d', 'g', 't'),\n",
       " ('d', 'g', 'o'),\n",
       " ('o', 'c', 'a'),\n",
       " ('o', 'c', 't'),\n",
       " ('o', 'c', 'd'),\n",
       " ('o', 'c', 'g'),\n",
       " ('o', 'a', 'c'),\n",
       " ('o', 'a', 't'),\n",
       " ('o', 'a', 'd'),\n",
       " ('o', 'a', 'g'),\n",
       " ('o', 't', 'c'),\n",
       " ('o', 't', 'a'),\n",
       " ('o', 't', 'd'),\n",
       " ('o', 't', 'g'),\n",
       " ('o', 'd', 'c'),\n",
       " ('o', 'd', 'a'),\n",
       " ('o', 'd', 't'),\n",
       " ('o', 'd', 'g'),\n",
       " ('o', 'g', 'c'),\n",
       " ('o', 'g', 'a'),\n",
       " ('o', 'g', 't'),\n",
       " ('o', 'g', 'd'),\n",
       " ('g', 'c', 'a'),\n",
       " ('g', 'c', 't'),\n",
       " ('g', 'c', 'd'),\n",
       " ('g', 'c', 'o'),\n",
       " ('g', 'a', 'c'),\n",
       " ('g', 'a', 't'),\n",
       " ('g', 'a', 'd'),\n",
       " ('g', 'a', 'o'),\n",
       " ('g', 't', 'c'),\n",
       " ('g', 't', 'a'),\n",
       " ('g', 't', 'd'),\n",
       " ('g', 't', 'o'),\n",
       " ('g', 'd', 'c'),\n",
       " ('g', 'd', 'a'),\n",
       " ('g', 'd', 't'),\n",
       " ('g', 'd', 'o'),\n",
       " ('g', 'o', 'c'),\n",
       " ('g', 'o', 'a'),\n",
       " ('g', 'o', 't'),\n",
       " ('g', 'o', 'd')]"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "characters = ['c','a','t','d','o','g']\n",
    "get_words(characters)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d372279e-9a09-494d-a663-53fec06f252b",
   "metadata": {},
   "source": [
    "### P-1.30 \n",
    "### Write a Python program that can take a positive integer greater than 2 as input and write out the number of times one must repeatedly divide this number by 2 before getting a value less than 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "id": "a1a4a42a-60d9-4eb9-ac47-78a05201671b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def count_division_by_2(n,count=0):\n",
    "    if n<2:\n",
    "        return count\n",
    "    return count_division_by_2(n/2,count+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "id": "b4d06db1-b55f-4cd0-95d7-7146f6c7adad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 209,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count_division_by_2(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "id": "bbed2941-e1a4-4829-a06d-a813265114c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 210,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count_division_by_2(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "889059ff-4f27-4483-bd66-f67adc4cdf81",
   "metadata": {},
   "source": [
    "### P-1.31\n",
    "### Write a Python program that can “make change.” Your program should take two numbers as input, one that is a monetary amount charged and the other that is a monetary amount given. It should then return the number of each kind of bill and coin to give back as change for the difference between the amount given and the amount charged. The values assigned to the bills and coins can be based on the monetary system of any current or former government. Try to design your program so that it returns as few bills and coins as possible"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "id": "9520a5fe-1156-42e1-b0f9-71d7945e784e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_change(charged,given):\n",
    "    monetary = {\n",
    "        'hundred':100,\n",
    "        'fifty':50,\n",
    "        'twenty':20,\n",
    "        'ten': 10,\n",
    "        'five':5,\n",
    "        'dollar':1,\n",
    "        'quarter':0.25,\n",
    "        'dime':0.10,\n",
    "        'nickle':0.05,\n",
    "        'penny': 0.01\n",
    "    }\n",
    "    balance = given-charged\n",
    "    change = dict()\n",
    "    for k,v in monetary.items():\n",
    "        while balance >= v:\n",
    "            balance-=v\n",
    "            if change.get(k):\n",
    "                change[k] +=1\n",
    "            else:\n",
    "                change[k]=1\n",
    "    return change"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "id": "77acd34e-37ff-4efb-b0a5-7f4166b6463a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'dollar': 2, 'quarter': 1, 'penny': 3}"
      ]
     },
     "execution_count": 212,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "make_change(27.72,30)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34c4fb69-775b-4ab2-9873-78a90f0fe0fe",
   "metadata": {},
   "source": [
    "### P-1.32 and P-1.33\n",
    "### Write a Python program that can simulate a simple calculator, using the console as the exclusive input and output device. That is, each input to the calculator, be it a number, like 12.34 or 1034, or an operator, like + or =, can be done on a separate line. After each such input, you should output to the Python console what would be displayed on your calculator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "id": "7cac80a6-1553-41f7-b126-ade4d13ce698",
   "metadata": {},
   "outputs": [],
   "source": [
    "def add(a,b):\n",
    "    return a+b\n",
    "\n",
    "def sub(a,b):\n",
    "    return a-b\n",
    "\n",
    "def multiply(a,b):\n",
    "    return a*b\n",
    "\n",
    "def division(a,b):\n",
    "    try:\n",
    "        return a/b\n",
    "    except ZeroDivsionError as zde:\n",
    "        print('Can not divided by zero')\n",
    "        \n",
    "def calculate():\n",
    "    input_feed = None\n",
    "    operations = []\n",
    "    arithmetic = {\n",
    "        '+': add,\n",
    "        '-': sub,\n",
    "        '*': multiply,\n",
    "        '/': division\n",
    "    }\n",
    "    while input_feed != '=':\n",
    "        input_feed = input(\"Enter a number or arthmetic operation(+,-./,*), else type = to end?\")\n",
    "        if input_feed != '=':\n",
    "            try: \n",
    "                operations.append(float(input_feed))\n",
    "            except ValueError as ve:\n",
    "                operations.append(input_feed)\n",
    "    total = operations[0]\n",
    "    get_method = None\n",
    "    \n",
    "    for i in range(1,len(operations)):\n",
    "        if operations[i] in arithmetic:\n",
    "            get_method = arithmetic[operations[i]]\n",
    "            continue\n",
    "        else:\n",
    "            total = get_method(total,operations[i])\n",
    "    return total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "id": "9eee9e15-9b71-4688-927c-88df896e5ae5",
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "Interrupted by user",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[214], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[43mcalculate\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
      "Cell \u001b[1;32mIn[213], line 26\u001b[0m, in \u001b[0;36mcalculate\u001b[1;34m()\u001b[0m\n\u001b[0;32m     19\u001b[0m arithmetic \u001b[38;5;241m=\u001b[39m {\n\u001b[0;32m     20\u001b[0m     \u001b[38;5;124m'\u001b[39m\u001b[38;5;124m+\u001b[39m\u001b[38;5;124m'\u001b[39m: add,\n\u001b[0;32m     21\u001b[0m     \u001b[38;5;124m'\u001b[39m\u001b[38;5;124m-\u001b[39m\u001b[38;5;124m'\u001b[39m: sub,\n\u001b[0;32m     22\u001b[0m     \u001b[38;5;124m'\u001b[39m\u001b[38;5;124m*\u001b[39m\u001b[38;5;124m'\u001b[39m: multiply,\n\u001b[0;32m     23\u001b[0m     \u001b[38;5;124m'\u001b[39m\u001b[38;5;124m/\u001b[39m\u001b[38;5;124m'\u001b[39m: division\n\u001b[0;32m     24\u001b[0m }\n\u001b[0;32m     25\u001b[0m \u001b[38;5;28;01mwhile\u001b[39;00m input_feed \u001b[38;5;241m!=\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124m=\u001b[39m\u001b[38;5;124m'\u001b[39m:\n\u001b[1;32m---> 26\u001b[0m     input_feed \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43minput\u001b[39;49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mEnter a number or arthmetic operation(+,-./,*), else type = to end?\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[0;32m     27\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m input_feed \u001b[38;5;241m!=\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124m=\u001b[39m\u001b[38;5;124m'\u001b[39m:\n\u001b[0;32m     28\u001b[0m         \u001b[38;5;28;01mtry\u001b[39;00m: \n",
      "File \u001b[1;32me:\\zm developer\\program files\\python39\\lib\\site-packages\\ipykernel\\kernelbase.py:1282\u001b[0m, in \u001b[0;36mKernel.raw_input\u001b[1;34m(self, prompt)\u001b[0m\n\u001b[0;32m   1280\u001b[0m     msg \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mraw_input was called, but this frontend does not support input requests.\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m   1281\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m StdinNotImplementedError(msg)\n\u001b[1;32m-> 1282\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_input_request\u001b[49m\u001b[43m(\u001b[49m\n\u001b[0;32m   1283\u001b[0m \u001b[43m    \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mprompt\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m   1284\u001b[0m \u001b[43m    \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_parent_ident\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mshell\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m   1285\u001b[0m \u001b[43m    \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mget_parent\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mshell\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m   1286\u001b[0m \u001b[43m    \u001b[49m\u001b[43mpassword\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mFalse\u001b[39;49;00m\u001b[43m,\u001b[49m\n\u001b[0;32m   1287\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[1;32me:\\zm developer\\program files\\python39\\lib\\site-packages\\ipykernel\\kernelbase.py:1325\u001b[0m, in \u001b[0;36mKernel._input_request\u001b[1;34m(self, prompt, ident, parent, password)\u001b[0m\n\u001b[0;32m   1322\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mKeyboardInterrupt\u001b[39;00m:\n\u001b[0;32m   1323\u001b[0m     \u001b[38;5;66;03m# re-raise KeyboardInterrupt, to truncate traceback\u001b[39;00m\n\u001b[0;32m   1324\u001b[0m     msg \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mInterrupted by user\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m-> 1325\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mKeyboardInterrupt\u001b[39;00m(msg) \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m\n\u001b[0;32m   1326\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mException\u001b[39;00m:\n\u001b[0;32m   1327\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mlog\u001b[38;5;241m.\u001b[39mwarning(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mInvalid Message:\u001b[39m\u001b[38;5;124m\"\u001b[39m, exc_info\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m)\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: Interrupted by user"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Enter a number or arthmetic operation(+,-./,*), else type = to end? 2\n"
     ]
    }
   ],
   "source": [
    "calculate()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58b1fdf4-128b-439c-902b-2e35af1d8cf0",
   "metadata": {},
   "source": [
    "### P-1.34\n",
    "### A common punishment for school children is to write out a sentence multiple times. Write a Python stand-alone program that will write out the following sentence one hundred times: “I will never spam my friends again.” Your program should number each of the sentences and it shouldmake eight different random-looking typos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "38307bb2-e873-4210-bdd9-0eaf19a725d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def punishment(string,counter,errors=8):\n",
    "    if counter != 0:\n",
    "        if random.randint(1,101) < 50 and errors != 0:\n",
    "            print(string.upper())\n",
    "            errors -=1\n",
    "        else:\n",
    "            print(string)\n",
    "        punishment(string,counter-1,errors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "736548c9-995c-4655-8add-6b3c93a9f84a",
   "metadata": {},
   "outputs": [],
   "source": [
    "punishment(\"I will not spam my friend again\", 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99534d57-754a-4461-871d-cc67eb9c4b86",
   "metadata": {},
   "source": [
    "# Ch2 Object-Oriented Programming"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33e6abda-7ae7-46c0-a68a-86fced2fab7b",
   "metadata": {},
   "source": [
    "\n",
    "## Ch2 Object-Oriented Programming:\n",
    "\n",
    "    Objects are instance of a class\n",
    "    Classes are blue print that are composed of \n",
    "        1. data member or attributes\n",
    "        2. methods are functions\n",
    "\n",
    "### Software goals are:\n",
    "        1. Robustness - being able to handle various inputs that are not explicit and return expected behavior. Avoid errors as much as possible\n",
    "        2. Adaptability(evolvability) - the ability pf spftware tp run with minmal change on different hardware and operating systems\n",
    "        3. Reusability - software code should be usable as component for different systems in various applications\n",
    "\n",
    "    \n",
    "###  Principles in OOP:\n",
    "        1. Modularity - organizing principle in which different components of software are divided into separate function unit\n",
    "            module - is a collection of closely related functions and classes that are defined together in a single file\n",
    "            Being modules allows to easily debug and trace where issues are \n",
    "        2. Abstraction - \n",
    "            - distill a system to its fundamental parts\n",
    "            - python support abstract data type using Abstract Base Class or (ABC) \n",
    "            - ABC can not have concrete class or implementation of that class\n",
    "        3. Encapsulation\n",
    "            - components of software should not reveal the internal details of their respective implementations.Main purpose of encapsulation is to\n",
    "              have loose coupling\n",
    "\n",
    "###  Design Patterns:\n",
    "        - Design patterns to address common problems\n",
    "        - Purpose is to \n",
    "            1. Solving algorithm design problems \n",
    "            2. Solving software engineering problem\n",
    "\n",
    "        Algo Design Patterns:\n",
    "            1. Recursion\n",
    "            2. Amortization\n",
    "            3. Prunch and search\n",
    "            4. Brute Force\n",
    "            5. Dynamic Programming\n",
    "            6. Greedy method\n",
    "\n",
    "        Software engineering Design Pattern:\n",
    "            1. Itearator \n",
    "            2. Adapter\n",
    "            3. Position\n",
    "            4. Compostion\n",
    "            5. Template method\n",
    "            6. Locator\n",
    "            7. Factor Method \n",
    "\n",
    "        Software Development Phases:\n",
    "            1. Design\n",
    "                - very important phase\n",
    "                - dividing the programming into modules/classes\n",
    "                - interactions of each classes\n",
    "                - data each will store\n",
    "                - actions each class will perform\n",
    "                \n",
    "                Rules for Design:\n",
    "                    1. Responsiblities - describe the actors responsibilities. Use action verbs \n",
    "                    2. Independence - define the work for each class to be as independent from other classes as possible. \n",
    "                       Give data to the class that has juridiction over the action that requires access to this data\n",
    "                    3. Behavior - define the behaiors for each class carefully and precisely, so consequences of each action performed by a class will\n",
    "                       be understood\n",
    "\n",
    "                UML\n",
    "                    - uml diagrams are standard visual notation to express object-oriented software designs\n",
    "                        - class diagram - \n",
    "                            defines the fields \n",
    "                                1. name of the class\n",
    "                                2. variables\n",
    "                                3. methods\n",
    "                PEP8 \n",
    "                    - standard coding for python\n",
    "                    - url: https://peps.python.org/pep-0008/\n",
    "                    - 4 space or indentation\n",
    "                    - using meaniful name for indentifier \n",
    "                    -  Class\n",
    "                        - should be a noun\n",
    "                        - Capitalized first letter or Camel Case if multiple word\n",
    "                    - Function\n",
    "                        - should be lower case\n",
    "                        - multiple words underscore and still lowercase eg. do_something\n",
    "                        - typically a verb\n",
    "                    - instances\n",
    "                        - lowercase \n",
    "                        - name that described the object\n",
    "                    - comments\n",
    "                        - \"\"\" block comments\"\"\"\n",
    "                        - # this is a comment \n",
    "                        - use comments sparingly, functions should describe the intended action of what is expected\n",
    "                        - if comments are needed try add docstring\n",
    "                            url: https://peps.python.org/pep-0257/\n",
    "                \n",
    "            2. Implementation\n",
    "            3. Testing and debugging\n",
    "                    Testing:\n",
    "                        - Is the process of experimentally checking the correctness of a program\n",
    "                        - A careful test plan is estential part of writing a program\n",
    "                        - Programs tend to fail on special cases of input\n",
    "                        - consider min,max, dependency,impact,worst and best case sceanrios\n",
    "                        - testing strategies:\n",
    "                            1. Top down\n",
    "                                - processed from the top to the bottom of the application/program\n",
    "                                - typically used with stubbing - replacing low level components with stub\n",
    "                                - stub is a replacement of a component the simulate the functionally of the original\n",
    "                            2. Bottom up\n",
    "                                - testing from lower level components to high level compenents\n",
    "                                - utilized unit testing\n",
    "                                    - isolate errors and determine root cause\n",
    "                                - utilizing the unittest module\n",
    "                                - regression testing is used, whereby all previous tests are re-executed to ensure that changes to the software do \n",
    "                                  not introduct new bugs in previously tested compnent \n",
    "                    Debugging:\n",
    "                        - Is the process of tracking the execution of a program and diverying the error in it\n",
    "                        - Simplest form of debugging is print statement. This is a bad approach. Instead of littering the program with \n",
    "                          print. Only use debug level. \n",
    "                        - Using a debugger as well to identify the break point and inspect the variable\n",
    "                    Testing and debugging is the most time consuming task in development\n",
    "        \n",
    "###     Class Definition:\n",
    "            - Composes of attributes(data) and methods(functions/behavior)\n",
    "            - classes act a blueprint for instances\n",
    "            - self keyword:\n",
    "                - refer to the instance it self\n",
    "            - constructor:\n",
    "                - creation of an object using the __init__(self,) function\n",
    "            - data members:\n",
    "                _variable_name or _function is used to describe a non public attribute or method\n",
    "                __varible_name or __function_name is used to describe a private attibute or method \n",
    "                - generale rule to treat all data members as non public \n",
    "            - polymorphism \n",
    "                - taking on many forms with functions using overloaded\n",
    "            \n",
    "                    Overloaded operations:\n",
    "                        Common Syntax Special Method Form or magic methods \n",
    "                        \n",
    "                        a+b a.add(b);alternatively b.radd(a)\n",
    "                        a−b a.sub(b); alternatively b.rsub(a)\n",
    "                        a*b a.mul(b); alternativelyb.rmul(a)\n",
    "                        a/b a.truediv(b);alternatively b.rtruediv(a)\n",
    "                        a//b a.floordiv(b);alternatively b.rfloordiv(a)\n",
    "                        a%b a.mod(b);alternatively b.rmod(a)\n",
    "                        a**b a.pow(b);alternatively b.rpow(a)\n",
    "                        a<<b a.lshift(b); alternativelyb.rlshift(a)\n",
    "                        a>>b a.rshift(b); alternativelyb.rrshift(a)\n",
    "                        a&b a.and(b);alternatively b.rand(a)\n",
    "                        aˆb a.xor(b);alternatively b.rxor(a)\n",
    "                        a|b a.or(b);alternatively b.ror(a)\n",
    "                        a+=b a.iadd(b)\n",
    "                        a−=b a.isub(b)\n",
    "                        a=b a.imul(b)\n",
    "                        +a a. pos ( )\n",
    "                        −a a. neg ( )\n",
    "                        ˜a a. invert ( )\n",
    "                        abs(a) a.abs()\n",
    "                        a<b a.lt(b)\n",
    "                        a<=b a.le(b)\n",
    "                        a>b a.gt(b)\n",
    "                        a>=b a.ge(b)\n",
    "                        a==b a.eq(b)\n",
    "                        a!=b a.ne(b)\n",
    "                        vina a.contains(v)\n",
    "                        a[k] a.getitem(k)\n",
    "                        a[k]=v a.setitem(k,v)\n",
    "                        del a[k] a.delitem(k)\n",
    "                        a(arg1,arg2,...) a.call(arg1,arg2,...)\n",
    "                        len(a) a.len()\n",
    "                        hash(a) a.hash()\n",
    "                        iter(a) a.iter()\n",
    "                        next(a) a.next()\n",
    "                        bool(a) a.bool()\n",
    "                        float(a) a.float()\n",
    "                        int(a) a.int()\n",
    "                        repr(a) a.repr()\n",
    "                        reversed(a) a.reversed()\n",
    "                        str(a) a.str()\n",
    "                        \n",
    "            \n",
    "###     Iterators\n",
    "            - Iteration - is an imporatant concept in design of data structure\n",
    "            - an iterator for a collection provides one key behavior. The __next__() that returns the next eleemnt of the collection\n",
    "                until a StopIteration exception has been tossed\n",
    "            - use generator over implementing an iterator class\n",
    "            - Python helps by providing an automatice iterator\n",
    "            - an Example is SequenceIterator to go under the hood of an Iterator class\n",
    "\n",
    "###     Range\n",
    "            - range used to be an expensive function creating a list of number specified\n",
    "            - current implementation of range is now using lazy evaulation\n",
    "            - recommend create a r= range(8,140,5)\n",
    "\n",
    "###     Inheritence\n",
    "            - Using hierachal method to structure a software package\n",
    "            - in mathematical notation of subset to define set is a part of superset\n",
    "            - is a relationship - between the superset and the subset\n",
    "            - inheritence is a mechanism for a modular and hierachial orgnization\n",
    "            - there is a \n",
    "                1. base class, parent class, or super class \n",
    "                2. Subclass or child class\n",
    "                    - differs in behavior by 2 ways\n",
    "                        1. new implemntation that overrides the existing method\n",
    "                        2. subclass extends it superclass by providing a new method\n",
    "            - Overriding means having two methods with the same method name and parameters but different class(i.e., method signature).\n",
    "              Different implementation\n",
    "                - eg. class B inherits from Class A, both have method called foo, but have different behavior\n",
    "            - Overloading occurs when two or more methods in one class have the same method name but different parameters.\n",
    "                - eg. class a has two methods call foo, but  one foo has a arguement of 2 while ther other has 1\n",
    "            - super() method - inheritence constructor\n",
    "\n",
    "\n",
    "### Protected Members\n",
    "            - _ is considered protected\n",
    "            - __ is considered private\n",
    "\n",
    "### Abstract Base Class\n",
    "            - A class is abstract base class, if its only purpose is to serve as base class through inheritance\n",
    "            - Abstract Bass Class can not be instantiated \n",
    "            - Concrete classes can be instatiated\n",
    "            - Template method pattern - when an abstract base class provides concrete behavior that rely upon class to other behavior\n",
    "\n",
    "### Name spaces and Object Orientation\n",
    "            - Namespace - is an abstraction that manages all of the indentifiers that are defined in a particular scope, mapping each name to its \n",
    "              assocated\n",
    "            - Class and modules are first class objects and so the value assocaited with an identifier in a namespace may in fact be a function, class\n",
    "              or module\n",
    "            - instance namespace - manages attributes specific to an individual object or instance\n",
    "            - class namespace - each class that has been defined, this namespace is used to manage members that are to be shared by all nstances of a \n",
    "                                class\n",
    "\n",
    "### Shallow and deep copying\n",
    "            - shallow copy - when instantiated a object or create a new instance. This is known as shallow copy. \n",
    "                - this is referential\n",
    "            - deep copy - the new copy reference it own copies of those objects "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "id": "40748b9a-d607-41e0-83df-c849c5f52198",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a class call credit card\n",
    "class CreditCard:\n",
    "    _currency_symbol = {\n",
    "        'DOLLAR': '$',\n",
    "        'EURO': '€'\n",
    "    }\n",
    "    \n",
    "    def __init__(self,customer,bank,acnt,limit,_currency='DOLLAR'):\n",
    "        self._customer = customer\n",
    "        self._bank = bank\n",
    "        self._account = acnt\n",
    "        self._limit = float(limit)\n",
    "        self.__balance = 0.00\n",
    "        self._currency = self._currency_symbol[_currency]\n",
    "\n",
    "    def get_customer(self):\n",
    "        return self._customer\n",
    "\n",
    "    def get_bank(self,):\n",
    "        return self._bank\n",
    "\n",
    "    def get_account(self,):\n",
    "        return self._account\n",
    "\n",
    "    def get_limit(self,):\n",
    "        return self._limit\n",
    "\n",
    "    def get_balance(self,is_currency=False):\n",
    "        if is_currency:\n",
    "            return f'{self.get_currency()} {self.__balance}'\n",
    "        return self.__balance\n",
    "        \n",
    "\n",
    "    def get_currency(self):\n",
    "        return self._currency\n",
    "\n",
    "    def set_currency(self,currency):\n",
    "        if self._currency_symbol.get(currency):\n",
    "            self.currency = self._currency_symbol.get(currency)\n",
    "    \n",
    "    def charge(self,price):\n",
    "        if price + self.__balance > self._limit:\n",
    "            return False\n",
    "        else:\n",
    "            self.__balance+=price\n",
    "            return True\n",
    "\n",
    "    def make_payment(self,amount):\n",
    "        self.__balance-=amount\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "id": "72d5f761-c7b9-465a-983d-584c7b8c4495",
   "metadata": {},
   "outputs": [],
   "source": [
    "cc = CreditCard('Fanny Reguieg', 'Societe Generale', '5112-1224-7845-1','100000','EURO')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "id": "481fb35c-3af2-4a78-9259-908ee6f23c7d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 217,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cc.get_balance()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "id": "b3a459e7-c15e-4245-98b6-8c51192ea2db",
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'CreditCard' object has no attribute '__balance'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[218], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[43mcc\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m__balance\u001b[49m\n",
      "\u001b[1;31mAttributeError\u001b[0m: 'CreditCard' object has no attribute '__balance'"
     ]
    }
   ],
   "source": [
    "cc.__balance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "id": "458365bc-28c3-4198-88b7-1505afc061a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'€ 0.0'"
      ]
     },
     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cc.get_balance(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "id": "61caa1b1-bafc-4c4f-81a6-fc01ad51d239",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100000.0"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cc.get_limit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "id": "6f9ef6c7-c91c-4f9e-9987-bb3b6b56badd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Customer is Fanny Reguieg\n",
      "Bank is Societe Generale\n",
      "Account is 5112-1224-7845-1\n",
      "Credit Card Limit is 100000.0\n",
      "Credit Card Balance is € 1496.0\n",
      "Credit Card new balance is € 1396.0\n",
      "Credit Card new balance is € 1296.0\n",
      "Credit Card new balance is € 1196.0\n",
      "Credit Card new balance is € 1096.0\n",
      "Credit Card new balance is € 996.0\n",
      "Credit Card new balance is € 896.0\n",
      "Credit Card new balance is € 796.0\n",
      "Credit Card new balance is € 696.0\n",
      "Credit Card new balance is € 596.0\n",
      "Credit Card new balance is € 496.0\n",
      "Credit Card new balance is € 396.0\n",
      "Credit Card new balance is € 296.0\n",
      "Credit Card new balance is € 196.0\n",
      "Credit Card new balance is € 96.0\n",
      "\n",
      "Customer is Fanny Reguieg\n",
      "Bank is BNP Paribas\n",
      "Account is 1425-8597-4457-2\n",
      "Credit Card Limit is 10000.0\n",
      "Credit Card Balance is € 816.0\n",
      "Credit Card new balance is € 716.0\n",
      "Credit Card new balance is € 616.0\n",
      "Credit Card new balance is € 516.0\n",
      "Credit Card new balance is € 416.0\n",
      "Credit Card new balance is € 316.0\n",
      "Credit Card new balance is € 216.0\n",
      "Credit Card new balance is € 116.0\n",
      "Credit Card new balance is € 16.0\n",
      "\n",
      "Customer is Fanny Reguieg\n",
      "Bank is Credit Agricole CIB\n",
      "Account is 7477-5779-9998-3\n",
      "Credit Card Limit is 1000000.0\n",
      "Credit Card Balance is € 1496.0\n",
      "Credit Card new balance is € 1396.0\n",
      "Credit Card new balance is € 1296.0\n",
      "Credit Card new balance is € 1196.0\n",
      "Credit Card new balance is € 1096.0\n",
      "Credit Card new balance is € 996.0\n",
      "Credit Card new balance is € 896.0\n",
      "Credit Card new balance is € 796.0\n",
      "Credit Card new balance is € 696.0\n",
      "Credit Card new balance is € 596.0\n",
      "Credit Card new balance is € 496.0\n",
      "Credit Card new balance is € 396.0\n",
      "Credit Card new balance is € 296.0\n",
      "Credit Card new balance is € 196.0\n",
      "Credit Card new balance is € 96.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "wallet = []\n",
    "wallet.append(cc)\n",
    "wallet.append(CreditCard('Fanny Reguieg', 'BNP Paribas', '1425-8597-4457-2','10000','EURO'))\n",
    "wallet.append(CreditCard('Fanny Reguieg', 'Credit Agricole CIB', '7477-5779-9998-3','1000000','EURO'))\n",
    "\n",
    "for val in range(1,17):\n",
    "    for cc in wallet:\n",
    "        cc.charge(val)\n",
    "        if cc.get_bank() == 'BNP Paribas':\n",
    "            cc.charge(val*5)\n",
    "        else:\n",
    "            cc.charge(val*10)\n",
    "for cc in wallet:\n",
    "    print(f'Customer is {cc.get_customer()}')\n",
    "    print(f'Bank is {cc.get_bank()}')\n",
    "    print(f'Account is {cc.get_account()}')\n",
    "    print(f'Credit Card Limit is {cc.get_limit()}')\n",
    "    print(f'Credit Card Balance is {cc.get_balance(True)}')\n",
    "    while cc.get_balance() > 100:\n",
    "        cc.make_payment(100)\n",
    "        print(f'Credit Card new balance is {cc.get_balance(True)}')\n",
    "    print()\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "id": "abc3a9e3-0915-4453-a42a-bb7241a459e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "### Over loaded operations with a list as the object\n",
    "class Vector:\n",
    "    \"\"\"Represent a multidimension space\"\"\"\n",
    "    def __init__(self,dimension:int):\n",
    "        self._coords = [0] * dimension\n",
    "\n",
    "    def __len__(self):\n",
    "        \"\"\"Return the demsion of the ventor\"\"\"\n",
    "        return len(self._coords)\n",
    "\n",
    "    def __getitem__(self,j):\n",
    "        \"\"\"Return jth coordinate of vector\"\"\"\n",
    "        return self._coords[j]\n",
    "\n",
    "    def __setitem__(self,j,val):\n",
    "        \"\"\"Set jth coordinate of vector to given value\"\"\"\n",
    "        self._coords[j] = val\n",
    "\n",
    "    def __add__(self,other):\n",
    "        \"\"\"return sum of two vectors\n",
    "            vector must be same length in order to get the sum\n",
    "        \"\"\"\n",
    "        if len(self) != len(other):\n",
    "            raise ValueError('dimensions must agree')\n",
    "        result = Vector(len(self))\n",
    "        for j in range(len(self)):\n",
    "            result[j] = self[j] + other[j]\n",
    "        return result\n",
    "\n",
    "    def __eq__(self,other):\n",
    "        \"\"\"Return True if vector has same coordinates as other\"\"\"\n",
    "        return self._coords == other._coords\n",
    "\n",
    "    def __ne__(self,other):\n",
    "        \"\"\"Return True if vector differ from other\"\"\"\n",
    "        return not self == other\n",
    "\n",
    "    def __str__(self,):\n",
    "        \"\"\"Produce string representation of vector\"\"\"\n",
    "        return f'< {str(self._coords)[1:-1]} >'\n",
    "        \n",
    "        \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "id": "f56f943a-742a-41b1-b340-df63a083e77d",
   "metadata": {},
   "outputs": [],
   "source": [
    "v= Vector(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "id": "b176a7fe-ec90-496b-aaee-c15bc91c7243",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 224,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "id": "602f8d45-8e14-4102-9215-fd393dd4157a",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(0,4):\n",
    "    v[i] = i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "id": "0ddece0c-781b-4bfa-a735-4a58bc3b0a3d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n",
      "3\n"
     ]
    }
   ],
   "source": [
    "for i in range(0,4):\n",
    "    print(v[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "id": "b03ad913-e9be-48a2-8a0b-1ef8c83b7a9a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 227,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v[4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "id": "d8740d48-3c7f-44b6-81f2-fc56c5704196",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'< 0, 1, 2, 3, 0 >'"
      ]
     },
     "execution_count": 228,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "id": "9f3e8b28-73f7-4ded-8441-55a405d0bfff",
   "metadata": {},
   "outputs": [],
   "source": [
    "other = Vector(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "id": "6360c3c7-495a-4235-96af-5a2e37f04942",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 230,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v == other"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "id": "c0c600c7-1418-438e-acbb-a90069834b51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 231,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v != other"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "id": "d68972c4-b438-48f6-886f-9035c8b3e1ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(len(other)):\n",
    "    other[i] = (i+5)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "id": "f6309945-485e-4046-ae2e-4366aa4f0b12",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'< 25, 36, 49, 64, 81 >'"
      ]
     },
     "execution_count": 233,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(other)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "id": "0464245c-f101-4f08-9e8c-391783196d45",
   "metadata": {},
   "outputs": [],
   "source": [
    "combo_vector = other + v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "id": "9c604b67-43b0-4edd-bf35-75d5b751fd94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<__main__.Vector at 0x1d45cc3a7c0>"
      ]
     },
     "execution_count": 235,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "combo_vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "id": "1458db13-edf0-4c7c-8874-fdcf7fa9c9c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'< 25, 37, 51, 67, 81 >'"
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(combo_vector)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "id": "f00e2e6d-44cf-4d01-aed0-db0bca7558e5",
   "metadata": {},
   "outputs": [],
   "source": [
    "class SequenceIterator:\n",
    "\n",
    "    def __init__(self,sequence):\n",
    "        # create an iterator for a given sequence \n",
    "        self._seq = sequence # keep a reference of the underlying data\n",
    "        self._k = -1 # will increment to 0 on the first call to next \n",
    "\n",
    "    def __len__(self,):\n",
    "        return len(self._seq)\n",
    "    \n",
    "    def __next__(self,):\n",
    "        \"\"\" Return the next element, or else raise StopIteration error.\"\"\"\n",
    "        self._k +=1\n",
    "        if self._k < len(self._seq):\n",
    "            return(self._seq[self._k])\n",
    "        else:\n",
    "            raise StopIteration()\n",
    "\n",
    "    def __iter__(self):\n",
    "        \"\"\"By convention, an iterator must return iteself as an iterator\"\"\"\n",
    "        return self"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "id": "0f211d31-ddb9-4f1b-bc91-1792b9bf6f93",
   "metadata": {},
   "outputs": [],
   "source": [
    "si = SequenceIterator([1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "id": "579fc378-ff9d-47ca-b95f-d80fb04d3123",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 239,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(si)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "id": "622f82df-c7d3-42a6-b257-1103c11c7622",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n"
     ]
    }
   ],
   "source": [
    "for _ in range(len(si)):\n",
    "    print(next(si))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "id": "8670e1e3-5dc2-4523-9bc0-218ac326dc7b",
   "metadata": {},
   "outputs": [
    {
     "ename": "StopIteration",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mStopIteration\u001b[0m                             Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[241], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[38;5;28;43mnext\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43msi\u001b[49m\u001b[43m)\u001b[49m\n",
      "Cell \u001b[1;32mIn[237], line 17\u001b[0m, in \u001b[0;36mSequenceIterator.__next__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m     15\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_seq[\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_k])\n\u001b[0;32m     16\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m---> 17\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mStopIteration\u001b[39;00m()\n",
      "\u001b[1;31mStopIteration\u001b[0m: "
     ]
    }
   ],
   "source": [
    "next(si)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "id": "0ee1d51d-8e07-4fc8-af97-1eec61bd5624",
   "metadata": {},
   "outputs": [],
   "source": [
    "r = range(8,140,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "id": "a8d279b5-9659-4064-8256-0c0a62f45e3a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "27"
      ]
     },
     "execution_count": 243,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "id": "98852eb3-8990-40b5-a348-dd4a19da53d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "83"
      ]
     },
     "execution_count": 244,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r[15] # use the __getitem__() function "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "id": "99cd02d8-1438-4251-9549-52aaa796e46e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 245,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "id": "9c47d4b5-9de7-486f-b913-8473802279d2",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Range:\n",
    "    \"\"\" A class that mimics the built-in range class\"\"\"\n",
    "    def __init__(self,start,stop=None, step=1):\n",
    "        if step == 0:\n",
    "            raise ValueError(\"Step cannot be 0\")\n",
    "\n",
    "        if stop is None:\n",
    "            start,stop = 0, start\n",
    "\n",
    "        self._length = max(0,(stop - start + step -1) // step)\n",
    "        self._start = start\n",
    "        self._step = step\n",
    "\n",
    "    def __len__(self,):\n",
    "        return self._length\n",
    "\n",
    "    def __getitem__(self,k):\n",
    "        if k < 0:\n",
    "            k += len(self)\n",
    "        \n",
    "        if not 0 <= k < self._length:\n",
    "            raise IndexError('index out of range')\n",
    "\n",
    "        return self._start + k *self._step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "id": "85854aef-607b-4ba8-84d1-8ac2dabfedcc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "stop is None\n",
      "0 10\n"
     ]
    }
   ],
   "source": [
    "start = 10\n",
    "stop = None\n",
    "if stop is None:\n",
    "    print(f'stop is None')\n",
    "    start,stop = 0,start \n",
    "print(start,stop)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "id": "7ac11383-b6cb-4c35-8429-89592af4899c",
   "metadata": {},
   "outputs": [],
   "source": [
    "r1 = Range(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "id": "23a1b04c-dfc1-49de-a547-b0df19d30bfa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 249,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(r1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "id": "e63423bb-7b03-4932-a596-0a9184a96072",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 250,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r1[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "id": "5fec7f9c-d015-4e2c-ac8e-cf5e4440cc8e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 251,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r1[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "id": "693c71b7-31b3-4864-b50b-599850932bc0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 252,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r1[-10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "id": "9a51f215-bfba-48a9-84d8-b1fc48217db8",
   "metadata": {},
   "outputs": [],
   "source": [
    "class PredatoryCreditCard(CreditCard):\n",
    "    def __init__(self,customer,bank,acnt,limit,apr,_currency='DOLLAR'):\n",
    "        super().__init__(customer,bank,acnt,limit) # call super on the constructor\n",
    "        self._apr = apr\n",
    "\n",
    "    def charge(self,price):\n",
    "        success = super().charge(price)\n",
    "        if not sucess:\n",
    "            self._balance +=5\n",
    "        return sucess\n",
    "\n",
    "    def process_month(self):\n",
    "        if self._balance > 0:\n",
    "            monthly_factor = pow(1 + self._apr, 1/12)\n",
    "            self._balance *= monthly_factor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "id": "5766ac2e-5afd-4cb4-bd9d-e82192222f24",
   "metadata": {},
   "outputs": [],
   "source": [
    "pcc = PredatoryCreditCard('Fanny Reguieg', 'Societe Generale', '5112-1224-7845-1','100000','EURO')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "id": "8a8c5dad-a67f-41c7-8269-f7d230ee9e5e",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Progression:\n",
    "    def __init__(self,start=0):\n",
    "        self._current = start\n",
    "\n",
    "    def _advance(self,):\n",
    "        self._current+=1\n",
    "\n",
    "    def __next__(self):\n",
    "        if self._current is None:\n",
    "            raise StopIteration()\n",
    "        else:\n",
    "            answer = self._current\n",
    "            self._advance()\n",
    "            return answer\n",
    "\n",
    "    def __iter__(self):\n",
    "        return self\n",
    "\n",
    "    def print_progression(self,n):\n",
    "        print( ' '.join(str(next(self)) for j in range(n)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "id": "68f61ab3-200c-4a1b-bd71-90a6bf5ac089",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2 3\n",
      "4\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "progression = Progression()\n",
    "print(next(progression))\n",
    "print(next(progression))\n",
    "progression.print_progression(2)\n",
    "print(progression._current)\n",
    "print(next(progression))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 294,
   "id": "fcdacfd4-94ca-4d4b-aa13-a6f17fdfee22",
   "metadata": {},
   "outputs": [],
   "source": [
    "class ArithmeticProgression(Progression):\n",
    "    def __init__(self,start=0,increment=1):\n",
    "        super().__init__(start)\n",
    "        self._increment = increment\n",
    "\n",
    "    def _advance(self):\n",
    "        self._current += self._increment\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 309,
   "id": "de029ffe-08f6-4e23-b571-7c5f80138dea",
   "metadata": {},
   "outputs": [],
   "source": [
    "arithmetic_progression = ArithmeticProgression(4,8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 310,
   "id": "654d506e-9b13-439b-9189-b48c7a6c2654",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 310,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "assert 4  ==  arithmetic_progression._current\n",
    "next(arithmetic_progression)\n",
    "arithmetic_progression._current\n",
    "next(arithmetic_progression)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 312,
   "id": "e5f871cc-1fbd-4d5d-82a9-a78b2a394342",
   "metadata": {},
   "outputs": [],
   "source": [
    "class GeometricProgression(Progression):\n",
    "    def __init__(self,base=2,start=1):\n",
    "        super().__init__(start)\n",
    "        self._base = base\n",
    "\n",
    "    def _advance(self):\n",
    "        self._current *= self._base"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 316,
   "id": "fb8a3dde-39c0-403a-832e-2183fd72be46",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 316,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gm = GeometricProgression()\n",
    "next(gm)\n",
    "next(gm)\n",
    "next(gm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 320,
   "id": "791dc23d-c65b-4a73-98b5-76c20240fef7",
   "metadata": {},
   "outputs": [],
   "source": [
    "class FibonacciProgression(Progression):\n",
    "    def __init__(self,first=0,second=1):\n",
    "        super().__init__(first)\n",
    "        self._prev = second - first\n",
    "\n",
    "    def _advance(self):\n",
    "        self._prev, self._current = self._current, self._prev + self._current"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 322,
   "id": "932a324d-7e19-4750-a0f1-882b0ae7fb13",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "1\n",
      "2\n",
      "3\n",
      "5\n",
      "8\n",
      "13\n",
      "21\n",
      "34\n"
     ]
    }
   ],
   "source": [
    "fp = FibonacciProgression()\n",
    "for i in range(10):\n",
    "    print(next(fp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 323,
   "id": "4e881ce2-60fb-40f5-bde3-210a914e41d7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5 6 7 8 9 10 11 12 13 14\n"
     ]
    }
   ],
   "source": [
    "progression.print_progression(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 324,
   "id": "2c6dad64-7d45-4eed-8a87-480d081f5855",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20 28 36 44 52 60 68 76 84 92\n"
     ]
    }
   ],
   "source": [
    "arithmetic_progression.print_progression(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 325,
   "id": "267a19fe-e458-480b-b85e-2a6c1473809e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8 16 32 64 128 256 512 1024 2048 4096\n"
     ]
    }
   ],
   "source": [
    "gm.print_progression(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 327,
   "id": "9115f460-7dce-49da-b74c-d99765d0904a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "55 89 144 233 377 610 987 1597 2584 4181\n"
     ]
    }
   ],
   "source": [
    "fp.print_progression(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "01c49483-ffe7-401e-b17a-c89a165a49df",
   "metadata": {},
   "outputs": [],
   "source": [
    "from abc import ABCMeta, abstractmethod\n",
    "\n",
    "class Sequence(metaclass=ABCMeta):\n",
    "\n",
    "    @abstractmethod\n",
    "    def __len__(self):\n",
    "        \"\"\"Return length of a sequence\"\"\"\n",
    "\n",
    "    @abstractmethod\n",
    "    def __getitem__(self,j):\n",
    "        \"\"\"Return the element at index j of sequence\"\"\"\n",
    "\n",
    "    def __contains__(self,val):\n",
    "        \"\"\"Returns True if val found else False \"\"\"\n",
    "        for j in range(len(self)):\n",
    "            if self[j] == val:\n",
    "                return True\n",
    "        return False\n",
    "\n",
    "    def index(self,val):\n",
    "        \"\"\" Return leftmost index at which val is found (or raise ValueError)\"\"\"\n",
    "        for j in range(len(self)):\n",
    "            if self[j] == val:\n",
    "                return j\n",
    "        raise ValueError('Value not in sequence')\n",
    "\n",
    "    def count(self,val):\n",
    "        count = 0 \n",
    "        for i in range(len(self)):\n",
    "            if self[i] == val:\n",
    "                count+=1\n",
    "        return count\n",
    "        \n",
    "            \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7339af92-580d-404a-a2ec-6afff9a7c6d4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n",
      "2207031366592 2207031116352 2207031117952\n",
      "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 100]\n",
      "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 100]\n",
      "[0, 1, 2, 3, 4, 5, 6, 7, 8]\n",
      "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11]\n"
     ]
    }
   ],
   "source": [
    "# Deep vs shallow copy\n",
    "import copy\n",
    "nums = list(range(10))\n",
    "nums2 = nums\n",
    "print(nums)\n",
    "nums_shallow_copy = copy.copy(nums)\n",
    "nums_deep_copy = copy.deepcopy(nums)\n",
    "print(id(nums),id(nums_shallow_copy),id(nums_deep_copy))\n",
    "[{'original':id(orginal), 'shallow':id(shallow),'deep':id(deep)} for orginal,shallow,deep in zip(nums,nums_shallow_copy,nums_deep_copy)]\n",
    "nums2.append(100)\n",
    "nums_shallow_copy.pop()\n",
    "nums_deep_copy.append(11)\n",
    "print(nums)\n",
    "print(nums2)\n",
    "print(nums_shallow_copy)\n",
    "print(nums_deep_copy)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a7cefd4-f6f7-40fd-b7f5-16a28db16bd8",
   "metadata": {},
   "source": [
    "### R-2.4 \n",
    "Write a Python class, Flower, that has three instance variables of type str,\n",
    "int, and float, that respectively represent the name of the flower, its number of petals, and its price. Your class must include a constructor method\n",
    "that initializes each variable to an appropriate value, and your class should\n",
    "include methods for setting the value of each type, and retrieving the value\n",
    "of each type."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a024d3ef-397a-4793-9595-bd2e4cbf7d9a",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Flower:\n",
    "    def __init__(self,name,num_of_petals,price):\n",
    "        self._name = name\n",
    "        self._petals = num_of_petals\n",
    "        self._price = price\n",
    "\n",
    "    def get_name(self,):\n",
    "        return self._name\n",
    "\n",
    "    def set_name(self,name):\n",
    "        if type(name) == str:\n",
    "            self._name = name\n",
    "        else:\n",
    "            raise TypeError(\"name arg not type of str\")\n",
    "\n",
    "    def get_petals(self,):\n",
    "        return self._petals\n",
    "\n",
    "    def set_petals(self,petals):\n",
    "        if type(petals) == int:\n",
    "            selt._petals = petals\n",
    "        else:\n",
    "            raise TypeError(\"petals arg not type of int\")\n",
    "\n",
    "    def get_price(self,):\n",
    "        return self._price\n",
    "\n",
    "    def set_price(self,price):\n",
    "        if type(price) == float:\n",
    "            self._price = price\n",
    "        else:\n",
    "            raise TypeError(\"price arg not type of float\")\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "b81ed2a7-7392-4a08-bce7-132734684af9",
   "metadata": {},
   "outputs": [],
   "source": [
    "rose = Flower(\"rose\",20,2.00)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "fb5f9e4f-5b93-443e-b880-e7bdd46b51c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'rose'"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rose.get_name()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "a96cec26-8589-474f-a991-46dc07611ec5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rose.get_price()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "611e5829-f192-4793-bef1-de3f806187ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rose.get_petals()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "3e8563bd-bc85-463b-a0ee-f459f5d2f9ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "rose.set_price(11.00)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "54a833a0-ccdd-4081-8a08-e336d843b07d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11.0"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rose.get_price()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "2fd38c87-0ec3-4ebc-bb42-76c9b71ff08e",
   "metadata": {},
   "outputs": [],
   "source": [
    "rose.set_name('Tulip')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "da4fb284-3884-456a-a919-755460e12b95",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Tulip'"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rose.get_name()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "84d88f13-c836-44a2-a7bd-a33ea6df0fc1",
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "petals arg not type of int",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[27], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[43mrose\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mset_petals\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mhello\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n",
      "Cell \u001b[1;32mIn[16], line 23\u001b[0m, in \u001b[0;36mFlower.set_petals\u001b[1;34m(self, petals)\u001b[0m\n\u001b[0;32m     21\u001b[0m     selt\u001b[38;5;241m.\u001b[39m_petals \u001b[38;5;241m=\u001b[39m petals\n\u001b[0;32m     22\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m---> 23\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mpetals arg not type of int\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "\u001b[1;31mTypeError\u001b[0m: petals arg not type of int"
     ]
    }
   ],
   "source": [
    "rose.set_petals('hello')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ac9e07b-ae92-4275-ac0c-652725acde65",
   "metadata": {},
   "source": [
    "### R-2.5\n",
    "Use the techniques of Section 1.7 to revise the charge and make payment\n",
    "methods of the CreditCard class to ensure that the caller sends a number\n",
    "as a parameter\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e32f7d39-62b9-4d42-97c5-0264a16feb80",
   "metadata": {},
   "source": [
    "### R-2.6 \n",
    "If the parameter to the make payment method of the CreditCard class\n",
    "were a negative number, that would have the effect of raising the balance\n",
    "on the account. Revise the implementation so that it raises a ValueError if\n",
    "a negative value is sent."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7865d7a-364c-41b6-aa25-900cb7d8dd2f",
   "metadata": {},
   "source": [
    "### R-2.7 \n",
    "The CreditCard class of Section 2.3 initializes the balance of a new account to zero. Modify that class so that a new account can be given a\n",
    "nonzero balance using an optional fifth parameter to the constructor. The\n",
    "four-parameter constructor syntax should continue to produce an account\n",
    "with zero balance."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f752a19-dd7a-4173-abf0-107375065cde",
   "metadata": {},
   "source": [
    "### R-2.8 \n",
    "Modify the declaration of the first for loop in the CreditCard tests, from\n",
    "Code Fragment 2.3, so that it will eventually cause exactly one of the three\n",
    "credit cards to go over its credit limit. Which credit card is it?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "5a7729cd-d973-47ff-b07a-a8fb61bc1097",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a class call credit card\n",
    "class CreditCard:\n",
    "    _currency_symbol = {\n",
    "        'DOLLAR': '$',\n",
    "        'EURO': '€'\n",
    "    }\n",
    "    \n",
    "    def __init__(self,customer,bank,acnt,limit,balance=0.00, _currency='DOLLAR'):\n",
    "        self._customer = customer\n",
    "        self._bank = bank\n",
    "        self._account = acnt\n",
    "        self._limit = float(limit)\n",
    "        self.__balance = balance\n",
    "        self._currency = self._currency_symbol[_currency]\n",
    "\n",
    "    def check_type(type_to_check):\n",
    "        def decorator(func):\n",
    "            def wrapper(*args, **kwargs):\n",
    "                if not isinstance(args[1], type_to_check):\n",
    "                    raise TypeError(f\"Argument {args[1]} is not of type {type_to_check}\")\n",
    "                return func(*args, **kwargs)\n",
    "            return wrapper\n",
    "        return decorator\n",
    "    \n",
    "    def get_customer(self):\n",
    "        return self._customer\n",
    "\n",
    "    def get_bank(self,):\n",
    "        return self._bank\n",
    "\n",
    "    def get_account(self,):\n",
    "        return self._account\n",
    "\n",
    "    def get_limit(self,):\n",
    "        return self._limit\n",
    "\n",
    "    def get_balance(self,is_currency=False):\n",
    "        if is_currency:\n",
    "            return f'{self.get_currency()} {self.__balance}'\n",
    "        return self.__balance\n",
    "\n",
    "    def get_currency(self):\n",
    "        return self._currency\n",
    "\n",
    "    def set_currency(self,currency):\n",
    "        if self._currency_symbol.get(currency):\n",
    "            self.currency = self._currency_symbol.get(currency)\n",
    "\n",
    "    def __str__(self,):\n",
    "        return f\"{self._customer},{self._bank},{self._account},{self._limit},{self.get_balance()},{self._currency}\"\n",
    "    \n",
    "    @check_type(float)\n",
    "    def charge(self,price):\n",
    "        if price + self.__balance > self._limit:\n",
    "            return False\n",
    "        else:\n",
    "            self.__balance+=price\n",
    "            return True\n",
    "\n",
    "    def make_payment(self,amount):\n",
    "        if amount > 0:\n",
    "            self.__balance-=amount\n",
    "        else:\n",
    "            raise ValueError(f'Ammount {amount} is a negative')\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "20b701ac-1431-4289-87ff-be5c0af78a13",
   "metadata": {},
   "outputs": [],
   "source": [
    "cc = CreditCard('Fanny Reguieg', 'JPM Chase', '1234-123-1222',100000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "d501b2c0-60c1-4725-817a-c99eb9259026",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cc.charge(float(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "73457f18-993f-497b-a996-ab68017252a7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fanny Reguieg,JPM Chase,1234-123-1222,100000.0,10.0,$\n",
      "Fanny Reguieg,Wells Fargo,4132-123-1122,100000.0,0.0,$\n",
      "Fanny Reguieg,Bank Of America,1211-123-1342,100000.0,0.0,$\n",
      "Fanny Reguieg,JPM Chase,1234-123-1222,100000.0,9010.0,$\n",
      "Fanny Reguieg,Wells Fargo,4132-123-1122,100000.0,3000.0,$\n",
      "Fanny Reguieg,Bank Of America,1211-123-1342,100000.0,1000.0,$\n",
      "Fanny Reguieg,JPM Chase,1234-123-1222,100000.0,15010.0,$\n",
      "Fanny Reguieg,Wells Fargo,4132-123-1122,100000.0,11000.0,$\n",
      "Fanny Reguieg,Bank Of America,1211-123-1342,100000.0,2000.0,$\n",
      "Fanny Reguieg,JPM Chase,1234-123-1222,100000.0,19010.0,$\n",
      "Fanny Reguieg,Wells Fargo,4132-123-1122,100000.0,18000.0,$\n",
      "Fanny Reguieg,Bank Of America,1211-123-1342,100000.0,9000.0,$\n",
      "Fanny Reguieg,JPM Chase,1234-123-1222,100000.0,28010.0,$\n",
      "Fanny Reguieg,Wells Fargo,4132-123-1122,100000.0,25000.0,$\n",
      "Fanny Reguieg,Bank Of America,1211-123-1342,100000.0,15000.0,$\n",
      "Fanny Reguieg,JPM Chase,1234-123-1222,100000.0,36010.0,$\n",
      "Fanny Reguieg,Wells Fargo,4132-123-1122,100000.0,28000.0,$\n",
      "Fanny Reguieg,Bank Of America,1211-123-1342,100000.0,21000.0,$\n",
      "Fanny Reguieg,JPM Chase,1234-123-1222,100000.0,44010.0,$\n",
      "Fanny Reguieg,Wells Fargo,4132-123-1122,100000.0,34000.0,$\n",
      "Fanny Reguieg,Bank Of America,1211-123-1342,100000.0,30000.0,$\n",
      "Fanny Reguieg,JPM Chase,1234-123-1222,100000.0,46010.0,$\n",
      "Fanny Reguieg,Wells Fargo,4132-123-1122,100000.0,35000.0,$\n",
      "Fanny Reguieg,Bank Of America,1211-123-1342,100000.0,34000.0,$\n",
      "Fanny Reguieg,JPM Chase,1234-123-1222,100000.0,50010.0,$\n",
      "Fanny Reguieg,Wells Fargo,4132-123-1122,100000.0,39000.0,$\n",
      "Fanny Reguieg,Bank Of America,1211-123-1342,100000.0,39000.0,$\n",
      "Fanny Reguieg,JPM Chase,1234-123-1222,100000.0,57010.0,$\n",
      "Fanny Reguieg,Wells Fargo,4132-123-1122,100000.0,43000.0,$\n",
      "Fanny Reguieg,Bank Of America,1211-123-1342,100000.0,44000.0,$\n",
      "Fanny Reguieg,JPM Chase,1234-123-1222,100000.0,61010.0,$\n",
      "Fanny Reguieg,Wells Fargo,4132-123-1122,100000.0,47000.0,$\n",
      "Fanny Reguieg,Bank Of America,1211-123-1342,100000.0,49000.0,$\n",
      "Fanny Reguieg,JPM Chase,1234-123-1222,100000.0,65010.0,$\n",
      "Fanny Reguieg,Wells Fargo,4132-123-1122,100000.0,56000.0,$\n",
      "Fanny Reguieg,Bank Of America,1211-123-1342,100000.0,52000.0,$\n",
      "Fanny Reguieg,JPM Chase,1234-123-1222,100000.0,70010.0,$\n",
      "Fanny Reguieg,Wells Fargo,4132-123-1122,100000.0,59000.0,$\n",
      "Fanny Reguieg,Bank Of America,1211-123-1342,100000.0,57000.0,$\n",
      "Fanny Reguieg,JPM Chase,1234-123-1222,100000.0,78010.0,$\n",
      "Fanny Reguieg,Wells Fargo,4132-123-1122,100000.0,63000.0,$\n",
      "Fanny Reguieg,Bank Of America,1211-123-1342,100000.0,65000.0,$\n",
      "Fanny Reguieg,JPM Chase,1234-123-1222,100000.0,84010.0,$\n",
      "Fanny Reguieg,Wells Fargo,4132-123-1122,100000.0,72000.0,$\n",
      "Fanny Reguieg,Bank Of America,1211-123-1342,100000.0,67000.0,$\n",
      "Fanny Reguieg,JPM Chase,1234-123-1222,100000.0,89010.0,$\n",
      "Fanny Reguieg,Wells Fargo,4132-123-1122,100000.0,77000.0,$\n",
      "Fanny Reguieg,Bank Of America,1211-123-1342,100000.0,70000.0,$\n",
      "Fanny Reguieg,JPM Chase,1234-123-1222,100000.0,96010.0,$\n",
      "Fanny Reguieg,Wells Fargo,4132-123-1122,100000.0,82000.0,$\n",
      "Fanny Reguieg,Bank Of America,1211-123-1342,100000.0,78000.0,$\n",
      "Fanny Reguieg,JPM Chase,1234-123-1222,100000.0,97010.0,$\n",
      "Fanny Reguieg,JPM Chase,1234-123-1222,100000.0,97010.0,$\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "wallet = [cc, CreditCard('Fanny Reguieg', 'Wells Fargo', '4132-123-1122',100000),CreditCard('Fanny Reguieg', 'Bank Of America', '1211-123-1342',100000)]\n",
    "\n",
    "is_over_limit = False\n",
    "while not is_over_limit:\n",
    "    for c,multiplier in zip(wallet,[random.randrange(1,10),random.randrange(1,10),random.randrange(1,10)]):\n",
    "        print(c)\n",
    "        if not c.charge(1000.00*multiplier):\n",
    "            is_over_limit = (True,cc)\n",
    "            break\n",
    "print(is_over_limit[1])\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "raw",
   "id": "9a387dec-706f-4fdc-9e61-47f33bc57494",
   "metadata": {},
   "source": [
    "## Magic method\n",
    "__init__(self[, ...]): Initialize an object (constructor).\n",
    "__del__(self): Clean up an object before it's destroyed (destructor).\n",
    "__repr__(self): Return the canonical string representation of an object.\n",
    "__str__(self): Return the informal string representation of an object.\n",
    "__len__(self): Return the length of an object.\n",
    "__getitem__(self, key): Get an item from an object using square bracket notation.\n",
    "__setitem__(self, key, value): Set an item in an object using square bracket notation.\n",
    "__delitem__(self, key): Delete an item from an object using square bracket notation.\n",
    "__iter__(self): Return an iterator object.\n",
    "__next__(self): Return the next item from the iterator.\n",
    "__contains__(self, item): Check if an item is contained in an object.\n",
    "__eq__(self, other): Implement equality comparison (==).\n",
    "__ne__(self, other): Implement non-equality comparison (!=).\n",
    "__lt__(self, other): Implement less-than comparison (<).\n",
    "__le__(self, other): Implement less-than or equal to comparison (<=).\n",
    "__gt__(self, other): Implement greater-than comparison (>).\n",
    "__ge__(self, other): Implement greater-than or equal to comparison (>=).\n",
    "__add__(self, other): Implement addition (+).\n",
    "__sub__(self, other): Implement subtraction (-).\n",
    "__mul__(self, other): Implement multiplication (*).\n",
    "__truediv__(self, other): Implement true division (/).\n",
    "__floordiv__(self, other): Implement floor division (//).\n",
    "__mod__(self, other): Implement modulus (%).\n",
    "__pow__(self, other[, modulo]): Implement exponentiation (**).\n",
    "__iadd__(self, other): Implement in-place addition (+=).\n",
    "__isub__(self, other): Implement in-place subtraction (-=).\n",
    "__imul__(self, other): Implement in-place multiplication (*=).\n",
    "__itruediv__(self, other): Implement in-place true division (/=).\n",
    "__ifloordiv__(self, other): Implement in-place floor division (//=).\n",
    "__imod__(self, other): Implement in-place modulus (%=).\n",
    "__ipow__(self, other[, modulo]): Implement in-place exponentiation (**=).\n",
    "__abs__(self): Implement absolute value (abs()).\n",
    "__round__(self[, n]): Implement rounding (round()).\n",
    "__enter__(self): Enter a runtime context (with statement).\n",
    "__exit__(self, exc_type, exc_value, traceback): Exit a runtime context (with statement).\n",
    "__call__(self[, args...]): Make an instance callable.\n",
    "__getattr__(self, name): Retrieve an attribute that doesn't exist.\n",
    "__setattr__(self, name, value): Set an attribute.\n",
    "__delattr__(self, name): Delete an attribute.\n",
    "__dir__(self): List the attributes of an object.\n",
    "__hash__(self): Return the hash value of an object.\n",
    "__enter__(self): Enter a runtime context (context manager).\n",
    "__exit__(self, exc_type, exc_value, traceback): Exit a runtime context (context manager)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3bf72b4f-d2dd-43bd-914c-3783856e2876",
   "metadata": {},
   "source": [
    "### R-2.9 \n",
    "Implement the sub method for the Vector class of Section 2.3.3, so\n",
    "that the expression u−v returns a new vector instance representing the\n",
    "difference between two vectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "id": "4438fcd6-756e-4b6f-8a0b-416c96132001",
   "metadata": {},
   "outputs": [],
   "source": [
    "### Over loaded operations with a list as the object\n",
    "class Vector:\n",
    "    \"\"\"Represent a multidimension space\"\"\"\n",
    "    def __init__(self,dimension):\n",
    "        if isinstance(dimension,(tuple,list,set)):\n",
    "            self._coords = dimension\n",
    "        else:\n",
    "            self._coords = [0] * dimension\n",
    "\n",
    "    def __len__(self):\n",
    "        \"\"\"Return the demsion of the ventor\"\"\"\n",
    "        return len(self._coords)\n",
    "\n",
    "    def __getitem__(self,j):\n",
    "        \"\"\"Return jth coordinate of vector\"\"\"\n",
    "        return self._coords[j]\n",
    "\n",
    "    def __setitem__(self,j,val):\n",
    "        \"\"\"Set jth coordinate of vector to given value\"\"\"\n",
    "        self._coords[j] = val\n",
    "\n",
    "    def __add__(self,other):\n",
    "        \"\"\"return sum of two vectors\n",
    "            vector must be same length in order to get the sum\n",
    "        \"\"\"\n",
    "        if len(self) != len(other):\n",
    "            raise ValueError('dimensions must agree')\n",
    "        result = Vector(len(self))\n",
    "        if isinstance(other, Vector):\n",
    "            for j in range(len(self)):\n",
    "                result._coords[j] = self._coords[j] + other._coords[j]\n",
    "        elif isinstance(other, list):\n",
    "            for j in range(len(self)):\n",
    "                result._coords[j] = other[j] + self._coords[j]\n",
    "        return result\n",
    "\n",
    "    def __radd__(self,other):\n",
    "        \"\"\"return sum of two vectors\n",
    "            using the right hand syntax\n",
    "        \"\"\"\n",
    "        return self.__add__(other)\n",
    "\n",
    "    def __eq__(self,other):\n",
    "        \"\"\"Return True if vector has same coordinates as other\"\"\"\n",
    "        return self._coords == other._coords\n",
    "\n",
    "    def __ne__(self,other):\n",
    "        \"\"\"Return True if vector differ from other\"\"\"\n",
    "        return not self == other\n",
    "\n",
    "    def __str__(self,):\n",
    "        \"\"\"Produce string representation of vector\"\"\"\n",
    "        return f'< {str(self._coords)[1:-1]} >'\n",
    "\n",
    "\n",
    "    def __sub__(self,other):\n",
    "        \"\"\"return diff of two vectors\n",
    "            vector must be same length in order to get the sum\n",
    "        \"\"\"\n",
    "        if len(self) != len(other):\n",
    "            raise ValueError('dimensions must agree')\n",
    "        result = Vector(len(self))\n",
    "        for j in range(len(self)):\n",
    "            result[j] = self[j] - other[j]\n",
    "        return result\n",
    "\n",
    "    def __mul__(self,multiplier):\n",
    "        results = Vector(len(self))\n",
    "        for i in range(len(self._coords)):\n",
    "            results._coords[i] = self._coords[i] *multiplier\n",
    "        return results\n",
    "\n",
    "    def __rmul__(self,multiplier):\n",
    "        return self.__mul__(multiplier)\n",
    "\n",
    "    def __neg__(self,):\n",
    "        if len(self._coords) > 0: \n",
    "            for i in range(len(self._coords)):\n",
    "                self._coords[i] *= -1 \n",
    "        else:\n",
    "            raise ValueError(\"Dimension of vector is less than 1\")\n",
    "\n",
    "    def get_coords(self):\n",
    "        return self._coords\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "id": "f6b6d95c-a05d-492d-95f0-a0d77b39079c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "< 0, 2, 8, 18, 32 > < 0, 1, 2, 3, 4 >\n"
     ]
    }
   ],
   "source": [
    "v = Vector(5)\n",
    "v2 = Vector(5)\n",
    "for i in range(5):\n",
    "    v[i] = i\n",
    "    v2[i] = i*2*i\n",
    "print(str(v2),str(v))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 301,
   "id": "c6ac763e-fad6-4d4c-bc3b-e320312ac4a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "v3 = v - v2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 302,
   "id": "7d93e632-aba7-42ae-b000-d2aba9567ee0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "< 0, -1, -6, -15, -28 >\n"
     ]
    }
   ],
   "source": [
    "print(str(v3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e707ae2-5af3-4266-aa42-496b6bb33a91",
   "metadata": {},
   "source": [
    "### R-2.10 \n",
    "Implement the neg method for the Vector class of Section 2.3.3, so\n",
    "that the expression −v returns a new vector instance whose coordinates\n",
    "are all the negated values of the respective coordinates of v."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 303,
   "id": "2f89802b-122a-4b15-adb3-8dbae2dc5da4",
   "metadata": {},
   "outputs": [],
   "source": [
    "-v3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "id": "e33e6c7e-87b5-4002-b6ed-3582e4ce79a5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "< 0, 1, 6, 15, 28 >\n"
     ]
    }
   ],
   "source": [
    "\n",
    "print(v3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "716c91be-4193-42c5-8fa1-ee79524aad5a",
   "metadata": {},
   "source": [
    "### R-2.11\n",
    "In Section 2.3.3, we note that our Vector class supports a syntax such as\n",
    "v = u + [5, 3, 10, −2, 1], in which the sum of a vector and list returns\n",
    "a new vector. However, the syntax v = [5, 3, 10, −2, 1] + u is illegal.\n",
    "Explain how the Vector class definition can be revised so that this syntax\n",
    "generates a new vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 305,
   "id": "c16f43ea-e264-4ba6-bb9f-cb7b92281597",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'< 0, 3, 10, 21, 36 >'"
      ]
     },
     "execution_count": 305,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(v + v2) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 306,
   "id": "7970db53-b53b-43a0-a458-73fe7d9b5eb9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'< 1, 3, 5, 7, 9 >'"
      ]
     },
     "execution_count": 306,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(v + [1,2,3,4,5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 307,
   "id": "7d5c7990-9b25-4aa2-a8b5-8cac1473db2f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'< 1, 3, 5, 7, 9 >'"
      ]
     },
     "execution_count": 307,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str([1,2,3,4,5] + v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 308,
   "id": "5e572b4a-b365-45bf-9aeb-581a6eb3ee10",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 5, 0, 1, 2, 3, 4]"
      ]
     },
     "execution_count": 308,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[1,2,3,4,5] + v.get_coords()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4c3d10f-309f-4b8f-921a-19e487ed84fd",
   "metadata": {},
   "source": [
    "### R-2.12 \n",
    "Implement the mul method for the Vector class of Section 2.3.3, so\n",
    "that the expression v*3 returns a new vector with coordinates that are 3\n",
    "times the respective coordinates of v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 309,
   "id": "2139df01-c52f-4266-90ec-dd0b4fbb01aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'< 0, 3, 18, 45, 84 >'"
      ]
     },
     "execution_count": 309,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(v3*3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1f9feb7-2441-4539-a39f-7d7ef7857443",
   "metadata": {},
   "source": [
    "### R-2.13\n",
    "Exercise R-2.12 asks for an implementation of mul , for the Vector\n",
    "class of Section 2.3.3, to provide support for the syntax v * 3. Implement\n",
    "the rmul method, to provide additional support for syntax 3 * v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 310,
   "id": "e249ae21-75cb-4b14-9b88-2810989fb2ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'< 0, 3, 18, 45, 84 >'"
      ]
     },
     "execution_count": 310,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(3*v3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "710d6e28-161d-4c1f-9e87-1664ed202f43",
   "metadata": {},
   "source": [
    "### R-2.15\n",
    "The Vector class of Section 2.3.3 provides a constructor that takes an integer d, and produces a d-dimensional vector with all coordinates equal to\n",
    "0. Another convenient form for creating a new vector would be to send the\n",
    "constructor a parameter that is some iterable type representing a sequence\n",
    "of numbers, and to create a vector with dimension equal to the length of\n",
    "that sequence and coordinates equal to the sequence values. For example,\n",
    "Vector([4, 7, 5]) would produce a three-dimensional vector with coordinates <4, 7, 5>. Modify the constructor so that either of these forms is\n",
    "acceptable; that is, if a single integer is sent, it produces a vector of that\n",
    "dimension with all zeros, but if a sequence of numbers is provided, it produces a vector with coordinates based on that sequence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 311,
   "id": "39990595-79f0-417a-802f-752a4d847ab5",
   "metadata": {},
   "outputs": [],
   "source": [
    "v4 = Vector([4,7,5])\n",
    "v5 = Vector([1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 312,
   "id": "b969f341-fa24-40da-819e-acf5b7cddc53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'< 4, 7, 5 >'"
      ]
     },
     "execution_count": 312,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(v4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 313,
   "id": "7c4ae768-b72e-4fd9-906d-5e72e92f4ec8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'< 5, 9, 8 >'"
      ]
     },
     "execution_count": 313,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(v4+v5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "807e9fef-cd7e-4ee6-8de6-029960e349d0",
   "metadata": {},
   "source": [
    "## Ch3 Recursion:\n",
    "\n",
    "\n",
    "### Recursion\n",
    "        1. Recursion is a technique by which a function makes one or more calls to itself during execution\n",
    "        2. Examples of recursion:\n",
    "                1. Factorial function - classical mathemaical function has a natural recursive defintion\n",
    "                2. English Ruler - fractal structure\n",
    "                3. Binary Search - locate a desired value in data \n",
    "                4. File sys - computer file system of directories\n",
    "\n",
    "        Binary Search\n",
    "            - locate a target value within a sorted sequence of n elements \n",
    "            - standard apprach to seaech for a value in an unsorted sequence is to loop through each element. This is ineffective due to o(n) or  \n",
    "              linear search\n",
    "            - when a sequence is sorted and indexable, there is more effient alog or o(log(n))\n",
    "            - mid calculation\n",
    "                mid = (high+low)/2\n",
    "            - cases:\n",
    "                - if the target equals data[mid], then we have found the item we are looking for, search terminate\n",
    "                - if target < data[mid], then we recur on the fight half of the sequence that is on the interval of indices from low to mid-1\n",
    "                - if target > data[mid], then we recur on the second hald the sequence that is, on the interval of indidevs mid +1 to hig\n",
    "\n",
    "### Designing Recursive Algorithms:\n",
    "\n",
    "        Characteristics of Recurisive Algos:\n",
    "            1. Test for base cases\n",
    "                - We begin by testing for a set of base cases \n",
    "                - These base cases should be definded so that every\n",
    "            2. Recur - if not basze case, we perform one or more recursive calls. \n",
    "\n",
    "        - using stack data structure as an option to recursion\n",
    "        \n",
    "        Tail recursion:\n",
    "            A recursion is a tail recursion if any recursive call that is made from one context is the very last operation in that conext, with the \n",
    "            return value of the recurive call\n",
    "                eg return recursive_call(n-1) * n\n",
    "\n",
    "        \n",
    "                \n",
    "                "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0c550c0b-80f8-47ff-9a19-34f83e90a7f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def factorial(n):\n",
    "    if n == 0:\n",
    "        return 1\n",
    "    else:\n",
    "        return factorial(n-1)*n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4ed77a54-324e-4a43-9dd4-619d7b0b395e",
   "metadata": {},
   "outputs": [],
   "source": [
    "assert factorial(5) == 120 # return 120 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5cdb9032-ee14-4c42-8594-01358c92458d",
   "metadata": {},
   "outputs": [],
   "source": [
    "## binary search\n",
    "def binary_search(data, target,low,high):\n",
    "    if low>high:\n",
    "        return False\n",
    "    else:\n",
    "        print(f'{low} {high}')\n",
    "        mid = (low +  high)//2\n",
    "        if target == data[mid]:\n",
    "            return True\n",
    "        elif target < data[mid]:\n",
    "            return binary_search(data,target,low,mid-1)\n",
    "        else:\n",
    "            return binary_search(data,target,mid+1,high)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "04c69e26-88d0-4a41-8772-527f24344626",
   "metadata": {},
   "outputs": [],
   "source": [
    "l1 = [2,4,5,7,8,12,14,17,19,22,25,27,28,33,37]\n",
    "binary_search(l1,22,0,15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c85bd8a0-5150-45db-8c37-d99c398e836f",
   "metadata": {},
   "outputs": [],
   "source": [
    "binary_search(l1,37,0,15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "51033ab4-c720-4167-b2ca-6e283761ffed",
   "metadata": {},
   "outputs": [],
   "source": [
    "binary_search(l1,5,0,15)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4642431b-425d-4b24-b855-e3015f7606b1",
   "metadata": {},
   "source": [
    "### Linear sum\n",
    "    - sequenece is sequence \n",
    "    - lenght_of_sequence is lenght of sequence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bd234dc4-5f45-49e9-9060-ada41f788b2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# linear sum\n",
    "def linear_sum(sequenece, lenght_of_sequence):\n",
    "    if lenght_of_sequence == 0:\n",
    "        return 0\n",
    "    else:\n",
    "        return linear_sum(sequenece,lenght_of_sequence-1) + sequenece[lenght_of_sequence-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d6db0014-842f-444d-8059-44c2719b51a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "linear_sum([1,2,3],3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7173e0e-85b6-4ab7-8285-3969228084cc",
   "metadata": {},
   "source": [
    "### Reverse a sequence\n",
    "    - s = sequence\n",
    "    - start - start of the string\n",
    "    - stop - stop of the string "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c204c5eb-00f2-49e1-849e-b4d8ee43fe75",
   "metadata": {},
   "outputs": [],
   "source": [
    "def reverse(sequence, start, stop):\n",
    "    if start < stop -1:\n",
    "        print(f'{start},{stop}')\n",
    "        sequence[start],sequence[stop-1] = sequence[stop-1],sequence[start]\n",
    "        reverse(sequence,start+1,stop-1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6c930db2-107a-4d69-a2dd-05ed98977006",
   "metadata": {},
   "outputs": [],
   "source": [
    "l1 = [i for i in range(0,100)]\n",
    "reverse(l1,0,len(l1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cd8da1a2-b105-4e2b-b928-fc13acab4ce3",
   "metadata": {},
   "outputs": [],
   "source": [
    "l1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ea90d4cd-0307-468e-a80e-056db77f92a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_reverse(sequence):\n",
    "    return [i for i in range(len(sequence)-1,-1,-1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "adb7d2e6-8406-4923-827e-31aa908efa6c",
   "metadata": {},
   "outputs": [],
   "source": [
    "l2 = [i for i in range(0,10)]\n",
    "linear_reverse(l2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "46b8be64-32a5-4d5a-9ccc-bac0968658bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_reverse(sequence):\n",
    "    return [i for i in range(len(sequence)-1,-1,-1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "676e5f4e-238b-402c-ac40-e37522ea8acf",
   "metadata": {},
   "outputs": [],
   "source": [
    "l2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a18d264a-952e-44d4-bf01-581506bacfb7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def org_linear_reverse(sequence):\n",
    "    for i in range(0,len(sequence)):\n",
    "        sequence.insert(i,sequence.pop())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3c9a191b-3f43-4b5a-9164-2a6cdd8b0054",
   "metadata": {},
   "outputs": [],
   "source": [
    "org_linear_reverse(l2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7cad43a9-db73-400a-bbf3-637fa7d196f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "l2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6440288-2f5f-42a8-9f4d-95c23def5e01",
   "metadata": {},
   "source": [
    "### C-4.9 \n",
    "### Write a short recursive Python function that finds the minimum and maximum values in a sequence without using any loops."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "87c92faa-ee07-4c92-8b14-93a31f6df744",
   "metadata": {},
   "outputs": [],
   "source": [
    "def minmax(sequence,count=0,min=None,max=None):\n",
    "    if len(sequence) == 0:\n",
    "        return min,max\n",
    "    if not min or not max:\n",
    "        min,max = sequence[0],sequence[0]\n",
    "\n",
    "    if min > sequence[count]:\n",
    "        min = sequence[count]\n",
    "    if max < sequence[count]:\n",
    "        max = sequence[count]\n",
    "    return minmax(sequence[count+1:],count+1,min,max)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2e1d9061-980c-4ebc-adb8-a9f5e7bc717f",
   "metadata": {},
   "outputs": [],
   "source": [
    "l1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2df495e6-d096-41e6-bb92-948f90a60e37",
   "metadata": {},
   "outputs": [],
   "source": [
    "minmax(l1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "13565b27-48d6-4f06-bf59-f9ae7a0d8073",
   "metadata": {},
   "outputs": [],
   "source": [
    "minmax(l2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9aa3e845-9ebd-45f3-97b3-17356433896f",
   "metadata": {},
   "source": [
    "### C-4.12 \n",
    "### Give a recursive algorithm to compute the product of two positive integers, m and n, using only addition and subtraction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "caf0f9aa-180b-447a-aef4-5cc93a8471b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def product(m,n):\n",
    "    if n == 0:\n",
    "        return 0\n",
    "    else:\n",
    "        return product(m,n-1) + m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8518f7ce-e4e1-4c46-a076-666e8374f8b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "product(2,5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab5dfff1-7bc0-4c29-9401-414e08dbc40d",
   "metadata": {},
   "source": [
    "### C-4.15\n",
    "### Write a recursive function that will output all the subsets of a set of n elements (without repeating any subsets)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fa2c79c3-3b52-410d-82ec-3d7eb7ac3ca8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def subset(seq,n,ss=[]):\n",
    "    if not seq:\n",
    "        return ss\n",
    "    else:\n",
    "        rs = seq[0:n]\n",
    "        if not  rs in ss:\n",
    "            ss.append(seq[0:n])\n",
    "        remain = seq[n:]\n",
    "        return subset(remain,n,ss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e25bc2e5-e758-4798-81e1-cc1052d7eb6a",
   "metadata": {},
   "outputs": [],
   "source": [
    "subset(l2,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3baf765f-8c06-4d7e-9457-ea629260899f",
   "metadata": {},
   "outputs": [],
   "source": [
    "l3 = [1,2,1,2,3,4,5,6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2cc1bcff-a86f-468f-be41-84c5ed3a6e47",
   "metadata": {},
   "outputs": [],
   "source": [
    "subset(l3,2,[])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3077db16-7010-4f91-8b83-6f0c6f16f185",
   "metadata": {},
   "source": [
    "### C-4.16 \n",
    "Write a short recursive Python function that takes a character string s and\n",
    "outputs its reverse. For example, the reverse of pots&pans would be\n",
    "snap&stop ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "22837b92-6292-4a70-8d78-984381d776d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def reverse_str(s):\n",
    "    if s == '':\n",
    "        return s\n",
    "    return reverse_str(s[1:]) + s[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "060af02f-8782-4481-9e0b-22923e0897c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "reverse_str('hello')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d488e0e-1435-41cd-844c-5b1ec53c6c10",
   "metadata": {},
   "source": [
    "### C-4.17 \n",
    "Write a short recursive Python function that determines if a string s is a\n",
    "palindrome, that is, it is equal to its reverse. For example, racecar and\n",
    "gohangasalamiimalasagnahog are palindromes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 314,
   "id": "6d49814d-9bec-4160-8591-1943fa2a5c5e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_palindrome(s):\n",
    "    if len(s) <= 1:\n",
    "        return True\n",
    "\n",
    "    if s[0] == s[-1]:\n",
    "        return is_palindrome(s[1:-1])\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 315,
   "id": "c251a88a-d91b-4e6a-8ad8-58c25389c066",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 315,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_palindrome('radar')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 316,
   "id": "17892e46-6e21-426b-a28a-f1686eddad13",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 316,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_palindrome('hello')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16a7395a-b908-4cf9-a3e8-5549d3e602f8",
   "metadata": {},
   "source": [
    "### C-4.18 \n",
    "Use recursion to write a Python function for determining if a string s has\n",
    "more vowels than consonants."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "426e1f97-df27-4a56-93f8-a4f6f903b7ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "def has_more_vowels(string):\n",
    "    string = string.lower()\n",
    "    def count_vowels(string,count=0):\n",
    "        vowels = ['a','e','i','o','u']\n",
    "        if not string:\n",
    "            return count\n",
    "        if string[0] in vowels:\n",
    "            count+=1\n",
    "        if string[-1] in vowels and len(string)>1:\n",
    "            count+=1\n",
    "        return count_vowels(string[1:-1],count)\n",
    "\n",
    "    count = count_vowels(string)\n",
    "    return count > (len(string) - count)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "0afaf494-820b-4f9b-bb97-b33c7e4fdd02",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "has_more_vowels('AUDIO')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "14a06a3c-0ce0-40aa-b1c0-5b4c70658bcd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "has_more_vowels('Hello')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf3d0710-c8ba-4cb2-90ce-811e5bcce989",
   "metadata": {},
   "source": [
    "### C-4.19\n",
    "Write a short recursive Python function that rearranges a sequence of integer values so that all the even values appear before all the odd values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "c596d12d-d83e-4df3-a088-0d6a240f1fda",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-1 + -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e10041c5-4092-417c-89ff-f097f6e13fce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5, 6]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nums = [2,4,5,6,1,3]\n",
    "nums[2:-2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "fb41ebfa-36ef-47ba-922f-6a6b5f8f0f51",
   "metadata": {},
   "outputs": [],
   "source": [
    "def rearrange_even_odd(seq):\n",
    "\n",
    "    def even_odds_sort(seq,count=0,sorted_arr=[]):\n",
    "        if count != len(seq):\n",
    "            if seq[count] % 2 == 0:\n",
    "                sorted_arr.insert(0,seq[count])\n",
    "                return even_odds_sort(seq,count+1,sorted_arr)\n",
    "            else:\n",
    "                sorted_arr.append(seq[count])\n",
    "                return even_odds_sort(seq,count+1,sorted_arr)\n",
    "        else:\n",
    "            return sorted_arr\n",
    "\n",
    "    return even_odds_sort(seq)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "b9f5ebcb-2021-474f-ab86-2a76bb0908e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "nums = [i for i in range(0,10)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7e207747-ea3a-4ced-b4b7-9cd7f2618905",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[8, 6, 4, 2, 0, 1, 3, 5, 7, 9]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rearrange_even_odd(nums)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "5cc7252a-c97a-469b-a4cd-39f7bb634f38",
   "metadata": {},
   "outputs": [],
   "source": [
    "## true answer here cause original sequence sorted\n",
    "\n",
    "def rearrange_e_o(seq):\n",
    "    def even_odds_sort(seq,index=0,count=0):\n",
    "        if len(seq) != count:\n",
    "            if seq[index] % 2 == 0:\n",
    "                seq.insert(0,seq.pop(index))\n",
    "                index+=1\n",
    "            else:\n",
    "                seq.append(seq.pop(index))\n",
    "            count+=1\n",
    "            return even_odds_sort(seq,index,count)\n",
    "        else:\n",
    "            return seq\n",
    "    return even_odds_sort(seq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "59eec10e-f79f-4ade-955c-2e0789b197d6",
   "metadata": {},
   "outputs": [],
   "source": [
    "nums = [i for i in range(1,5)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "84d49815-c0ba-40f9-bdeb-8d4c69dfe056",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4, 2, 1, 3]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rearrange_e_o(nums)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31af9f39-5013-4674-973d-afa6ccc3d1b5",
   "metadata": {},
   "source": [
    "### C-4.20 \n",
    "Given an unsorted sequence, S, of integers and an integer k, describe a\n",
    "recursive algorithm for rearranging the elements in S so that all elements\n",
    "less than or equal to k come before any elements larger than k. What is\n",
    "the running time of your algorithm on a sequence of n values?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "241cb05c-bb6f-46b0-ae4f-51800b4aa11d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# this is o(n), reason it has to go through each item to determin if its less than or equal to k\n",
    "\n",
    "def sort_before_k(seq,k):\n",
    "\n",
    "    def sort_k(seq,k,count=0):\n",
    "        if count != len(seq):\n",
    "            if seq[count] <= k:\n",
    "                seq.insert(0,seq.pop(count))\n",
    "            count+=1\n",
    "            return sort_k(seq,k,count)\n",
    "        else:\n",
    "            return seq\n",
    "    return sort_k(seq,k)\n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "007957e9-e223-4272-9bc6-af644fc8e16e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 46, 14, 80, 65, 57, 13, 39, 65, 69]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[13, 14, 1, 46, 80, 65, 57, 39, 65, 69]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "l1 = [random.randrange(1,100) for _ in range(0,10)]\n",
    "print(l1)\n",
    "sort_before_k(l1,20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "37f16f09-2faa-440c-a2ce-6bbaaca271e0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 4, 5, 6, 7, 8, 9]\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Strategy here take list \n",
    "left sort - left to right append  without mid \n",
    "right sort - right to left insert without mid\n",
    "\"\"\"\n",
    "\n",
    "def sort_even_odds(nums):\n",
    "    mid = (len(nums)//2)\n",
    "    def left_sort(nums,mid,count=0):\n",
    "        if mid == count:\n",
    "            return nums\n",
    "        if nums[count]%2 != 0:\n",
    "            nums.append(nums.pop(count))\n",
    "        \n",
    "    def right_sort(nums,mid,count=0):\n",
    "        pass\n",
    "    \n",
    "l1 = [i for i in range(1,10)]\n",
    "print(l1)\n",
    "sort_even_odds(nums)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b833b859-d65e-4833-97ba-c163a36fb63a",
   "metadata": {},
   "source": [
    "### C-4.21\n",
    "Suppose you are given an n-element sequence, S, containing distinct integers that are listed in increasing order. Given a number k, describe a\n",
    "recursive algorithm to find two integers in S that sum to k, if such a pair\n",
    "exists. What is the running time of your algorithm?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "c933fe38-52f1-4cef-9b75-3ebb95d619bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "o notation for this at: o(n)\n",
    "\"\"\"\n",
    "\n",
    "def two_sum(iterable,k):\n",
    "\n",
    "    def find_k_index(iterable):\n",
    "        try:\n",
    "            return iterable.index(k)\n",
    "        except ValueError as e:\n",
    "            mid = iterable[len(iterable)//2]\n",
    "            index = None\n",
    "            if mid < k:\n",
    "                for i in range(len(iterable[mid:])):\n",
    "                    if iterable[i] < k:\n",
    "                        index = i\n",
    "            else:\n",
    "                for i in range(len(iterable[:mid])):\n",
    "                    if iterable[i] < k:\n",
    "                        index = i\n",
    "            return index\n",
    "    \n",
    "    def find_sum(iterable,k,k_index=find_k_index(iterable),count=0):\n",
    "        if not iterable:\n",
    "            return None\n",
    "        \n",
    "        diff = k-iterable[count]\n",
    "        \n",
    "        if diff in iterable[count+1:k_index]:\n",
    "            return iterable[count],diff\n",
    "        else:\n",
    "            count+=1\n",
    "            return find_sum(iterable[count:k_index],k,k_index,count)\n",
    "\n",
    "\n",
    "    return  find_sum(iterable,k)\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "04970ac2-9a26-4a8e-83da-86c1264796a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 4)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l1 = [2,4,5,8]\n",
    "two_sum(l1,6)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a88fb40e-32f1-4804-8a05-0f89234f2293",
   "metadata": {},
   "source": [
    "### C-4.22\n",
    "Develop a nonrecursive implementation of the version of power from\n",
    "Code Fragment 4.12 that uses repeated squaring."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "46de6392-81eb-4db9-b17c-0c4e3f57c5f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def power(base,exp):\n",
    "    return base**exp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "fb2ac34f-98a5-4d56-962f-40bfe02b04ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "power(2,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "50287186-2fb3-4080-a242-99eb3e8c3fbe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "power(4,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "36239111-6dbe-4b0f-8b4c-4005d868f5a7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "500000.0   1\n",
      "250000.0   2\n",
      "125000.0   3\n",
      "62500.0   4\n",
      "31250.0   5\n",
      "15625.0   6\n",
      "7812.5   7\n",
      "3906.25   8\n",
      "1953.125   9\n",
      "976.5625   10\n",
      "488.28125   11\n",
      "244.140625   12\n",
      "122.0703125   13\n",
      "61.03515625   14\n",
      "30.517578125   15\n",
      "15.2587890625   16\n",
      "7.62939453125   17\n",
      "3.814697265625   18\n",
      "1.9073486328125   19\n",
      "0.95367431640625   20\n"
     ]
    }
   ],
   "source": [
    "count = 0\n",
    "items = 1000000\n",
    "while items >= 1:\n",
    "    items /=2 \n",
    "    count+=1\n",
    "    print(items,' ',count)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "e8a7cc9c-f8b8-4290-9c0c-90beeaf963ab",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " 0 Test\n",
      "500000 453335\n",
      "250000 453335\n",
      "125000 453335\n",
      "62500 453335\n",
      "31250 453335\n",
      "15625 453335\n",
      "7812 453335\n",
      "3906 453335\n",
      "1953 453335\n",
      "976 453335\n",
      "488 453335\n",
      "244 453335\n",
      "122 453335\n",
      "61 453335\n",
      "30 453335\n",
      "15 453335\n",
      "7 453335\n",
      "(453335, 18)\n",
      "\n",
      " 1 Test\n",
      "500000 414830\n",
      "250000 414830\n",
      "125000 414830\n",
      "62500 414830\n",
      "31250 414830\n",
      "15625 414830\n",
      "7812 414830\n",
      "3906 414830\n",
      "1953 414830\n",
      "976 414830\n",
      "488 414830\n",
      "244 414830\n",
      "122 414830\n",
      "61 414830\n",
      "30 414830\n",
      "15 414830\n",
      "7 414830\n",
      "3 414830\n",
      "(414830, 19)\n",
      "\n",
      " 2 Test\n",
      "500000 666285\n",
      "250000 666285\n",
      "125000 666285\n",
      "62500 666285\n",
      "31250 666285\n",
      "15625 666285\n",
      "7812 666285\n",
      "3906 666285\n",
      "1953 666285\n",
      "976 666285\n",
      "488 666285\n",
      "244 666285\n",
      "122 666285\n",
      "61 666285\n",
      "30 666285\n",
      "15 666285\n",
      "7 666285\n",
      "4 666285\n",
      "2 666285\n",
      "(666285, 20)\n",
      "\n",
      " 3 Test\n",
      "500000 497540\n",
      "250000 497540\n",
      "125000 497540\n",
      "62500 497540\n",
      "31250 497540\n",
      "15625 497540\n",
      "7812 497540\n",
      "3906 497540\n",
      "1953 497540\n",
      "976 497540\n",
      "488 497540\n",
      "244 497540\n",
      "122 497540\n",
      "61 497540\n",
      "30 497540\n",
      "15 497540\n",
      "7 497540\n",
      "4 497540\n",
      "(497540, 19)\n",
      "\n",
      " 4 Test\n",
      "500000 238460\n",
      "250000 238460\n",
      "125000 238460\n",
      "62500 238460\n",
      "31250 238460\n",
      "15625 238460\n",
      "7812 238460\n",
      "3906 238460\n",
      "1953 238460\n",
      "976 238460\n",
      "488 238460\n",
      "244 238460\n",
      "122 238460\n",
      "61 238460\n",
      "30 238460\n",
      "15 238460\n",
      "8 238460\n",
      "4 238460\n",
      "2 238460\n",
      "(238460, 20)\n",
      "\n",
      " 5 Test\n",
      "500000 371957\n",
      "250000 371957\n",
      "125000 371957\n",
      "62500 371957\n",
      "31250 371957\n",
      "15625 371957\n",
      "7812 371957\n",
      "3906 371957\n",
      "1953 371957\n",
      "976 371957\n",
      "488 371957\n",
      "244 371957\n",
      "122 371957\n",
      "61 371957\n",
      "30 371957\n",
      "15 371957\n",
      "7 371957\n",
      "4 371957\n",
      "(371957, 19)\n",
      "\n",
      " 6 Test\n",
      "500000 395787\n",
      "250000 395787\n",
      "125000 395787\n",
      "62500 395787\n",
      "31250 395787\n",
      "15625 395787\n",
      "7812 395787\n",
      "3906 395787\n",
      "1953 395787\n",
      "976 395787\n",
      "488 395787\n",
      "244 395787\n",
      "122 395787\n",
      "61 395787\n",
      "30 395787\n",
      "15 395787\n",
      "7 395787\n",
      "3 395787\n",
      "(395787, 19)\n",
      "\n",
      " 7 Test\n",
      "500000 850034\n",
      "250000 850034\n",
      "125000 850034\n",
      "62500 850034\n",
      "31250 850034\n",
      "15625 850034\n",
      "7812 850034\n",
      "3906 850034\n",
      "1953 850034\n",
      "976 850034\n",
      "488 850034\n",
      "244 850034\n",
      "122 850034\n",
      "61 850034\n",
      "30 850034\n",
      "15 850034\n",
      "8 850034\n",
      "4 850034\n",
      "2 850034\n",
      "(850034, 20)\n",
      "\n",
      " 8 Test\n",
      "500000 570590\n",
      "250000 570590\n",
      "125000 570590\n",
      "62500 570590\n",
      "31250 570590\n",
      "15625 570590\n",
      "7812 570590\n",
      "3906 570590\n",
      "1953 570590\n",
      "976 570590\n",
      "488 570590\n",
      "244 570590\n",
      "122 570590\n",
      "61 570590\n",
      "30 570590\n",
      "15 570590\n",
      "7 570590\n",
      "(570590, 18)\n",
      "\n",
      " 9 Test\n",
      "500000 394186\n",
      "250000 394186\n",
      "125000 394186\n",
      "62500 394186\n",
      "31250 394186\n",
      "15625 394186\n",
      "7812 394186\n",
      "3906 394186\n",
      "1953 394186\n",
      "976 394186\n",
      "488 394186\n",
      "244 394186\n",
      "122 394186\n",
      "61 394186\n",
      "30 394186\n",
      "15 394186\n",
      "7 394186\n",
      "3 394186\n",
      "2 394186\n",
      "(394186, 20)\n"
     ]
    }
   ],
   "source": [
    "# Binary search with recursion with sorted array\n",
    "import random\n",
    "count = 1\n",
    "items = 1000000\n",
    "items = [i for i in range(1,1000001)]\n",
    "def find_item(iterable,target,count=0):\n",
    "    count+=1\n",
    "    mid = len(iterable)//2\n",
    "    if  target < iterable[0] or target > iterable[-1]:\n",
    "        return None, count\n",
    "    elif target > iterable[mid]:\n",
    "        print(mid,target)\n",
    "        return find_item(iterable[mid:],target,count)\n",
    "    elif target < iterable[mid]:\n",
    "        print(mid,target)\n",
    "        return find_item(iterable[:mid],target,count)\n",
    "    return target,count\n",
    "\n",
    "for i in range(0,10):\n",
    "    print('\\n',f'{i} Test',)\n",
    "    print(find_item(items,random.randrange(1,1000000)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "f59aff0c-bc1f-48cf-8f0d-1d67d646b98d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define the range of values for x (size of input data)\n",
    "x = np.arange(1, 10)\n",
    "\n",
    "# Define the functions\n",
    "y_n_log_n = x * np.log(x)\n",
    "y_log_n = np.log(x)\n",
    "y_n = x\n",
    "y_n_squared = x**2\n",
    "\n",
    "# Plot the functions\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(x, y_n_log_n, label='n log n')\n",
    "plt.plot(x, y_log_n, label='log n')\n",
    "plt.plot(x, y_n, label='n')\n",
    "plt.plot(x, y_n_squared, label='n^2')\n",
    "\n",
    "# Add labels and legend\n",
    "plt.xlabel('Size of Input Data (n)')\n",
    "plt.ylabel('Time Complexity')\n",
    "plt.title('Comparison of Time Complexities')\n",
    "plt.legend()\n",
    "\n",
    "# Show the plot\n",
    "plt.grid(True)\n",
    "plt.show()\n"
   ]
  },
  {
   "attachments": {
    "befc6f79-97f3-4db5-b3c6-4f833bedce65.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "d4d3ad26-c8eb-4323-b1ff-754e24bca38e",
   "metadata": {},
   "source": [
    "### Sorting Algo O notation\n",
    "\n",
    "![image.png](attachment:befc6f79-97f3-4db5-b3c6-4f833bedce65.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f0f399cf-8de9-4777-9e0b-f0a16a8fa951",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ecefb1d2-aa89-44a1-b99f-56ff800d5ab1",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "3984aae3-21f2-4433-a8da-528be613c511",
   "metadata": {},
   "source": [
    "## Ch3 Array-Based Sequences:\n",
    "### Sequence Types\n",
    "    - The list, tuple, str class are built type within python for sequence based\n",
    "    - These types are innately built in but can be expanded to other classes to override behaviors\n",
    "### Array:\n",
    "    - reference in memory is using an array is example\n",
    "    - array are sequence type and of the same data type\n",
    "    - arrays in python are dynamic in size or known as dynnamic arrays\n",
    "### Dynamic Array:\n",
    "    - Even tho array can increase it size, there is limitation in terms of the size of the array. Therefore resize is needed\n",
    "    - Implementation of dynamic array:\n",
    "        1. Allocate a new array B with larger capacity\n",
    "        2. Set B[i] = A[i], for i = 0 ... n -1 where n denotes the current number of items\n",
    "        3. Set A = B, that is, we henceforth use B as the array supporting the list\n",
    "        4. Insert the new alement in the new array\n",
    "### Tuple vs List Class\n",
    "    - tuples are immutable and much memory efficient\n",
    "    - list are mutable and expensive for memory\n",
    "\n",
    "        Operation             Running Time\n",
    "            len(data)             O(1)\n",
    "            data[j]               O(1)\n",
    "            data.count(value)     O(n)\n",
    "            data.index(value)     O(k+1)\n",
    "            value in data         O(k+1)\n",
    "            data1 == data2        O(k+1) (similarly !=, <, <=, >, >=)\n",
    "            data[j:k]             O(k− j +1)\n",
    "            data1 + data2         O(n1 +n2)\n",
    "            c * data              O(cn)\n",
    "            data[j] = val         O(1)\n",
    "            data.append(value)    O(1)∗\n",
    "            data.insert(k, value) O(n−k+1)∗\n",
    "            data.pop( )           O(1)∗\n",
    "            data.pop(k)           O(n−k)∗\n",
    "            del data[k]\n",
    "            data.remove(value)     O(n)∗\n",
    "            data1.extend(data2)    O(n2)∗\n",
    "            data1 += data2\n",
    "            data.reverse( )        O(n)\n",
    "            data.sort( )           O(nlog n)\n",
    "\n",
    "### Insertation Sort Algo\n",
    "    - Start with sequeunce array \n",
    "    - Then as items are added, we compare the last with the previous item, if there the item is less than the current we swap the items \n",
    "\n",
    "    Algo insertationSort(A):\n",
    "        Input is a A as array \n",
    "        Output is an Array with elements with nondecreating order\n",
    "        for k from 1 to n -1 do\n",
    "            Insert A[k] at its proper location within A[0], A[1], ... A[K]\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f2d798a-86ea-4e96-a70d-c073810dd4b5",
   "metadata": {},
   "source": [
    "### R-5.1 \n",
    "Execute the experiment from Code Fragment 5.1 and compare the results\n",
    "on your system to those we report in Code Fragment 5.2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "a76d0332-35a0-453a-96f0-ef7cdb7d0fe5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2531519850768 2531519850768 2531519850800\n",
      "24 24 28 28\n",
      "8448728 8000040 4000112\n"
     ]
    }
   ],
   "source": [
    "# memory analysis and reference of the variabels in memory\n",
    "import sys\n",
    "import numpy\n",
    "array = [i for i in range(1000000)]\n",
    "tup = tuple(array)\n",
    "nparry = numpy.array([i for i in range(1000000)])\n",
    "num = 1\n",
    "print(id(array[0]),id(tup[0]),id(num))\n",
    "print(sys.getsizeof(array[0]),sys.getsizeof(tup[0]),sys.getsizeof(nparry[0]),sys.getsizeof(num))\n",
    "print(sys.getsizeof(array),sys.getsizeof(tup),sys.getsizeof(nparry))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "0fe19320-7c06-43f1-b8ca-a654563cc3aa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Length: 0; Size in bytes: 56\n",
      "Length: 1; Size in bytes: 88\n",
      "Length: 2; Size in bytes: 88\n",
      "Length: 3; Size in bytes: 88\n",
      "Length: 4; Size in bytes: 88\n",
      "Length: 5; Size in bytes: 120\n",
      "Length: 6; Size in bytes: 120\n",
      "Length: 7; Size in bytes: 120\n",
      "Length: 8; Size in bytes: 120\n",
      "Length: 9; Size in bytes: 184\n",
      "Length: 10; Size in bytes: 184\n",
      "Length: 11; Size in bytes: 184\n",
      "Length: 12; Size in bytes: 184\n",
      "Length: 13; Size in bytes: 184\n",
      "Length: 14; Size in bytes: 184\n",
      "Length: 15; Size in bytes: 184\n",
      "Length: 16; Size in bytes: 184\n",
      "Length: 17; Size in bytes: 248\n",
      "Length: 18; Size in bytes: 248\n",
      "Length: 19; Size in bytes: 248\n",
      "Length: 20; Size in bytes: 248\n",
      "Length: 21; Size in bytes: 248\n",
      "Length: 22; Size in bytes: 248\n",
      "Length: 23; Size in bytes: 248\n",
      "Length: 24; Size in bytes: 248\n",
      "Length: 25; Size in bytes: 312\n",
      "Length: 26; Size in bytes: 312\n"
     ]
    }
   ],
   "source": [
    "data = []\n",
    "for k in range(27):\n",
    "    a = len(data)\n",
    "    b = sys.getsizeof(data)\n",
    "    print(f'Length: {a}; Size in bytes: {b}')\n",
    "    data.append(None)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51e2f7ef-90d6-4efa-88c0-b95c881dbae4",
   "metadata": {},
   "source": [
    "### R-5.3 \n",
    "Modify the experiment from Code Fragment 5.1 in order to demonstrate\n",
    "that Python’s list class occasionally shrinks the size of its underlying array\n",
    "when elements are popped from a list."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "b9662a44-3e23-4a27-9fa4-27bc303a8328",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Length: 27; Size in bytes: 312\n",
      "Length: 26; Size in bytes: 312\n",
      "Length: 25; Size in bytes: 312\n",
      "Length: 24; Size in bytes: 312\n",
      "Length: 23; Size in bytes: 312\n",
      "Length: 22; Size in bytes: 312\n",
      "Length: 21; Size in bytes: 312\n",
      "Length: 20; Size in bytes: 312\n",
      "Length: 19; Size in bytes: 312\n",
      "Length: 18; Size in bytes: 312\n",
      "Length: 17; Size in bytes: 312\n",
      "Length: 16; Size in bytes: 312\n",
      "Length: 15; Size in bytes: 216\n",
      "Length: 14; Size in bytes: 216\n",
      "Length: 13; Size in bytes: 216\n",
      "Length: 12; Size in bytes: 216\n",
      "Length: 11; Size in bytes: 216\n",
      "Length: 10; Size in bytes: 216\n",
      "Length: 9; Size in bytes: 184\n",
      "Length: 8; Size in bytes: 184\n",
      "Length: 7; Size in bytes: 152\n",
      "Length: 6; Size in bytes: 152\n",
      "Length: 5; Size in bytes: 120\n",
      "Length: 4; Size in bytes: 120\n",
      "Length: 3; Size in bytes: 120\n",
      "Length: 2; Size in bytes: 120\n",
      "Length: 1; Size in bytes: 88\n"
     ]
    }
   ],
   "source": [
    "data = [None for _ in range(27)]\n",
    "for k in range(27):\n",
    "    a = len(data)\n",
    "    b = sys.getsizeof(data)\n",
    "    print(f'Length: {a}; Size in bytes: {b}')\n",
    "    data.pop()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3d0fed8-ac08-4530-90f7-b4ebd804ce82",
   "metadata": {},
   "source": [
    "#### R-5.4 \n",
    "Our DynamicArray class, as given in Code Fragment 5.3, does not support\n",
    "use of negative indices with getitem . Update that method to better\n",
    "match the semantics of a Python list."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ecd28d0-af06-412a-b0b3-010d1cd1c553",
   "metadata": {},
   "source": [
    "### R-5.6\n",
    "Our implementation of insert for the DynamicArray class, as given in\n",
    "Code Fragment 5.5, has the following inefficiency. In the case when a resize occurs, the resize operation takes time to copy all the elements from\n",
    "an old array to a new array, and then the subsequent loop in the body of\n",
    "insert shifts many of those elements. Give an improved implementation\n",
    "of the insert method, so that, in the case of a resize, the elements are\n",
    "shifted into their final position during that operation, thereby avoiding the\n",
    "subsequent shifting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "id": "6ee6f6cf-1e01-4f87-adb8-97f7a30581c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import ctypes\n",
    "\n",
    "class DynamicArray:\n",
    "\n",
    "    def __init__(self):\n",
    "        self._n = 0\n",
    "        self._capacity = 1\n",
    "        self._A = self._make_array(self._capacity)\n",
    "\n",
    "    def __len__(self):\n",
    "        return self._n\n",
    "\n",
    "    def __getitem__(self,k):\n",
    "        if not k < self._n:\n",
    "            raise IndexError('invalid index')\n",
    "        if k < 0:\n",
    "            index = k + 3\n",
    "            if index > 0:\n",
    "                return self._A[index]\n",
    "            else: \n",
    "                raise IndexError('invalid index')\n",
    "        return self._A[k]\n",
    "\n",
    "    def append(self,obj):\n",
    "        if self._n == self._capacity:\n",
    "            self._resize(2 * self._capacity)\n",
    "        self._A[self._n] = obj\n",
    "        self._n += 1\n",
    "\n",
    "    def insert(self,k,value):\n",
    "        if self._n == self._capacity:\n",
    "            # self._resize(2*self._capacity)\n",
    "            B = self._make_array(2*self_capcity)\n",
    "            for i in range(len(b)):\n",
    "                if i == k:\n",
    "                    B[k] == value\n",
    "                elif i < k:\n",
    "                    B[i] = self._A[i]\n",
    "                else:\n",
    "                    B[i] = self._A[i-1]\n",
    "            self._A = B\n",
    "            self._n += 1\n",
    "            self._capacity = c*2\n",
    "        for j in range(self._n,k,-1):\n",
    "            self._A[j] = self._A[j-1]\n",
    "        self._A[k] = value\n",
    "        self._n += 1\n",
    "\n",
    "    def _resize(self,c):\n",
    "        B = self._make_array(c)\n",
    "        for k in range(self._n):\n",
    "            B[k] = self._A[k]\n",
    "        self._A = B\n",
    "        self._capacity = c\n",
    "\n",
    "    def _make_array(self,c):\n",
    "        return (c * ctypes.py_object)()\n",
    "\n",
    "    def __str__(self,):\n",
    "        return f\"{self._capacity}, {self._n}\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "77042095-fd84-4984-b29f-860aeaf28a01",
   "metadata": {},
   "outputs": [],
   "source": [
    "da = DynamicArray()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "b0039a78-9488-4d7a-9768-dd153ed23e3d",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(5):\n",
    "    da.append(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "f0fc9dde-cfc3-4567-81a0-a1627aef0597",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'8, 5'"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(da)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "73fc5fa7-7b1e-4f30-98fd-08b79c6398ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'128, 105'"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for i in range(100):\n",
    "    da.append(i)\n",
    "str(da)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "a0275761-241a-4a61-8730-efad6370dcaa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "da[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "489a30a9-7155-4714-8288-eb991b8e2a71",
   "metadata": {},
   "outputs": [],
   "source": [
    "da.insert(1,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "3edd90ba-b697-4af3-8e93-79127107629e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "da[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "05c15387-6e8c-42f8-b7e6-ddf09a0da63e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "da2 = DynamicArray()\n",
    "print(da2._capacity)\n",
    "da2.append(1)\n",
    "da2.append(2)\n",
    "da2.append(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "id": "10e26e61-15ba-4834-baf9-040d7146f2ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "da2[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "id": "c6296af3-cf9c-42b0-92ba-834794441f73",
   "metadata": {},
   "outputs": [],
   "source": [
    "da2.insert(2,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "id": "51dd7a1f-752a-4465-94af-446d6283b22c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "da2._n\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "f0b809f7-78fd-439b-a819-8a793fb15fbd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "da2[3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "60750ec4-85d4-4b44-b960-86755952926a",
   "metadata": {},
   "outputs": [],
   "source": [
    "class GameEntry:\n",
    "    def __init__(self,name,score):\n",
    "        self._name = name\n",
    "        self._score = score\n",
    "\n",
    "    def get_name(self,):\n",
    "        return self._name\n",
    "\n",
    "    def get_score(self,):\n",
    "        return self._score\n",
    "\n",
    "    def __str__(self):\n",
    "        return f\"{self._name} {self._score}\"\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fd679f08-179b-4c39-8690-67f76d704816",
   "metadata": {},
   "outputs": [],
   "source": [
    "class ScoreBoard:\n",
    "\n",
    "    def __init__(self,capacity=10):\n",
    "        self._board = [None] * capacity\n",
    "        self._n = 0 \n",
    "\n",
    "    def __getitem__(self,k):\n",
    "        return self._board[k]\n",
    "\n",
    "    def __str__(self,):\n",
    "        return ','.join(str(self._board[j]) for j in range(self._n))\n",
    "\n",
    "    def add(self,entry):\n",
    "        score = entry.get_score()\n",
    "        good = self._n < len(self._board) or score > self._board[-1].get_score()\n",
    "\n",
    "        if good:\n",
    "            if self._n < len(self._board):\n",
    "                self._n +=1\n",
    "\n",
    "            j = self._n -1\n",
    "            while j > 0 and self._board[j-1].get_score() < score:\n",
    "                print(j,self._board[j-1].get_score(), score)\n",
    "                self._board[j] = self._board[j-1]\n",
    "                print(str(self))\n",
    "                j -= 1\n",
    "            self._board[j] = entry \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "06a1ed2f-44ac-466f-8609-6a84e2bf2345",
   "metadata": {},
   "outputs": [],
   "source": [
    "player_scores = [('Fanny', 100),('Ray',10),('Caitlin',10),('Silvia',22),('Monika',10),('Fanny', 1000),('Ray',99),('Caitlin',12),('Silvia',22),('Monika',20),('Monika',55)]\n",
    "#print(len(player_scores))\n",
    "game_entries = [GameEntry(name,score) for name,score in player_scores]\n",
    "sb = ScoreBoard()\n",
    "for ge in game_entries:\n",
    "    sb.add(ge)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "54a6d347-c165-4350-aecd-e4dcc86fba28",
   "metadata": {},
   "outputs": [],
   "source": [
    "str(sb)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ff8cbe4-082d-42b9-bff7-85ddcd15a831",
   "metadata": {},
   "source": [
    "### R-5.7\n",
    "Let A be an array of size n ≥ 2 containing integers from 1 to n−1, inclusive, with exactly one repeated. Describe a fast algorithm for finding the\n",
    "integer in A that is repeated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "id": "4c6a03b9-e98a-4507-a629-8a615006eff2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### this is an o(n log n) which is worse than iterating over o(n)\n",
    "from collections import Counter \n",
    "def find_repeat(array):\n",
    "    item_counts = Counter(array)\n",
    "    sorted_counts = sorted(item_counts.items(), key=lambda x: x[1], reverse=True)\n",
    "    for k,v in sorted_counts:\n",
    "        if v == 2:\n",
    "            return k\n",
    "\n",
    "find_repeat([1,2,3,3,4])  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "id": "ae600fbf-ca0a-43b7-b804-6faaac8ab5b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This is o(n)\n",
    "def find_repeat(array):\n",
    "    for i in range(1,len(array)):\n",
    "        if array[i-1] == array[i]:\n",
    "            return array[i]\n",
    "\n",
    "find_repeat([1,2,3,4,4])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa12eb51-5631-4352-af6e-3c0fa4c3eb72",
   "metadata": {},
   "source": [
    "### R-5.8\n",
    "Experimentally evaluate the efficiency of the pop method of Python’s list\n",
    "class when using varying indices as a parameter, as we did for insert on\n",
    "page 205. Report your results akin to Table 5.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "3436f4ec-211b-48c5-859c-d7f728179429",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              100           1000          10000         100000        1000000\n",
      "k = 0    2.200000e-06  1.000000e-06  8.000001e-06  7.610000e-05  1.191700e-03\n",
      "k= n//2  3.000005e-07  3.000005e-07  1.600001e-06  1.630000e-05  4.270000e-04\n",
      "k=n      5.000002e-07  3.000005e-07  3.000005e-07  1.999997e-07  8.000006e-07\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "list_of_lists = []\n",
    "sizes = [100,1000,10000,100000,1000000]\n",
    "time_series_arrays = []\n",
    "def insert_k(k,array):\n",
    "    indices = [0,len(array)//2,len(array)-1]\n",
    "    lapse = []\n",
    "    for index in indices:\n",
    "        start = time.perf_counter()\n",
    "        array.insert(index,k)\n",
    "        end = time.perf_counter()\n",
    "        diff = end-start\n",
    "        lapse.append(diff)\n",
    "        array.pop(index)\n",
    "    return lapse\n",
    "    \n",
    "for size in sizes:\n",
    "    list_of_lists.append([i for i in range(0,size)])\n",
    "\n",
    "for i in list_of_lists:\n",
    "       time_series_arrays.append(insert_k(-1,i))\n",
    "\n",
    "insertations = [\"k = 0\", \"k= n//2\",\"k=n\"]\n",
    "\n",
    "df = pd.DataFrame(time_series_arrays,columns=insertations,index=sizes)\n",
    "df = df.transpose()\n",
    "\n",
    "print(df)\n",
    "for index,row in df.iterrows():\n",
    "    plt.plot(df.columns, row,label=index)\n",
    "\n",
    "plt.xlabel('ArraySize')\n",
    "plt.ylabel('Time(secs)')\n",
    "plt.title('Insert Time')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "0a1e0f96-48e6-4ab3-8cd7-73f5bfc4e32b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              100           1000          10000         100000        1000000\n",
      "k = 0    2.499999e-06  6.999999e-07  1.920000e-05  5.420000e-05  7.251000e-04\n",
      "k= n//2  3.999994e-07  1.000000e-06  1.099999e-06  1.260000e-05  2.636000e-04\n",
      "k=n      3.000005e-07  5.000002e-07  6.000009e-07  3.999994e-07  8.000006e-07\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Popping the \n",
    "\"\"\"\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "list_of_lists = []\n",
    "sizes = [100,1000,10000,100000,1000000]\n",
    "time_series_arrays = []\n",
    "def pop_k(array):\n",
    "    indices = [0,(len(array)//2)-1,len(array)-3]\n",
    "    lapse = []\n",
    "    for index in indices:\n",
    "        start = time.perf_counter()\n",
    "        array.pop(index)\n",
    "        end = time.perf_counter()\n",
    "        diff = end-start\n",
    "        lapse.append(diff)\n",
    "    return lapse\n",
    "    \n",
    "for size in sizes:\n",
    "    list_of_lists.append([i for i in range(0,size)])\n",
    "\n",
    "for i in list_of_lists:\n",
    "       time_series_arrays.append(pop_k(i))\n",
    "\n",
    "removal = [\"k = 0\", \"k= n//2\",\"k=n\"]\n",
    "\n",
    "df = pd.DataFrame(time_series_arrays,columns=removal,index=sizes)\n",
    "df = df.transpose()\n",
    "\n",
    "print(df)\n",
    "for index,row in df.iterrows():\n",
    "    plt.plot(df.columns, row,label=index)\n",
    "\n",
    "plt.xlabel('ArraySize')\n",
    "plt.ylabel('Time(secs)')\n",
    "plt.title('K Pop Time')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "7d04ebe1-6651-4d6c-93ba-3200ede152b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6+vpgsViwefPmFbugButF8W0WEAmG4zhwHAeXy+W3yB+rJgMVKlYKVEJRERJ4ngfLsuA4TiKWT8riKRKFKBUjJxjxPPhLkakEo+KTBpVQVASFv9kSmqaDvuGf6ghEMCzLSpIygWowKlScylAJRUVABJJPEfW4ViqUjhrCIRi50KVKMCpONaiEosIv5LMl8sUSEBbQT3KEshgWIxjA/xS/SjAqVjpUQlHhhVBmS6JNeXk8HgwODsJkMiE5ORkMw0R72HGNQATj8XjgdrvBcRwmJiZQUFCgRjAqVjRUQlEhIdTZkmgilJmZGdTW1oJhGLjdbrAsi+TkZKSmpiI1NRVms3lJFtLljLB8CYZlWXR0dGDVqlVe6UU1glGx0qASigoAJ/W1QpktiYRQCCHo6+tDR0cHSktLkZeXBwCYn5/H1NQUpqam0N/fD0IIUlJSJIJJTEz8xHRKabVaAN6NEGKKTLVLVrESoBLKJxxiikvs4gplWC9cQnG73WhsbMTs7Cy2b9+OlJQUyQLYZDLBZDIhPz8fhBDYbDaJYHp6ekBRlEQuqampMBqNp+RCKv9OYgFfhJxgRFFN1c1SRTxCJZRPMCKVTwmHUKamplBXVwez2Yzq6mrodDqp/dh3GxRFwWw2w2w2o7CwEDzPY25uDlNTU5iYmEBnZyc0Go0XwRgMhrC/d7wtvIudy1AJRpXqV7HcUAnlEwp5VBLuAF4ohEIIQU9PD7q6urB69WoUFRWFvcDRNI3k5GQkJyejuLgYHMdhdnYWU1NTGBkZQVtbG/R6vRfB6PX6sPYRLwj3/IsEI/eCcbvdXlP8KsGoWGqohPIJQzBr3lCx2ByK2+1GfX097HY7qqqqkJycHNUxi2AYRiIOQChmz8zMYGpqCgMDA2hubobRaPQiGLEuEc+IpkFArkEm35ZKMCqWAyqhfILga80baddQsAjFarWirq4OKSkpqK6ujumCrtFokJ6ejvT0dABCO/L09LRUf2lsbITZbJbIJTk5GRqNcMvH2xyNUot7MIJxuVxS7UolGBWxgEoonwDIc+5KKAT7m0MhhKCrqws9PT2oqKhAQUHBki9QWq0WmZmZyMzMBAC4XC6pwN/W1gaXy4WkpCSYTCapGSEeZmBiSW6BpPoJIQsIRnWzVBEtVEI5xRGtb4k/+EYoTqcT9fX1cDqd2LlzJ5KSkqLavlLQ6/VYtWoVVq1aBeBki/LExAQIITh06NCyzMAsJxZzsxQ/QwgBwzAwGAyqVL+KkKESyimMWFnzygllcnIS9fX1SE9Px9atW6WUUjzCYDDAYDAgJSUFVqsVO3bskCKYgYEB8Dy/bDMwy7VYByKYkZERjI6OYtOmTV5S/aoXjIpgiN+nX0XEIITA7XbD7XbH5OEXi/Lt7e3o6+vD2rVrkZeXt6IWGIqi4mYGJp7qOXIBULHO4i+CUd0sVfiDSiinGMQUV1dXF2w2m/SGqSTEifrx8XHs2rULZrNZ0e0vB5ZqBibY/uMJ8iFX1c1SRahQCeUUgq81rzhjoiTGx8dRX18PANi9e3dURe1YHF84+w6GpZyBiacIRUSgaxOOm6VKMJ88qIRyCsB3tkR8Y1TSs0RMcQ0MDGDNmjVoaWk55QvYcsR6BibeFlue50NWTQjkZiknGDFFptoln9pQCWWFw3e2RJ4DV+rN1+FwoK6uDjzPo7q6GhqNBi0tLcsaYSw3QpmBSUxMlMglJSUlYMPCSopQFkOkbpYqwZwaUAllhcKfNa/8gVQqQhkdHUVjYyNyc3NRUVEhyc6Lx7ASEYuFy3cGxu12SwX+jo4OOJ3OBUOW8nRhvC2mSr0sqG6WnyyohLIC4Ttb4u/tLlpC4TgObW1tGB4exoYNG6RZDnF/4nGo8A+dTofs7GxkZ2cDEGZgxAimubkZLMsiKSlJSo3F27mMVfQZKsGoXjArEyqhrDCEOluymN5WMNjtdtTV1YGiKFRXV8NoNC7YtngsKkKDOAOTk5MDQoiXD4zVagXLsqirq4sbH5ilSmcGIhhRSRlQ7ZJXElRCWSEIxZpXjkhteoeHh9HU1ISCggKsWbPG74Mrf/hXKpbbsdFoNMJoNCIvLw9WqxXNzc1IS0uLGx8YsW14qbEYwXR3d6OgoAAmk0klmDiESigrAJHIp4Sb8uI4Di0tLRgbG8PmzZuRlZUV8LNqyktZiDWEgoICFBQUgOd52Gw2WK3WJZmB8YdQu7xiDV+CGRkZQW5urupmGadQCSXO4TtbEuqDEk6Xl81mQ21tLTQaDaqrq0NerCIlFPVh94bveaRpGklJSUhKSkJxcTF4npdalJfKByZeO/h4npfIAwjuZunbRaYi9lAJJU4hny0J1ZpXjlAiFEIIhoaG0NLSgqKiIpSXl4eUOlCiLXk5H/B4XFwWS1/KZ2A4jpMK/LHygVmulFcw+LNdkJuNAapd8nJDJZQ4BM/zYFk2KoXgxRZ8lmXR3NyMyclJnHbaaVK7q1LbVxE6wj2PDMMoNgMT7JjibdENxcdHTjByLxjVLnlpoBJKHGGx2ZJwECxCmZ2dRW1tLRISElBdXY2EhISwt68SirKIZkGLdgbGH+KRUMT7LdTIKZjZmOpmGRuohBInUMKaVw5/hEIIwcDAANra2lBSUoKysrKI93EqEEq8LJpKn0ffGRin0ykRTEtLC9xut5cPTFJS0oJFeqWkvMLBYgSjullGD5VQ4gDy2RJ5R0s08F3wPR4PmpqaMDU1ha1bt0rpkmi2H+kcCiEEY2Nj4Hke6enpS+77Ho+LQyyPKSEhATk5OX5nYAYHB8Hz/AKjsXjp8pJDPCaljssfwQRys1QJJjSohLKMCHe2JBzII5SZmRnU1tbCZDKhurpakY6gSOdcPB4PGhsbMT09DY1Gg+bmZikdk5aWFlI65lTDUkZ6vjMwhBDY7XaJYHp7e6WXGrF92WQyxcUCGmuSCyTVLxKMPEWmmo35h0ooy4RYWPPKIS74vb296OjoQFlZGUpKShR9uwt3IZydnUVNTQ1MJhOqqqrAMAw8Ho9XOsbj8Uhvy2lpaTCbzZ+Ih3W5viNFUUhMTERiYqLXDExzczMcDgc+/vjjBTMwCQkJy3K84kvXUiEYwcjNxlSCOQmVUJYBojnV6OgoKisrY3LzibWY3t5ebN++XWo5VQrhEAohBIODg2htbUVpaSlKS0ulLja577uYjrFarZiamkJ/fz8ALOvE+FIgnmpR4gyMwWBAeno6cnNzJR+Y0dHRJZmBCYSlJhRfBCOYDz74AEVFRUhLS/tEu1mqhLKEEFNcHo8HLpcLFoslJjfa1NQUamtrAQBVVVULtLiUQKiEIm9PXqx2I0/HiLa8c3NzXhPjWq1Wil6iXczipSgPxF9dRzw3NE0jJSUFKSkpKCkpAcdx0pDl4ODgghmYlJQU6HS6mBzTchOKL+QEw7IsNBqNlCoUI5hPmpulSihLBN8Ul0ajUVxckRCCnp4edHV1oaysDO3t7WHPH4SKUIry4gS+VquNqD2ZoiiviXH5YiYO9JlMJolgIpm3iAfEU4QiItDizTAM0tLSkJaWBkBYSKenp2G1WtHT0wO73R71DEwgxGPnmQiO4yRCAbwjGNFs7JNgl7zynr4VCDEqkc+WKO2o6HK50NDQALvdjqqqKpjNZrS3t8dssVosQhFFJgsLC7F69WpFFgL5YlZWVuZVf5HPW4jRS3Jyst/9xuPDG2/HFGr0ptFokJGRgYyMDADKzMAEQrxFKHL4O7ZAQpf+7JLFKf6V7mapEkoMEWy2hGEYxQjFarWirq4OKSkpqK6u9vLXiJXEfKAuL57n0dLSgtHR0UVFJqOFVqtFVlaWtA+n0ynVX4aGhsBxHFJSUiSCWW5J+ECIxwgl0nSgEjMwgRDPhCLaSQRDMIJhWVb6/Up2s1QJJUbwteb1vdmUiFAIIejq6kJPTw8qKipQUFAg3XhK6G0Fg79tOxwO1NbWgqIo7N69O2jtJhYPSEJCAnJzc5Gbm+vVDiumY0RNrKSkJMX3HS3ibcFQqr602AyMSPryGZhA+43H2RhAOC5CSNiRVyCC8edmefDgQaxfvx4VFRWx+AqKQSUUhSGXTwk2WxItoTidTtTX18PpdGLnzp1+F0ml02py+BLK+Pg46uvrkZubi8rKymV/k/TXDit2K42PjwMAPvjgAymFFsti8mI4lSKUYFhsBqavrw8AvAhGPgMTrxGK+IxFOz8VjGB++tOf4qtf/apKKJ8khDNbIi72kTy4k5OTqK+vR3p6OrZu3Rqw6Bnp8GEoEAmF53l0dHSgv78fGzZsQE5OTkz2Fy3k3Up5eXl47733UF5ejpmZGfT29sJmsyExMVFKj6WkpCzpgGW8vXkvRQHcl/TFrr6pqSlYLBZ0dXWBYRiJXMSaQ7xB/rwrCTnBiM0O8Q6VUBRCqNa8IuRvIaE+JDzPo7OzE319fVi7di3y8vKC/m008iiLgaIouN1ufPTRR/B4PNi9e3dYN3w8LAzp6elS/cXtdkv1l9bWVinXLxKM2WyO2QL7SYlQFoO8q6+oqMgrqhwbG8P09DRomkZzc7PXkOVyQ0zFxfL+sNvtMJvNMdm+klAJJUpEKp8i3nyhhvHz8/Ooq6sDy7IhL96xTHl5PB50dHRg1apVWLdu3YqSS/F3fXQ63YIBS7H+0t/fD0KItIilpaUpPmAZDwQrRzzUK3xnYLq7uzE9PQ29Xo+hoSG0trbCYDAsyQxMMIRSkI8WaoTyCUA08ilyQlkM4+PjaGhoQHZ2NtauXRvy4h2LCEVsBJibm0NOTg42btyo6PbjAf5y/WIqZnJyEl1dXdBoNFL0kpaWFvWAZbwhnoY+RVAUBYPBgLKyMgAnZ2BEDTIxbRmLGZhg4Hk+5i9UDocDJpMppvtQAiqhRIhIrXlFiIQikpE/8DyP9vZ2DAwMYP369cjNzQ17H0ouVm63G3V1dZifn5ce2EghFhxXAnxTMfIBS9Hx0mg0SgSTmpoa9kIWb4t3PBKKbzTvbwZGJJjOzk7Mz88rNgMTDLGOUHieVyOUUxW+syWRTrmKBbdAEYTD4UBdXR14nkd1dXVEbydKprxEORdx1qWhoWHFEEIgRHr8vtPiomOi1WpFV1eX10ImKigHW3Di8TyuBELxhU6nWzCXpNQMTDBwHBfTCMVutwOAWkM51eA7WxLtwFGgBX90dBSNjY3Izc1FRUVFxDerEnMocsXiNWvWoKioKOYzLisNvo6J4kJmtVrR1NQElmWlVti0tDS/A5bxtnjHo8xJuKklJWdglDyucOFwOABATXmdKlDSmlcO32l5juPQ1taG4eFhbNiwAatWrYpq+9FGKKJ3yczMDKqqqrxSXCqhBIbvQuZwOKQOst7eXmnAUiSYeDyP8RqhRGrGFu0MTDDEOuVlt9uh1WqXTNU5GqiEsgh8C+9KyiDIF3y73Y7a2lrQNI3q6mpFFIKjKcrLvUuqq6sXdM+sZEJZyoWSoiiYTCaYTCZpwFJUUB4bG0N7e7sktTE2NobU1NRlG7CUI14JRamFO9wZmNTUVBgMBr/nJNYRSjyZnC0GlVCCINzZknAhEooopFhQUIA1a9Yo9tBEUpT3513i73vHcsblVAZN00hOTkZycrIkB9/e3o7p6Wn09fWhqalJ6lQSJ/iXoyU7HtqGfRHLSfnFZmDa29uh0+kWGI0BsY9QREJZCVAJxQ9iac0rB0VR6O7uxuzsbEyEFMNNeYXrXbJSI5R4AsMwMJlM4DgOGzZskNR6rVYr2tra4HK5FjhYxrq2IV7XeCOUpazrBPOBEWdgEhISkJqaCo/HE9NjEVuG4+16+INKKD4QU1zHjx9HZWVlzOxObTYb5ufnAQDV1dUwGAyK7yOcKCJc75JoW5Lj4eGIF0KUH4evWq/cwXJwcBA8z3u9JcdioYlXQllOLa9APjBTU1OYmJiAx+PB0aNHvWZgIq33+MJut6sRykqEfLZkcnISHMfF5GEVZxe0Wi1KS0tjQiZA6It+JN4laoSiLALdZwaDAXl5eVIh2WazwWq1Snl+0e9dnIFRQopEvK7x2OUVLyQnn4ERm3bS0tIwNTWFrq4uOBwOrxmYaFKX4sDmSoBKKPCeLRHDapqmgw4dRgJ5SmnLli3o7u6O6aK8WMqL4zi0trZG5F2iEopyCPU8UhQFs9kMs9ks5flnZmZgtVoXSJGI9ZdI3pLVCCU88Dy/YAbG5XJJHWSiNlxSUpLXkGWo32WlTMkDKqGA53mwLLtAPoVhGEUJZXZ2FrW1tUhISJBSSr29vTEtbAdb9MPxLgm07WiOfTkXq3hbKCOFvP0YODlgKX9L9l3EQnlLls9ZxRPilVD8FeX1er2XNpx8yHJ4eBgsy3qJjyYmJgb8bmpRfgVgsdkSpRwVCSEYGBhAW1sbSkpKUFZWFhPXRn8IFKGMjY2hoaEhKu8StctLOSjVous7YOlyuaT6S3Nz84JFLNAgnxqhhIfF2oZFDTKDwSCZvzkcjpBnYFaK7ArwCSWUYNa8IpRIeXk8HjQ1NWFqaspv11SsF2Xf7cu1waL1Lokm5cXzPFpbWzE9PS0VOpWSwVBxEnq9fsGApdhB1tvbC4qivOov4pyFSijhIdy2YflsUn5+vlQbE69Nd3c3aJqWTPQsFosic2mB8JOf/AT//Oc/pZRpdXU1fvrTn0Zk5vWJIxT5bEkwD4NoU14zMzOora2VBgP9TbkuRYQiLg5OpxN1dXUReZcstu1wMD8/j9raWhBCsGrVKszMzKChocGreykW8vD+EC81oKUYIvRdxMQBS/mchV6vl9Iv4t/EE+JRDgaIXstLXhsrLCyUrs27776LZ599Fo2NjUhISIDNZsPZZ5+Ns88+G4WFhYod/zvvvINbb70VO3bsAMuy+N73vofzzjsPzc3NYafaPjGEEu5sSaSLPSEEfX196OjoQFlZGUpKShZ1bYwVaJqGx+ORHB4zMzMV8y6JJEKxWCyora1FdnY2KioqwHGc1xua1WqV5OG1Wq0UvcTL9PipBPmAZXFxMTiOk+ovQ0NDAICjR496OVguhRR8MMRrhKL0pLx4bS655BJccskluOmmm2A2m5GXl4ff/e53+Na3voXR0VHF9vnKK694/fejjz6KrKwsHDt2DHv37g1rW58IQonEtySSlJfb7UZjYyNmZ2exfft2qVgabB+xrkPMzMxgeHgYa9euRX5+vmLbDYdQCCHo6elBV1eXdBw8z3vJ2ci7l8QhMqvVKk2Pm81mr8UtHheWSBEPMicMwyA9PR3p6enIycnBRx99hJKSElitVnR0dMDpdCIpKUm6BsuRooxnQonlcTmdTuzZswe33XYbAKE2Fkv1hJmZGQCQZm7CwSlPKDzPw+12hz3xHm6EMjU1hbq6OiQlJfnVvvKHWLQmi3C73RgdHYXL5cLOnTuRlJSk6PZDJRSPx4OGhgbMzs6iqqoKycnJi/6N7xCZaM9rtVql4nJKSor0mXCH+5Z78faHeDom8VmRt8HKHSzFAUvxGsRqwNLfccXTeRKxFPL18hR1LEUieZ7HN77xDezZswcbNmwI++9PWUIRU1xiF1e48imhLvbyt+/Vq1dL8u6h7iMWsg2id4lWq0V6erriZAKERihzc3OoqamB0WgMmWT9wdeeV1SJFQuYonuiuLitBFVWOeTn0e0W/plMwHKtnf4iJt8uJXkRWT5gKdbAlPZ6Fw3Z4jFCWQq14aXq8rr11lvR2NiI9957L6K/PyUJJRprXhGhFOVdLhcaGhpgt9tDfvuWQ+kIxde7hBCC6elpxbYvx2IdauL0fXFxMcrLyxV7s/RViZUP9w0MDKC5uTkuxBXDxeysBj/7mQ6vvsrA7aawbh2Hm27yoKpq6VuzF0vB+SsiizpXIyMjaGtrQ0JCgpeDZbQyJOK9Fo+EEmu14aWSXvnqV7+KF154Ae+++27E6fFTjlDkUUk0UvOLpbwsFgvq6+uRmpqK6urqiB4YJWso/rxL+vv7Y1ajCdTlxfM82traMDQ0FBPBS3/HIS5aZWVl8Hg8UnqstbUVHo9Hmr0Qza1ExEuXl8dD4f7789HcrEFiIqDVAocPa9DSwuBnP3Ni69alJZVwazq+A5aizpXVakVPTw8aGxu9amCRWPHGK6GImZBYHZcYkcfSrZEQgq997Wt45pln8Pbbb6OkpCTibZ0yhBLKbEk4oGkabrfb7366urrQ09ODiooKFBQURLwfpQglkHdJLOdc/KW8nE4namtrwXGcYp4u4UKr1UriiqJLn0gwcnMrQIgw4yE9duyYCY2NJuTnE4iybqmpBD09FP76Vy22bnUt6fFE2yTg6/UuypBYrVa0tLRIJC9XUF5sf/GqLyYeV6wdG2OZ8rr11lvxxBNP4Nlnn4XZbMbo6CgAIDk5OWydwVOCUHyteZW46fxFKOKgkdPpVKTQHe0cymLeJdEqAgeDL6FYrVbU1tYiIyMD69evj4s0k9ylT+wsm52dhcViAQB8/PHHMBqNUvSyXK2xfX16EEJB/uxSFGA2A3V1S7+AKl2r8JUhkU+J9/f3A4BX/cWfkVW8ysGIKeuVnPJ66KGHAAD79u3z+vkjjzyCm266KaxtrWhCkcunKO1b4ltDEWc5MjIysHXrVkUWnmgilFC8S2LZliwSinzuJtqILdYQPS6Sk5PR19eHnTt3Sva8Ymus+Oacnp4escd4uDAaORAC8DwgX8ddLiA3d+nTcrHspvI3JS46WE5MTKCjo0MyspI3WcTSlygaxDoVx3Ec5ufnYxqhKPnSuWIJRYnCezCIBXOe59HZ2Ym+vj6sXbsWeXl5MbEADgehepfEUhFYTKfV1dVhenoaO3bs8PKcXwnQaDRe2lfy9NjAwAAASAub+OYcC1RVzeHppzMxOKhFXh4BTQMzMwDLApdeysZkn8GwlHMxcqdEccDSt8nCZDJJCyrLsss+YClHrNxcRdhsNgCIaQ1FScTPlQkDsbbmBYQIxePx4MMPPwTLsorIlfgiEkIJx7sklhGKy+WCzWaDRqPB7t2746IWES18vUdmZ2e9vN/FzqVopOH9ISPDjS9/eRSPPVaM/n7qxLEAn/oUiyuvPLUJxRe+M0gej0eSh+F5HocOHZIUlONBAy7WLcMOhwMAVHHIWECMStxut+RZEss3g9nZWeTl5WHt2rUxyZGGs+BH4l0Sq6L86Ogo2trawDAMtm/fHneF0lARLHqjKMrL+13eudTV1YX5+Xmpc0mJhW3XLhsOHJjHkSMaOBzAhg081q7ll2UWJR4m90VotVpkZWVBp9NhdnYWW7duleovogacqNIbyZBrtFiKlmG9Xh9XUVkwrIyjxEkyaW9vx/z8PDZu3BiTG0dsex0YGIBOp4toWjRUhDqHEql3idJFeZ7n0dHRgYGBARQXF2NsbGzFkkm48O1ccjqdUnpsaGhIEreUp8dCvT/Fa5SeDlx88dJHJL6IJ0IRIdZQfAcs7Xa7JNHf09MjdfHJFZRjiVhPyYteKPF2PQJhRRCK3JpX7IyKxQl2OByoq6sDz/NYv349urq6FN+HHKEs+NF4lyiZ8nK5XKirq4Pb7cauXbvgcrmk9sKVBiXunYSEBOTm5iI3NxezswRDQ/NgmEmpsCwq94oEEyw9Fm8LeDxqZvnrPJMPuYoDlmKaUj5gKScYpdKUImJ9rlaSnzwQ54TiO1tC0zQ0Gk1M9K9GR0fR2NiI3NxcVFRUYHZ2NmY6WyKCRShKeJcoFaFMT0+jpqYGqampUoeb2+2Om8HA5YLDAfzylzr8618azM8nIjU1A9df78GNNzoxOzstzb7IxS3T0tLCsn9dDsQbwQGhLdxiF5/YHCKmKcXoRRywFAkmkgFLXyyFjpcaoSgA39kScVCRYRiJYJQAx3Foa2vD8PAwNmzYgFWrVgGIvVcJEDiCUMq7JNoaitxt0lenTPWUB374Qz2efVaDhATAYCCYmKBw3306cBxwyy3pUiu3fLCvqakJLMt6vTXHcgGfmwOGh2no9QSFhQSh8NhKJRRfBBqwnJqaQktLC9xu9wIHy3D3sRQ6XmqEEgVCseZVKnKw2+2ora0FTdMLJrtjqQQs3wfP814PsJLeJdGkvDiOQ1NTEywWC7Zt27ZAyvpUIJRojr+zk8LBgxqYzQTifKvRKJDK449rcf31HojrgO9gn5j3t1gsUlrVaDTCYDAgLS1NEe8XQoA33mDw6qsaWCwUtFqC8nIe117LIj8/+PcW70eWBd58k8F77wn6YlVVHM4/n8VyrG9KpLl9r4PYJi4fsJQrKIdi8hbrorzNZlsxHV5AnBGK72yJP/kUpQhFbL8tKCjAmjVrFrxliBFKLN/WxBtRXNhESRelvEsiXfQdDgdqamqklmB/cy6fVE95jgP6+ykcPcrAbgdyc71/n5hIMDNDYWiIxpo1C8+Pb96f4zjU19dL0aAobilPj0WyYH34IY0nn9RArweKi3m4XEB9PQOHg8K3v+1GsFq1oE9F4b/+S4cXX9SAZSkABK+8wuCVVxj87GcuLPVYhNK1Cl8VBXHAcmpqChMTE+js7IRWq/Wa4PfXGr8UbcPLIWEUKeKGUEKdLYm2hsJxHFpaWjA2Nha0/VZ8iGP5BiLeiE6nE01NTZifn1fUu8RfBLQYxsfHUV9fj7y8PFRUVAR8WGIp6xKvePttBr/6lQ59fRRcLmBujsLsLIF8ntPlAnQ6grS00M4NwzDQ6XQwmUwoLi6G2+32q3slF7cM5VoeOsSA5ykUFAikptMBq1fz6Oqi0dhIY8eOwC8DhBDU1aXgpZc0SEkhMJtFG2ngww81ePZZDtdfv7TdaLEufssHLOUmb1NTUxgcHERLSwtMJpNEMKmpqdBoNEvSNqxGKGEgEmveSAllbm4OdXV10oR5sJZC8eaNZdFN3MfRo0eRkpKC6upqRfvNxfMYCqEQQtDZ2Yne3t6QmgCUSHktZ54+3H0fP07ju9/Vw2ajkJrKQ6cDRkeB/n4aWi0Po1Eo0ttsFK64gkVGRnjnRjwenU7nJW4pSsNMTU1J4pYiuQR6ayYEGBujkJTkfQw6nfC76enF0zgNDclwuymJTAAgIQFgGIK339accoTiC/mApahi7W8OCYCXNIzSUFNeYSAS+ZRICIUQgqGhIbS0tKCoqAjl5eWLXnx5hBILEEKkvG1BQQHKysoUX2DF77jYwu92u1FXV4f5+Xns2rUrJJkHJQhF/Pt4KwD7w5NPajE7S6Gw8OSwYWUlh9ZWBmNjFHQ6YcHdt4/Dd74TnjpwoPMo170SvV/EtljxfhbfmsW8P8MwoCggP5+gtpbGqlUnt+10Clphi5GdcDyBr0mgR6K7m8JHHzFwOimUl/PYsYODAuWgE/tc3lZmrVbrJdPjdDoxNTWFvr4+2Gw2vPvuu171l1AjycXgcDjUonwokM+WRGLNG+oNxrKsVFzesmWL1PGxGCiKillhXu5dAgC5ubkxWVTF8xMsLJ+ZmUFNTQ2Sk5PDipBOhaJ8OGhtpZGQQLwm1xMThcV5714WBw5wKCnhsXlzZNPtoVx/eVtsaWmpJEtitVrR3t4Ol8slpce2bctGS0sKurspZGURuN0UhocpbNjAY9264C9JhBBs3GjH228T2GzC9wSEdB7LUjjzzIXPxIsvavDII1pMTQlKyRoNUFXF4VvfcitSb4k3t8aEhATk5ORgenpaskoWr4V8wFKuoBwJ7HZ7RCMDy4VlIRRxviQSBVFxYQylGDY7O4va2lokJCQEFVEMhFgQiq93yTvvvBOzbrLFIpSBgQG0traivLwcxcXFYfuyi2rDKyHC8IdwCDE/n0d3twbAyb/heWHx3LqVx6c/HXkKKFJiFmVJxDqgKAtvtVrB8/3YvDkV9fWF6OtLRGKiDmecQePyy1ksJrtGCMGOHTbs38/h4EEGk5PC9+R5Clu3cvjUp7xtqwcGKDz6qBYsS7B2rUC6djtw+DCDF1/U4Jprok+PLXeEEghiStzXRVRUUB4dHUV7ezv0er2Xg2WonXxqDSUEiG//kSxGckIJNPUqn58oKSmJOJ2k5CxKIO+SWEvMAwvTdmJjwvj4eEDp+1C3HSnsdjv6+/uRlJS06CR5POCyy1gcOaLB+DiF9HQCjhPqFGlpBAcORL9gKkHKYtdSXl4eeJ7H5s1zOOecKXR2DsDlmsGqVTSs1jQAaVJR2R8IIdBqgf/6LxdOP12Dt99m4PEAu3ZxuOgiFr5O18eOMZiaAiorT0ZwJpPQRv3224xihBKPLy7+on+aphfowIkKyn19fWhqapI6+VJTU4PaVKuEEiIidVQURSEDvdWL6aTp6Wm/8xPhQKkW5WDeJbEmFN/2Xl9dsEhD8VDSaYEgdpKlpKTAYrGgublZIhZRaDHeFo9zz+UwOOjGww9rMTREg6aBvDwed9zhRlGRMrUkJSFf1NasEe5BcahPLCrLz7l8qE9ML+n1wCWXsLjkkuCE4PEIEYzvJdNoAJdLmevI83xcvnSEkinRaDRITz856Crv5Gtra5NSlXIHS3Gb6mDjEiDQQj8zM4Pa2lqYTCbs2bMn6gExJVJei3mXxHoiX17rmJiYQH19PXJycsLWBfO3XSC8xdC3kyw1NRUURcHlckmDfqIPibjQpaenx0QaP1zCoijg3/7Ng0svZVFbS0OnA7Zv56DUiECsCdTX+0Uubjk4OOglbunxeMI65xUVPPR6YHoaUgs1xwHT0zTOOccT7E9DRrymvCJ5ofLt5Jufn5fIfmBgAIQQtLe3w2KxgGXZmEYo7777Lu69914cO3YMIyMjeOaZZ3DZZZdFvL1ljVAihS+hyF0Dy8rKUFJSosgDGu1iLw5PBussi2WEIm6f4zh0dXWhu7sb69atQ15eXtTbDZdQPB4PGhoaMDc3h127diExMRFutxuAt9CimH+2WCwYHh5Ga2srTCaTlw/JctoLZ2QQ7N+vbM1rOZob5Odc7po4Pj6O6elpaDQasCwbkqjihg08zjmHxSuvaGCxAFotgc1Go6SEWzS6CRXxSijRDjbKByxFHx6bzYbu7m4cPHgQNTU1+OpXv4qXXnoJ+/fvxznnnKPI0LMIu92OzZs349/+7d9w+eWXR729FRuhiHpebrdbWqi2b9+O1NRUxfYTaYQSjndJrAkFAFpaWuB0OhUdmgyHUGw2G2pqamAwGLB7927odLqAfydP1cg7mSwWC1pbW+HxeKT2zPT09JDkMQIhkoWcEOHtW2l7iuWeyZG7JjY2Nkq6eXJRxUDiljQN3HqrBxUVPN55R4O5OWDrVg8OHFhc5iVUxCuhKD3YSFEUzGYzPv/5z+Omm27CunXrcPvtt8NiseChhx7Cyy+/jCeffFKx/V1wwQW44IILFNveiiUUjuMwNTWFuro6JCUlobq6WhENJH/7CQfyGsViw5NAbAlldnYWLMuCEILq6mpFc9ChEooovy86TIa7cMo7mcRBP4vFAqvViu7ubmi1WolcYiFPLoLjgPffZ3D4MIPpaWEC/cwzOWzYEP21iyZCcbuBmRkKRiNRTGNLnH8pLi4GACklKYpbchwnkXpaWhqMRiN0OgoXXsjhwgtj07EYb23DImKtNjw/P489e/agqqoKP/7xj+Ne7mhFprxomsbIyAgmJycXqOAqiXBTXpF4l8SKUIaGhtDc3AyNRoPVq1crvtAuRijyesnGjRslFedo9ykO+ok6WOL0ck9Pj5dMfHp6ekTqsYHwwgsaPP+8BjqdsHDX1DBob6dx000ebNkS/fUL9/4lBDhyhMG77zKwWgXL4O3bOezfzwXV6Qpt297dl3q9Hjk5OcjJyfErbilqXokEo/SLHRC/EcpSqA3LB43j8RzIseIiFJfLBbvdDrvdjqqqKiT79jAqiFBTXtF4lyg968LzPFpbWzEyMoLTTjsNLS0tim1bjkAtyYBQL6mvr4fdbg958j4SMAzj1T3jW2gGgNTUVKSnpyMtLS3sOSQRExMU3nmHQWoqQXa2QKDZ2QTt7TQOHtRg0yY3onlJDTVCmZkRpF4AYHKSwr/+pZF0w+x2Ci++qIHdTkXdphssGvAnbim2xPb39ysmbumLldQ2rBRYloXL5VLbhmMFi8WC+vp6MAyD/Pz8mJIJEFqEIvcuqa6uDrvFT8kIxel0oqamBoQQySq4ra0tpm3JvouhzWbD8ePHYTQasXv37iVt9fQtNPu69xkMBolcwsHQEIXpaQpr13qfx6wsHsPDFKanBfveaLDYYvnBBwyefZbB+DgFjUYglqwsHjt2COffbCbQ6wlqamjs3UshN3dxkrLbgaNHGUxMCNP0O3cKXWvhzIfJNa8AoaYpao+J4pby9FikZlHxGKGIVhuxOi6bzQYAMXshiwVWBKEQQiRp94qKCkxPTy/JfheLHpTwLlGKUCwWC+rq6pCVlYW1a9dKxxLLGo2v4nC09RIlQVGU13CZXKaktbUVPM+jpaUFWVlZiy50BoPQueRyCXpdIlyukxpe0WCxCKWpicIvf6mF1UrBZBJMskZHAZeLxurVvNSqm5oKjIxQsFgWJ5SeHgo/+YkOnZ00CKFA0wRr1ghzNdFEAzqdzstzRBS3FNOSDMN4pcdCbU+OR0IRn6tYRSh2ux0A1DmUUBDqDet0OlFfXw+XyyV1KdlstpibXwHe3WRyyAkuWu+SaBd8Qgh6enrQ1dWFyspKFBQUeP0+lppbcvkVpeslSsO3uP/OO+8gJSUFU1NTXsV9fx7wpaU8SksJ2tqEBVyrFd7ux8cpXHihMoZTwZ6Hv/9di74+CiUlBFqtkN7iOAqTk8DoKI2UFOH+sdkE8ktMDH69eR749a91aG+nUVpKoNMRuN1AczODhx7S4sorlZHT8SduKabH5OKWobSExyOhyEVtYwG73Q6DwRBzA6/Ozk7pv3t6elBbW4u0tDQUFhaGvb24jlAmJibQ0NCAjIwMycscUNa1MRgYhpFmJUTIlXmVaMONZtaFZVk0NDRgZmYmYD0p1pP4Ho8Hx48fj3m9REmICgKrVq1CYmKiVx1A9ID3ndy/+moPHn9ci64uGjwvRCxVVRwuuCD6OYtghD85SaGzU5CiNxqFz6WkEGRkEPT1URgfp7BmjUBwfX00tmzhF53c7+qi0NpKIy+PSGrAOh2Qm8ujsZHB6afrkZMTG7FSUcsKgFfUKJ8Yl0/vy2t1nzRCsdlsMfeT//jjj3HWWWdJ/33bbbcBAG688UY8+uijYW8vLgmF53l0dHSgv7/fbwTAMAxcrvAkwiOBb8pramoKtbW1inqXRLrgi7UKg8EQtGU61nMu9fX1SExMXPJ6iZKQ1wHKy8u9JveHhoZACEFqaiquvTYd4+OZ8HgSkJUlpIiUenkMtGjMzYkpNQo8f9ITPieHx+QkA4YRmgMSEoQur09/ml3UN35+noLHgwXS8jqd0IZ85Egq/vWvbLhcCdi2jcMVVyg3TyKHb9QoWvKKmlciAaWlpcUloYgF+Vgt+Ha7PeZujfv27VM0gxF3Ka/5+XnU1dWBZVns3r3bb4fDUkYoHMeBEILe3l50dnYq3qYcSZfXyMgIGhsbUVRUtGitIlYpr7GxMXg8HmRmZmLjxo1x2YETKXzbZMXJfat1BC5X24k0RBqmpk56kESDYNfHZBJSbrOzgq1wSgoPQoRU17p1HH74QzcIEWorBQXe8vqBUFzMIz2dYGKC8iKK8XEKViuFf/wjHwyjRUICjePHGbz2mga//KUTZWWxm+j3teSVK/aOjIxIGn0ZGRlejonLiaVoGVbKV2WpsKxXxHexGx8fR0NDA7Kzs70Ky76I1gY4VIg1lNraWszMzGDHjh1Ikfu9KgCapuHxhKZ3xPM82traMDQ0tOgEvnz7SkYo8nqJVqtFfn5+xDf8cnqqhHrM8ilyUTnW14NEPrkfaYoi0N9kZhKcdhqPmRnAaqUxNUXB5RKK7jfd5EFlJYFcUj8UJCUBV17J4ne/06Kri0JiIjA7S8HjEeozRiOLrCyhwM5xBH19NP74Ry3uuce9+MYVgq9i71tvvYXCwkLY7XZ0dnbC6XQGFLdcKiyF/e9KKsgDcZLyEhfKwcFBrF+/Hrm5uUE/v1QRisvlwszMDNLS0mIyiQ+EvuC7XC7U1tbC4/Fg9+7dId9oSi7avvMlYovyqYKGBhp//7sGdXXCzMmFF7K47DLWKzUkF1mUp2ksFgt6e3u90mehDvkFO4cUBZx5JgeNBmhrA2ZnBcOrqiouqC/8Yvj0p1kkJxO89JIGAwMUtm7lodUSPP88hcREDwAhfckwQkvy++9rwLJuxSVnQoHY+JGeni6lv0VBRavVKgmKyp0rY50qApYuQllJWHZCEaVKAIQ8xxFrQhG9S8Qp4G3btsUs7AyFUMTaTXp6OrZv3x7WW5FSEYq/+ZKV7tooP/aaGsEzfnJSKIBPTNBobtaho4PG977n9ptK8pemmZmZgcVikYb85JP7SUlJQQcGA8FkAs47j8P27RycTuH4ol1nKAo45xwO55zDgRDhv//yFw2ef56Sfi+CEMFLfrlKGOJ1kp87g8EAg8GwQNxybGzMy9AqFHHLSLEUEcpSEKOSWFZCEWsB4UiVAIHbeZWA3LukvLwcQ0NDMc1hBquhyFWU16xZg8LCwghk16mQCEVcW/1tfmxsDPX19QtqNiudUEQQAjz2mBYWi+CFLnw9gqkpCq++qsGnP80uapsLLOxikmtgNTQ0SBLx4nClqPMW6jkUZgeVP9/iNd+9m4PZTDA1pZNk+d1uwGajcNllixf7YwXx/g1GxnJxS5ZlMT09jampKUncUkyPpaamLhC3jBRqhLIQy0YohBCMjo5iw4YNYc8txCpC8fUucTgc6O/vV3w/cgSKIFiWRWNjI6ampqJSUfYdPvTF2Bjwyis0PvyQBk0TnH46wfnnC8Nyi82XnCqEMj8PNDXRSE31LmqnpBBYrRSam+mQCMUXvsV9m80Gi8WCsbExHDo0iPb2VSAkGSZTGlJTgRNWJcuG0lKCL37Rg5/9DOjv14JhaFAUsGEDh89/Xhlfk0iwGKH4QqPRICMjAxkZGQC8iX1oaAg8zy8Qt4zkpTHWwpAqoYQBiqKwdevWiNIxsSjK+/MucblcMVf39DeHYrfbUVNTA51Oh+rq6qgMpoKlvCwW4N57GbS0UEhNFTzDH3uMQlMThdtvd6KzM7ge16lCKBoNpGFFOcTTFq3YInBSltxsNqO/vwxPPaXB2BgPjmPh8Zhw6JANX/5yE9auFXSwounu4TiguZlGTw8NnY5g82YeOTmhXacbb/SAkAYMDa2H252A9et5HDiw0PZ3KeEv5RUO/BG71WrF5OSklNaWp8dCrZWqRfmFWPYaSiRQMkIJ5l2itHCjP/gu+KJ8SUFBAVavXh11SB0s5fXuuzRaWymsW0ekYqvTCRw7xuHRR9tw+ukIOl+ykglFvljrdMB557F47DEtkpMJDAaBTAYHaWRmEuzapVx6dXYW+N3vtLDbKWzcSIGiGIyMzGF8PBPvvGNAbm57xMV9QLh+v/+9FocPM3C7hdmVjAyCG25gsXfv4vcyRQGrV8/giitsSEqKj7kPUQpGqel9kdiLioq8hlpFv3ez2SwV+FNSUgI+g0uR8orGwnw5sOxtw5GAYRhFhNkW8y6JtT0vcJJQ5MOcSsqXBCPFpiYKBoO3WRTH2TE15YLNtgpbt6YHvUZLYQ62VPjc5zxoaxPmLjhOqKtkZBB885vuqIUf5aivZzA6SqG09GR6TaMhyMzk0d6eisLCTdiwgV+g4BvM4EqOt95i8PbbGuTn80hKIiAE6Ouj8PjjGqxZwyM7m2B4mMLQkCAyWVLCwzebGm/KvrEcagwkbmm1WtHc3AyWZQOKWy5FhKKmvJYA4kWM5g0hFO8SpYgrGMQF/+OPP4bL5Qo4zBnN9gPNuSQmEng8oq+J0E02OzsLkykXxcUaUFRwsljJEQrgXQxPTQUeeMCFI0cEn5OkJIK9e7mQVHvDAcsK0Y/3ek1A0xR4XkhXyYv7ZWVlXoucaHAlF1iUdwK99x6DhAQCURGIooCiIoKmJgrHjws1kQ8/ZGC3CweQns7jwAEOmzefvNbhqA0vBZaS4HzFLe12u9Se3N3dDY1GI6XG3G73knqhrASseEIJtx0wHO8S8WaJZWjrcDgwPz+PpKQkL70ypRAs5VVVRXDoEDA2RsDz4/B4PKCofKSna5CVxaG/Hygo8N/5JW47WkKJp8VLrwf27eOwb1/s0pzr1vFITwfGxk4qAhMCTE7SOOMMDmKGw+MBBgcpeDwUsrO9FzmxBjA+Po6Ojg4kJCRI5GKz5S6QVKEo4Vp1dtIYGaGQkUFQWEjA88DAAIWXXtIgN9eDzEzxeOLnmgDLp+Ml937xFbccHBzE3Nyc1D6/mLhlJHA4HGrbcDiIZsKapumwW4fD9S4Rb45YpHUIIRgYGEBraytomsbmzZtj8hAH6/LauZPg/PMd+Pvf7XC7jUhMNINlKdhsFL77XQ1oGti4keDb3+ZOTGR7Y6VHKMuBrCyCq67y4NFHtWhvp6DXA+PjiSgq4nHddUIabGCAwssva04QCpCWRrB7N4/qag407V0DEFtkrVYrOjs7YTDMoqGhECYTB5PJAK1Wi7k5Cno9gcMh+L+LpEXTQGEhQXMzjc5OGpmZApGqhOIfvpFjY2MjAKEjUxS3lKfHopVNUSOUJUS4hflIvEvEQqDShXmO49DU1ITJyUmsXbsW7e3tyzI4OTExiuLiBnznO2swP1+M/n6Chx+mMT8vtLByHHD4MIV//3cNHn/cA1+ll2gIxe12o62tDTqdDhkZGV7KsrEGIUB7ezI+/tgEm02H0lIee/ZwKC5e/LtwnGBK9cEHNGw2wXRr715OcnIMBVdeyaKggOCNNwRzq/Xrh3HddcnYsMEMux147jkNRkYoFBURaLWCxtZrrzFITibYuNH7Wvq2yGZkuDA5SaGlRYOEhBlwHA1CErB3rwcmkxFut3dET1EATQvy9cK5ISqhhIGkpCQUFhYuELfs7e31EreMxDFUVBteSTjlCSUa7xIxElKSUBwOB2pqasAwDKqrq8GybEwL2/4WfUIIOjo60NfXh82bNyE7OxsAwZ130nA4gJKSk2muxESgvx946SUaN93EL9h2JMc+NzcnTd17PB4MDg5KaQNxqjwWMjciXn2VwXPPFcNs1iE5mUJ7uwbHjjG46CIPcnIEe9/09IUEQQjw179q8MILGhAidIfV1jI4epTBbbe5Q663UJQwRLh7t3BfHT7cj+LitQCAri4aQ0MUVq8mkpLxqlUEnZ0U6uroBYTii9Wr9fjhDym8/roGtbVGaLUurFs3iYqKfhw5okNHRwG0WoKkJBMMBgOcThoMA4kQo23RjQXilVDkcyj+VBNEx9Dh4WHJMVTu/RIsvS2ak6kRShiI5i0olFkUJbxLlOz0mpiYQH19PXJzc1FRUQGapuFwOGLamuwboXg8HtTV1cHhcCxoAGhtpZCQ4F0zYRiAEAp9fQuvVSQRyujoKBoaGlBSUoKCggLp70VF38HBQbS0tMBsNkt+8UoK/1kswKuvaqDXs1izhoVez2BujuCttxjU1emRkUHAccDGjTy++EWP1/xGdzeFgwc1SEsTWnEBceaDwauvaiIe/pNHBA4HdULqxPszJhMwNRXa81JQQKRjsdkozM9nITk5E6WlHjidHDo6OOj1Vng8AMsasX07kJOjASEG6XrEU4QSzON+ORGstkrTNFJSUpCSkoLS0lJ4PB4pNdnR0bFA3DIpKWnBOVelV5YQi0UoSnmXKBGhyCfOfcUvxRsyVm9h8kV/bm4ONTU1MJlMfudL8vMJWlq8b2qBiwiysqKrocgjxU2bNiErKwsej0daLERl2dLSUrjdbnR0TOOVV1iMjVmQnT2A3bsprFoVnm2sP/T10bBaKaSluU508AlT8vPzwMQEhYkJCm43hZoaBkeOMPjBD9yorhauf2cnDbtdqDuIYBihU+r4cRo33oiI5UnExSQ1VYhMnE5va+HZWWDNmtDJ224XWohrahg4nUB6OsGePTRuvpng449ptLSkAHChqMiK/PwhHD9uhV6vlxQZlkJ8NVTEa4QSTtuwVquVREUBeKXHfMUt9Xo90tPTl6SG8uCDD+Lee++V5vB+9atfoaqqKuLtnXKEorR3SbRDlG63G/X19XA4HH4nzuWF/1g8NGKEIkYGxcXFKC8v93tOLruMx7vv0hgZEWooPA+MjADp6cCBAwujtMVkXUSIzpKzs7PSOQj2d7W1CXjggUKMjtKgKAJCONTVzeHqq1sAtCAxMVHSwwpXl0mjERZ9nhe+v9UqeIBwnPA2n57OIzOTYG6OwuAgjd/8RouKCsE/RIjWIIkpiuA4YbuR3mbyc1FayqOigkdDA43sbMEZcnxcaGPesiW0+5AQoQ5z5Iigmjw7S+Hjj2m88IIGV1/twQ03sLjgAg4URYOiMgBkgOM4TE1NYXJyEgDwwQcfICkpSTrPS1nj8kW8zcWIiKb702AwIC8vD3l5eQvELb/xjW9gbGwMWVlZOHToELKzsxW3zQCAv/3tb7jtttvw29/+Fjt37sTPf/5znH/++WhrawvJGsMflpX2o13ofbu8PB4Pamtr0dfXhx07dqC4uDjqGzGalNfMzAyOHDkCmqaxe/duv28b8gglFqAoCg6HA42Njdi0aVNQQ659+whuu41DYiIwOAiMjgptwz/+MYuSEv/bXoxQHA4Hjh49KsnuL/bGNTcH/OpXOkxM0Cgv57FmDUFhIY3W1lS0tOzA6aefjsLCQrhcLjQ2NuLQoUNoaGjA8PAwnE7noudj9Woe+fk8RkaM4HlB/NDlErxGjEYiiSLqdIDJRDA6KizGALBhg0AsQ0OUJKbpdAIzMxSqq7mICWV2VoveXg2cTkEC5lOfYrFvHweeF/xJVq/mcPnlnpCaBgCh3bi+nkZuLo/mZhqvvsqgqYlBczON//kfPe66Swen0ze1ySAjIwOlpaUAgKqqKqxatUqKat977z00NTVhZGRkSdxS5TgVIpRgEMUti4uLsXXrVjz77LO44447YLfbcd999yEjIwO7d+/GSy+9pMBRn8T999+Pm2++GZ///Oexbt06/Pa3v4XRaMQf//jHiLd5ykQos7OzUjpHSe+SSFNeYi2grKwMJSUlARfxWBKKx+NBd3e31Ca92MAkRQE33MDjoot41NZS0GqBbdtOLrIixMG8xQjFarWipqYGOTk5C4ZHA52PmhoGw8MUiotP2usaDEIq6J13GPzbv3nPZMhd/dra2mA0GqW3an+yGQYDcPXVLHp6PGhv18LtpuBwUNBoCJKSTn4Xl0vwAaFpwTIXEIrjV13F4okntGhqEqInmga2beNx3nnhy7NMTwP33afDv/61EzRtQGYmhc99zoMbbvDgwguFeRi3WzDECmc9nZoSvpPHA3z0EQOPh4JOJ8jrOJ3AM89ocdppPK67buExi9fTaDTCZDIhLy/Pq8A8NDSElhYhSpQXmGO54McrocRKHDI1NRVnn302vv71r2NiYgKjo6M4ePBgxFGDP7jdbhw7dgx33HGH9DOaprF//34cOXIk4u2uWEIRi/Kid0lraytKS0tRWlqqaHgcboTCcRxaWlowNjaGLVu2SO2cgSC2JitNKOKbpVarhcFgCGv6Pi0NOPvshUTR0kLhlVcotLcLyrw5OSnYvNmFkhIsMF7q7+9HW1sbKisrUVBQ4Hc//q7T/LyQjtJovPev0xGwLAWX66RYo69sucfjwdTUFCwWC5qbm6WJcl+5+A0beFx7bRd43gRCEnHsGI3XXmNgtdIwmXi4XMJxmc0EhFAoKzt5bfbv51BayqOujoHDARQXE2zdyoUtIMnzwLe/rcc772jAMG4kJgqprXvv1UGjIfjsZ1kYjVhA5qHAZCLQ64G6OhpOJ5CUJBCfxyN07bndwPPPa/wSir/70F+B2VeexHdyX8lnMF4JJZbHJQpD0jSN/Px8fP7zn1d0+5OTk+A47kSH50lkZ2ejtbU14u2uWEJhGAYejwcNDQ2YnJzE1q1bka6k6NIJhBOhzM/Po6amJqA2WLB9KEko8npJamoqmpubo95mQwOFn/+cgdUqSLbU1VEYHs5HZqYH+/czuOgiHnv2EBDCS4Qaiez+mjU8zGYCi4WSOqkIASYmaOzYEVz1VqvVIisrC1lZWQvk4tvb22EwGGS1Fzc2bnQhOTkBZ58NZGVp8Yc/aDE6SiEpSUx30di2jUN+vve1KS0lKC0NLyKx2YD332fQ2EhDpwPMZuCDDzRITyfgOA+MRj3MZiHF9thjWlx1FYtIPaGKiwlWr+bw+us6ECJENywr1HqSkoQC/9iY/wVf7DgLRgharRbZ2dnIzs6W5Enk6r06nc5L2DJa9Yd4JZRYyteLhBKPtaNgWLFtwxzHYXR0FGazGdXV1WEPDYWKUCOUyclJ1NXVYdWqVVi7dm1YD4BShEIIkWRlNm0S5kusVqsC8ijACy/QmJoC1q4VuoSmpwGdjsfMDIOmJgoDAwwoygmN5hg4jsPu3btDJlQ5iosJDhxg8fTTGszOUjAahdRQWhrB1VezIdcp5KqyoumSGL20trae6CTrwKpVq5CWloZbbzWiuprDc89p8O67DPr7hfmMjz5icMMNBnzpSx5cfHFkqsOzs8DPfqbD8eMMGEaITiYnKVitQFaWUDcSkZhIMDFBYXKSClly3hcMA1x+OYs332QwOKiF3U6g0wlkotUScBwVsB4T7lCjXJ6ksLAQHMdJ7bHd3d1oamqS2mPFFvBwn/t4bBvmeT6mxxXrluGMjAwwDIOxsTGvn4+NjUUlTLvsEUokswzDw8MYGhqCyWTCjh07YnqzLdblRQhBd3c3uru7gw5O8rywsJhMWPDmqURrsthNNj8/j127dkkpLiXIymYDurooZGUJLoZjY0BKCuBwEAwNaXH8OA2O49Hc7MJddyXhoovWRPzmRlHAF7/oQWEhwauvMrBYKGzfzuNTn2IXHeoLBl8v+Pfeew9msxkTExOSHlZ6ejrOPnsV3n47G5mZgocIRQEjIxTuv1+LggLeS0QxVLz9tjA4WVrKS63AbW0UOjs1mJ4mXjMnTicFk8m7nhMJ0tOBn/zEjauuYjA2JigLc5xQX0lNBa65xv/MTLRT8gzDSPNDq1evhtPphNVqhcVikdpj5QOsobSAx2OEIj5TsYpQxCn5WEUoOp0O27ZtwxtvvIHLLrsMgPCd3njjDXz1q1+NeLvLTijhQO5dkpeXB4/HE/MbLdhiL6bc5ubmAg5OEgI8+SSNn/+cQX8/BZMJuP56Dt/+Niflx6Nd9MXJ88TEROzatctrvkSJ+oxOJwgnOhxC6oRlhTTK0JAODgcNluVBCI+enmT85jcbsW0bi7y8xbcb6GHRaICLL2YjjghC2S9N01I7phi9WK1W/P3vdoyNzaOw0A2W1UGn0yI/n0FnJ43XXtNg82Z32Pv78EMaCQnEa66kvJygpoZgbIxCRgYNoxGYmRFqSJ/9LAslFDeKiwnuu8+Fe+/VYXBQ6EzLySG49loW+/cHtp1WchFLSEhAbm4ucnNzwfO8NMAqTo8bjUaJXJKTk/0u0LGWiY8E4poQywgl1tL1t912G2688UZs374dVVVV+PnPfw673R5VvWbFEIqvd8nk5CRGR0djvt9AKS+x6G00GrF79+6AXWWPPUbjW9/SgOOERXl2Fvj1rxl0d1P405+EFE40rcnyyfOysrIFi0GosyLBoNcD1dU8nnqKRmKiQCbj44DdToMQgWAAQUyyoQF45hkaX/3q4t9nbo6go4MGTdMoLeWxXNYP8uhFr9chMZGGXi9EfXa7/QThJ6KnhwXLcmHXBPytOQwDlJfzmJ+nMDmphd3OIDERuPRSFl/5SvikFQh793LYvHkedXUM3G5BYqW3l8ZPf6qDVgts3cph166TLzexTOP4DrDKmyhaWlrg8XiQkpIi1bnE4j7P82Grisca4mzMSk15AcDVV1+NiYkJ/OAHP8Do6ChOO+00vPLKKwsK9eFg2QkllJSXP++SWPnK+4JhmAV996JdcKBFXATLAg88wIDnhRSRCKcTePVVGvX1FDZvJhFFKPJ6ia/T5MQEcOSI0OFTVqYBx0Vfn7n0Uh7DwxSOHhWGAMfGhOum0/HQaGjwvNCR5HQCr722OKEcOULh73/XYXRUuAeys3l8+tMsdu6M7FidTmB0lEJKCkEoM2CBrtnq1QRvvklDr0+AwZAAQgCXyw2WpZCYOIxDh9q9Fr1Q0hI7dvCoqWEwP0+kbjCrVeimu+MOJz78sAarVq3Hhg1arF6tvHpzcrJALFYr8Ic/6NDRQSMlhQfHAe3tGnR1UbjxRhY63dIpDRMCvPtuAp5/vgCDg0UoK+Nw4YU2pKWNwmKxeFnzOhyOkMYAWBZ47TUGb7yhgc1GYft2Dp/6FOtX5SFanCp+8l/96lejSnH5YtkJJRiCeZfEwlfeH+QpL57n0draipGREZx22mmSjEIgCMOBFHz7BfR6YQGsrY2MUALVSwDglVdo/OxnDE4MPMNgSMTateU455yFrb3hwGwG/uM/OBw9SuHppzk8/jgDt1sDgAIgpPKMRiFl43AEX5C6uoDHH6fhcvEoLxfe9Pr7KTzxhBZZWW6UlIS+APC8INj41FNaWCzCuT7/fBZf+pIbi6lWEELg8QDt7TRmZiikphKcey6L55/XoLubRmamcE0mJhJQVERw6635yMxMlWoC3d3d0Gq1Us0gNTXVb/Sybx+LmhoaH3/MgKKEY9ZqgQsvZLFlC4+5uSlUVblhNMb2cfz4YwYdHTTWruWke8HhIKitZbBjB4/TTuOXbCr9r3/V4MEHdfB4hDbw3l4NPvwwGd/7ngHnnutd3LfZbJiZmcHU1JRE5L7aV4QA//u/OjzzjAY8L0SAR48K7eC/+IVLcaO0WNd1VqJbIxDHhLKYd8lSRig8z8PpdKK2thY8z2P37t0hhaPJyZCKoXJwnFB8FjtqwyEUsV5iNpsX1Et6e4H//V8GdrvQ2krTghjie+/l4tlnKVxxRXQP1QcfUPjJT3h0d7tB00YAQpQifk9x+rq0NPh+jh2jMT0teNmLQ5KlpQSNjTRqaxmUlIReO3nySQ1+8QsdNBogOZlgfp7CE09oYLFQ+MlPXEG7wgYGGPzpTzr09NAwGASXw8pKHt/+tgt//asWLS3CgrFjB4cvf9mDoiIC4KSirHzR6+rqwvz8PJKTk6VFT/TDMJuBb37TjSNHhGl1rRbYsoXD9u08aBpRpyRDRVsbjcRE3uvFwmgU5lOGhmicdhofVYTCsoLw5quvMrBaKWzYIESdFRXe9/bUFPD441rQNKSXB9Gq+OGHtTjzTA463cnivsPhQFJSEvR6vZf2lbw1uanJiOef1yAp6WSEyrJARweDJ5/U4rbblEsjArGPUBwOh0ooSiEU75KlIhSapjE/P4/Dhw+H5aUCCIRx4YU8nn6ahkYjFLcFzShh6nr/fl7aRyiEMjIygsbGxoCptnfeEVp7S0uFhZXnhXkKiiJ4+WUaV1wR+fkaGSH44Q9ZjIx4UF6ugd1O4/hxHm43daKFWCCVnByCyy8P/l0sFixwFQSEn1ksoR+T0wk89ZQWGg2QlycsTImJQovs++8zaGujUVm58FhYFnjhhXw880wWZmYYmM0EGRlAYSGP2lrhvx980IXhYeH85uYSv8Tk29EkCv5ZLBb09vZ6/T41NRXnnAOcc47/a7AUUYHBQOB20wB8CYyCVhudWyMhwG9+o8XTT2tBUYBeT/Dccxp88AGDH/3I5dWh19oqEI54zQDhpSIzk2BoiEZfH+WV+uN5Hnq9XiruE0KkyX1RIeH119dgbq4YGRk8CBFcFDUa4f5/+20Gt90W9lcKili6uAIr0wsFiANC8Q5bQ/cuWQpCIYTAarVidnYW69evR35+ftgP2z33sOjp0aK2loLTKaQ7MjOBP/yBDbnLK1i9RA6bTZDb6Ouj4HAID7lGQ8PlYjAxEdZhe4HneTzxxAiGhjKwfr0eCQk6mExAXh6LoSEGOh2DvDxBouWss3js3RucUAoLgXffFZWMxX0IE9z5+aG/rU9MULBYKCQne/9NUpJQR+rro1BZ6f03LAvcdZcOjz66Gi4XA40GmJ2lwLKAx0Nj3ToOzc0MJic5rwVvMYyNUThyxIyZmSTk5xeiqsoDj0eIXnp6eqR5DJFg5G5+SxWhbN4s1HKmpoSXHUKElujkZF4i3kgJpatLsBJOTj7pJSP47tD4y180+MlP3BIp63REGraU19pZVkhV+XYS+zYKUBQlFfdLSkrg8XhQX8+BEGBuzg6Ph4JWy8Bo1IBl9WAY5Rf+WHee2e12RaVWlgrLTigiwvUuEcUhY1VEFBVyrVYrTCZTQPmQxZCZCbz8sgdvvUWhuZlGVhbBRRfxkH+9YIQinhen07mgXuKLoiIeNhsDl0tIQ9G08BY/N6eX6gHhwuVyoba2FpOT2TCZjEhIEM41wwBlZW5wHAOGScAll/DYsYPgzDN5GI1Ci3FtrVDA37SJeE2479jB4913hfORnS3k7AWHQh47doR+nCkpBEYjgcNBITHx5KI8Py9Iv/szyTp8mMGLL2pBUSwSEoSoiOeFuo9eD4yO0jCbeczPh36OPvyQxgMP6KTpc4oC1q/X4M47GZSXp6G8vBxOpxMWiwVWqxV9fX1gGEZK1wh/E/sIZcsWHn19HN57T9BLI4QgNZXgkks4SZI/0i6vlhYGc3MUVq8+ef0oSrgGTU1CGla8dTdu5FFUxKOzk0ZxsTCHw7KCM+WePRwKCryv22L1Cq1Wi/379Xj8cS0GB9NO1Kl4aDQecByLM87oQ0vLnHS+legYi3WEotZQokAk3iVy2Xel3xRsNhtqamqQkJCAyspK9PT0RLU9jQY491yCc8/1H1EFIhR5vWT37t2LnpecHGGRtVqF6WuGEXwxEhJYZGbSIIQKSxF3dnYWx48fR0pKCs46qwhvvknD6Tw5T0HTgn3s5ZfzuOuuk9/tzTcp3H+/BoODwltwZibwla9wUiosKwv48pc5PPssIMoGVVdzuOgi1i8JBILZDFxwAYvHHtNCpxNqVg4HMDxMYetWHlu2LDynx44xcLkAjUaoF3AcfUI3jGB+Xhj8S0sjyMwM7TjsduChh3SwWCisWSO8ebtcQH09gz//WYPbbxcGCBMSEiS5cp7nMTMzA6vViv7+fgCQUryRTpOHAo0GuOIKFlu3cujtFdKwq1fzXhP5kb6g6fVEajiQP44ej0Du8jVcpwO+/W03fvhDPXp7T+6rrIzHN77hXnCPhtIoYDQSmM0EIyP0ib9nYLdrsGoVj2uuSYJW60Rvb6/fyf1IiCHWEYpaQ4kQg4ODaGxsDNu7RFxclS6OiXMdRUVFWL16NaxWa0wtegH/w5OL1Uv8geOA3bt5WK0UWlqE6KCyksBgGIXBkAOOo0Lu9BLPgyi46XIJHWkffywsuFotMDysQ3LyPK644uRq0dlJ4e67NZiZOVl7GBuj8L//K6TFdu4UFq/iYuDWW1lMTHCgaQphSn5JuPlmD6amKLz1lgbd3UK6ZPt2Hj/4gWuB6yEgEJxWCzAMAcMIJOLxCEN/TqewKO3fH7rY44cfMujspJCbK3SM6fXCv4wMgg8+YDA764FvsC16jaempqK0tBRvvfUWVq1ahdnZWQwMDEh2yGJxX0k7ZLEBorTU/8tNpF1e27dzyMoi6O8XZF0oSoiOp6cpXHutZ0Eaa+tWHg8/7MSbbzKYnBTqKWedxfpt+Q6lo+rwYQZpaULn3MAADY9HuAYuFzAxkYrt25NQXl4Ol8sl1bmGhoZORGmp0vkOVcJpKSIUtYYSAZKTk7Fjx46wDWTEi6lUHUVsUR4cHJR0sMT9xLpWI49QQq2X+ENGhpBaWrOGx1lnCQSj0wGvvkqQm8tBo1n8ARDdJQW/+ZP7T0gQ6kF//CODt98WajVbtrhw5pk9OO20ddLfv/oqDYsFKCs7WcjOzyfo6qLw/PM0du70PpepqQQ0HfnbuMkE3H23Gzfc4EFfH420NIJNm3i/ZAIIg3xPP62By8WDZYGEBAKnUyCVvDyCr3zFjdNPD+169/RQeOstBhYLDZrmodMJmmPp6YJmltNJweOhsLAIfhJi/SQ7OxuFhYVe0+QDAwNobm6OmR1yoOMJh1AmJykMDVHIzCT4+tfdeOABYc6FooQIdscODp/9rP+uvawsgmuuWbyjLxRCGRigYTIR5OUR5OWdvH7NzTTGx09+H71ej5ycHOTk5Ej2BxaLBaOjo5KAqEguKSkpAV9WT5U5FKWx7ISSlJS0wCgrFFAUpVhhXqwTiCZQ8jeDpSj+i/sIp17iD8XFwMaNBB9+SCE9XUhN9fRQMBp5bN/uARA8d8yyLOrr62Gz2fzuPzMT+M53OHz1q0JaZ37egoGBWa/PCIOKwj+WxQklAIHYBga8Fyol0zrl5QTl5Ytfpz17OJx7LotnnuEBCGTCMMDGjRzuu8+F7dtDi0anp4FDhxiYzTzS03nwPAWaJhgfp064LAppt7S00FJnFEVhdhZwOBikp3vbIYu1l/r6ehBCvKKXaOyQ/SFUQnE6gd/+VouXXxaGCA0GgjPO4PCTnzjR0CDUU0pLeezeHb60vy9CIZTsbB7Hjnl/hhAhBXeiTLUAcvuDkpISLwHRtrY2uN1urzZw+RBrLFNeooKzSigRYDnteYGT9Zu0tDRs27ZtQZ0iGlmUUEHTNOx2O44cORJyvcT/doBPf5pHZiaF48cpOJ0UKisJNmwYRmlpStC/dTgcOH78OPR6PXbt2hU0zWIyCf9GRxfKuhQVEbjdQHs7hbk54dqmpAjpoIqKpelmCgatFvje99xITe3E4GApKCoBW7bwuPhidtFBSDmGhmhMTVFYv57H+DiHd97RwOkU0oyzsxRKSwmuucazaM1KkNnX4Le/TcCRIzq4XEJKce9eFuefzyE7W+f1Ru3P6CpSO+RAxxPKNh5+WIsnntAiOZlg1SoedjuF55/XwOUC7rlHmPno7KRw/DiDrCwe5eX+W6+VOqbqah7vvw90d9PIy+PB80B/P41Vqwi2bw9tjfAVEJ2fn5fIvLu7GxqNRiJzt9sdtSx/MKiEsgzwZwMcKggh6O/vR3t7O9asWYPCwkK/5Camo2IpSWG32zExMYGysrKQ6yWBYDQC551HcOaZwsJuMgHvvDMflBQtFgtqa2uRm5uLioqKkBclf7I5mzfzcDg0mJ0VJqApCujvp5CURHD22d7HwHEcWJZVtEYQCnQ6YOfOSdxww8kuq8XAskK9ZHycQkkJLw2nUhSwbx+H9HSCujoGIyOCIdftt3uwbt3iLyIcB/zzn6vR369Derow9NfYyOCddxj8618cNmzgsWkTLykdy9tl3W63ZHTV2NgInue9opdILB1Cuc+np4EXX9TAbD7ZvKDXE9A0wZEjGtTUePDPf2px/DgDu11QT96xg8N//Ic7JFkcX4QSoVRU8Pj85z14+mkN+vpo0LTwcnPddZ6IbAAoioLRKAyxFhQUgOd5aYi1r68PNpsNOp1O6tZLSkpSNBWp1lCWAZFGKCzLoqmpCVardVETKDGs5bjwRQEXA8/z6OjowPj4OJKTk1FeXq7YtsXiMBBYL01OqovN/fiDv+3W1gqt0WazUJAFIP23kMsWPj87O4tjx47B7XZL2ljp6ekwGIxoaBD8SHJyeGzdyodlfxsOQp3/6O6mcPvtCWhro6WupY0bOWzZIlj06nQCkW7cKLTC7tnDhUQmANDQQKOjIxWrV3OYnNRgcpJGSgrBzAyFmhoGdXUMXnmFID+fR2Ulwde+5pYWSJ0uOjvkQOdkMUKZmKBgs1FIS/P+jmazMJj629/q0NLCIDeXR24uwdwc8NZbGhiNwHe+E/7EeqiNAnv2CNekp0fwsikt5f0O0EYCmqa92rzr6+tBURTm5+fR0NAgkbn4LxIvIBFiysscTsgcJ1h2QlnqlJfdbpescaurqxfNQcvbk5WEvF5SXFwMm82m6Pbl8NeWzPM8mpubMT4+HpGzIuCfUFpaKGRkCNLpNhsBIcL8QVsbJbWIyhWS09LSMD09jcnJSdTWDuIPf9iEtrY0eDwMDAYKmzbx+NnPlNdiChU8D3zrWwlobKSRkUEkGf+PPmKkjrHUVGGWwmKhsGoV8bIMXgwjIzQ8Hho6HYWxMUqSuR8fF+ZpxI6prCyChgYajz2mxbe/vbC1NlI75IXfd/HFOyODwGQisNkoGI0nr4vNJrQmd3bSWLWKl2aPkpMBliV4/30Go6PCOQoVhBAQQkKuVxiNwPr1sU1RA8L5TklJQUFBgReZy91BRXJJTU0Nq97icrnAcZxKKEuNcAUiRdXi/Px8rFmzJqQ3NqW7yQDh7bympgZJSUnYvXs3RkZGMDMzo9j2feHrieJyuVBTUyPpkkX6NuXPayUjQyjYUxSkmgQhwr+kJEEJobu7G5s2bUJ6ejo8Hg8SExORn5+Phx/WoamJQWKiB4mJTrhcFI4cScA3vsHh0UddMBqjrO5GgI8/ptHaSktNDoCQRvR4CNraaHzhC26Mj9PgOGFwcP16PqwW6KQkHjQtLM4sK6QJ3W6h6J2QIMxXzM4KApz5+TwaG2kMD1OLTvGHaofs60MSSoQiSAqxkh5XUhKB3U5hYoLC5s3CjItvtkawVKZgtYZHKOL9FW9WuPK2YV8yl/vrtLe3w+VyISUlRSIYuUqCP9jtdgBQU15LjVAjFEECogN9fX3YuHFjWBaXoueBUhGKOF8izncovX1/kHuizMzMoKamBqmpqdiwYUNUnSr+IpR9+3i88w6N4WFg1SqBSAYGgJQUHunpzRgYGMXOnTthNpvhdrvBcRwIIRgeZnDokFDkTUrSAdDBZOKg0fCoq9Ph738/jooKFunp6cjIyFCkAB0KLBYKbjf8Kkbb7RQKCwn27WMlBeFwcdppLHJy7BgZSQFFCWTsdgM8TyElRdBK0+mE9mZCALebCmuKHwhuhyz6kIjRi9vtDmnx/sIXPHC5KLz2GoPhYUFc88ILWXzucx5861sJmJ6mvGTjp6cpmM1CAT8ciM9FvDk2Bmsblhf3AaHhRax1iRpv8vSYbw3RZrNJNZyVhmUnlFinvOSppd27d0fUOaFEN5l8zsV3vmQpCIXneYnMysrKUFJSEvVbnz/zrt27CW68kcNTT9Foa6NOyG9w2Lu3BRkZU9i6VTAjE8+nSEqjozxcLoKUFCLbPoPERAbz8xQKC7ejtHQcFosFTU1N4DhOKkCHaiUrR6jfvbxckJKZm4PXgKJQQxDmHhhGaD2enKTQ2UkjPZ0P2dckIYHgM5/pwNGjq3D0qAZjYxQMBkE5WZCEEdJegsQ7hawsPiyNMX/w7Way2+2wWq2YmJjA1NQUGIZBe3t70FkMg0FQUL7hhpNzKKJkyvnns/jrX7XgOMBsFiIsm43CDTewAVt4AyFeCSWctmGxuJ+fn79AJUGcMxLJJSkpSerwWsqo7J577sGLL76I2tpa6HQ6TE9PR7SdZSeUaLDYQi++jScnJ0fcigtEP9wokprL5Vow5wIsTWvy8PAwrFZr2MOSweAvQqEo4LrreOzbx6OpiYLL5QAhx1FYmIgNG6qkcyk+kBqNBjzPo6xMcGy02SjodOSE5L+QSjEYCFavpvymcMQCtMlkkqIXX6+MxdDTQ+HwYQYej5CyOe00XqpRrF5NcM45LF54QXPCu0NIT/E8cP31Hkn+/ac/1eHJJ7VwOIQ6ws6dHH7609BqPzk5dtx7rxP19Rq88YYGPT0UBgcp9PXRkqRIe7sglXLppZ6o5zrkoCgKiYmJSExMRGFhITo6OmC320EIkWYx/LkoisjOJsjO9v6On/+8BwkJwMsvM5ieFjr8rrrKE9IQoy9WQsorHMhVEsrKyqROPYvFgoaGBnz5y19Gbm4u0tLS0N3drWijTjC43W5ceeWV2L17Nx5++OGItxMXhBKKa6M/BGobJoRgcHAQra2tKC8vR3FxcdSRUKQLvrxesmXLFr+kpoTveyCwLAuHw+HXjCtaBLtuubkAw4yivr5eSu8BkMiEpmnpmtA0jawsGldfzeGhhwQvE5alJF2oyy5zISvLBY+Hkv5OnsLxeDywWCywWCzS8J8YuQSTLiGE4K9/1eB3v9NhdhYnZNe1OHCAxR13uKUU1o9+5EJGhiDH7nAIb+M33ODB5z8v6HQ9+KAOv/+9Fgwj1Ap4Hnj3XQZf/nIC/vnP+YBT++IxAEK6bMcOHjt2uDE7C1itgnjm0aNCSqm0lMN553HYvTu2Q7ZiqmXNmjUghEjpGtFFUafTeUny+3tL1+uBm27y4DOf8cBqFYZsIy0HiDMo8UYoSg02yjv1eJ7HH/7wB/zlL39BS0sL1q1bh8LCQpx//vn49re/jaKiIgWO3D/uvvtuAMCjjz4a1XbiglAiBcMwcLu92xA5jkNzczMmJiawdetWpKenR72fSCMU0SpYXi/xh1hFKOKwIgCUlpYqPigVrB25p6cHXV1d2LhxI7Kzs0EIAc/zC8hEjmuu4fCXv2gwM3NS0TghgaC/n8HIiAa5uZzXdaBpwY9eq9V6tc/Ozs5K0iUtLS0LpEvEfbe1afHQQzpw3Emjp5kZ4PnnNdi4UTCHAoQi/Pe+58bXvuaG1UohO/tkgd7hAH75Sy1mZgQ9MKtVUD5OThYMwz74gMGePYvfOxRFoa2NxnvvMbBYhOM54wwOF17IgeMQlJSUhLzLi6IomEwmSW2b4zip2NzR0QGn0+nV8u0bvSQmwksFOtLjibd0FxAbLS+aprF7925MTk6ipqYGhw8fxttvv41XX301pjIvSmJFE4pGo8G8rELpcDhQW1sLmqZRXV0d0WCXP4S74Aerl/hDLGoo8mFFu90ek4fSH6HwPI/GxkZYrVap+C4SCYCgb5sHDwoWudXVgs6WXi9M/3d3M3jlFQO+9CX3CYVgTtqm73blXhmCqKVLil76+/sl0yuWZfH++3pJIkQ8pJQUgVRee00jEYoIs1moCchx//06TE6KkRZOeHIIEZZOJ3iy7NkT+ByK5++NNxj84Q86TE9T0GqBN98EXn9dg299y4Xy8qVrmQ42lc4wDDIyMpCRkQEAXtFLqHbI4WKpLInDRSylV0Sl4cTERFx88cW4+OKLY7KfWCAuCCWalJf4xjoxMYH6+nrk5OSgsrJS0QU0nKL8YvUSf1CSUAgh6OvrQ0dHhzSsKLYIKw3f6ya2IxNCsGvXLuj1eqmLC1i8sNraSoGmvYcyASEd1NxMSX8vnw0SyUWMgMTjEglG7vQnFkQtFgvcbjd6eyfgcpngdHLQ6bQntisoMofSxe12A3/+s/bEPk/+I0SYIdHpyAJvD3+w2zV45hkd3G5g7VpekoFvbaXx5JNa3HnnwrmTWCEcRQh5sTmYHXJ6erqXDlY4iMcIRXypidVx2Ww2RTq8vvvd7+KnP/1p0M+0tLSg0teFLgrEBaFECrGG0tnZiZ6eHqxfvx65ubmK7yfUlJfoH5KcnBywXhJo+0os+OKw4sTEhNewYqSEvRjkxz03N4djx44hJSUFGzdu9Cq+h5oDz8gQ6g/ioYp/wrKCh4q//YsPtUgq4j79pcbkBVGr1Yrq6iS8/z4Dh8OF+XkHBNtYHex2I7ZuXXi9CREiCbGWUlnJYXpaMOZyu08etzh3k5lJUF0d/L4hhGBgwIzRUQrl5ScjJZoWCt7NzbRUh1gKRCoxFK4dcqgmV/FIKOI9H6sIRSkdr9tvvx033XRT0M+ItU2lsKIJRcyXi+q8sZosDSXlFWq9xB+UIBTfYUV5ui9WbckiUY2Pj6Ourk7ybgEgRSbhFFTLynjMzADvvUcjIUHweddohOG+888PvjAvFr2IzRti9EIIwZlnsnjnHRoff5wEg4EA4DA9TZCRMYeCghrU1uq9JGG++109Hn1UKxHGc89pTnigECQkUHC5TpIJTQP/8R/uEGsfgc/PErkDy/anjGadwWDwMhQTo5fF7JB9oRJK5JDPwiwV4oJQIrmBZ2dn0dHRAUIIdu/erYitZyAES3nJ6yWnnXZaRBdQXOAifXgWG1ZUglCcTuCjjyhMTwsGShs2nFzp6urqwiq++0NLC4VHHtFCoxEWY7udwtycoFT8X//FoqoqvOP3jV7k/9xuN1iWhVbrwX//tx1PPqnHwYNauFwMzj+fw/XX65GTs1GqvXR2dqK9PQePPLIVNE2ktl2OE3xU3G6htVmvF3xiWBYoKOBx1VWLt8kSQlBYOIdVqwgGBykUFZ10Phwbo3D66VzIEvhKIBYLuFwHK5gdstiVJ3+W45FQxLUgVse1HMKQ/f390mwMx3Gora0FAJSXl4dFbnFBKOFiaGgIzc3NWLVqFSwWS0zJBAic8nK73aitrYXb7Q65XhJo+0BkD08ow4rRprza2ij8+McMurtPyoNUV3O4+OJOAMD27duRkpIScvHdH556SoOREQrbtvFwuwUrXmFqnEJBQeTS5+KxiOd1fn4ejY2NMBgMSE1NBU3zuOUWB774RdFjhz4RxZxUmmVZFs89J3RxMQwLjwegaaEBQKtlQNPCZLvbjRMqtzwefdQZsjBhYiKHz37Wg9//XouWFhparTDbUlQUmgS+koilqraIQHbIfX19CwzFYu2MGAnCfVkKF3a7HcmiENoS4Qc/+AH+9Kc/Sf+9ZcsWAMBbb72Fffv2hbydFUUoPM+jpaUFo6Oj2LJlC7RaLSYmJmK+X38pL3m9ZOvWrVF1tEQiQCnKyfT39y8aGUUTobhcwH//N4P2diEy0emAmRkezz3nxPx8Es4/fwhmszms4rs/1NYKA3DCLAgkvafOTgrt7TTOOiv6lN3c3Bxqa2uRmpqKdevWSedFPPZAtReNRgONRn+iRZk6kdbiwfMEPM/BbPbggQf6MDqaieLiBOzbF7rKrXjOzjmHQ16eIKBosQjT8Xv3cmHpXimBQIRCiCBDo9USKLnW+Q76iV15VqsVAwMDkjDk6Oio4nbIkSLWJOdwOJCXlxez7fvDo48+GvUMCrCCCGV+fh61tbUghKC6uhoGgwE2my3mboqAcNPLByijqZcE2j4QOqGwLIu6ujrY7faQhhWjGZysqaHQ2SmkYvR6Yd9utxVmsxEdHSU488x2cBzn1VkVCVJSBLdHOcR6hMkU/aIqDj0WFRV5RXKBCvvy1B0A7NkD/OlPWng8QtcZRdEn/p7C/v12lJfPIDW1+4SF80lJmFAWQPFYKit5VFbGXik3GPwRykcf0XjkES06OgRZ+N27Odx8sycmCtC+XXldXV2YnJz0a4ccriKCUohlyzAgdHmtRGFIIE4IZbGbQpypyM7Oxtq1a6WLKdY2Yh2mMwwDl8sFnufR1taGoaGhiOsl/iDOT4Sy6Nvtdhw/fhwGgyHk2lE00jGzs5BmQlwuF6anp2A0mqDTJWJ+HnA6Nejp6UFWVhaS5GJXYeLAAQ6NjRpMTwty54QAg4Oie2F0i+zg4CDa2tqwbt065OTkBPxcoMI+IQTnnefBGWd4cOiQFm73yQ60zEyC736XQUnJOi+P8qGhIbS2tkqOioEWwGi776angSNHGFitglBlVRWHaFyBfZ+lpiYaP/iBHlYrhYwMApYFXnhBg54eGr/6lTMsl8twQdM0EhISYDKZsGnTpiW3Qw6EWPvJOxwOlVBiAfnEtT8DKPmDH8sLLLYnf/zxx1HXSwIhlLTU5OQk6urqkJeXF7L8fqjbDoSSEmHaeWRkHjQ9g5SUZCQkGNDdLXRlVVWVYWpqAseOHYNGo5EG39LT08O6Jp/+NIfWVhoHD9KYmBBFJQn+4z88KCyMbNElhKCzsxODg4PYsmVLyO6MIuTRi0bD4y9/ceHhh1k8/bQWNhuFM8/04EtfcqKgAOA4ykvGXHRUFAv7g4ODoCgKaWlpyMjI8Co+R/oyVF9P46c/1WFggAZFCfWbjRs5fP/7bslJMVz4DjY+84wghSNvaU5KImhtpfHuuxpcdFFkjqkieB54/30Ghw4xsNsFo7LzzmMlZ0d5XVGnC80OWSTvWKWlYp3yWqn2v0AcE4rH40FjYyNmZmZQVVXlt0gld1OMJaG4XC5MTk4iMzMz6npJIARb9OXDiuvWrQs7vxpNUb60lMP69RN44w0zMjIy4HBoMDQkpH2uvJJFYWEuioqE4urU1BQmJyclD4jU1FRkZmZCq83EwIAROh3BunXEr8y7Tgf84AceXHYZhaYmGgaDkFoJw2nACxzHoampCbOzs6iqqor6BYCmBY+Pr38d+PrXPbK2ZAQcqpQvgDzPS5IwYvE5KSkJiYmJkolUOMTicgEPPCCQSWkpD41G6MQ7fpzBH/+ojcgZEVg4md7URMNk8m6K0OkEIujpiS4rQAjw619r8dRTWqmh4eBB4NVXNfjf/3UhPT1w56NcEcHXDlnuoBiNHXIgxPoFViWUKOH7IM3NzaGmpgZGoxHV1dUB89DijRZLX/Lh4WH09/cjISEBp512WsxSa4EIhed5NDU1YXJyEjt27EBKBKbckUYoYhfbpz/NYe3aKrz+ugY2G0FFBcGVV7I491ziVYsQ3w4rKipgt9sxMTGJJ57g8eKLHthsLiQkaFBeDnzzmxQ2bVq4P4oCNm8m2Lw5urqYqFZACEFVVVVM7o1IhipTUlKQkpLiVXweHR0Fx3F4//33T5y/DLjdadDpNMjMDNzdVldHo6+PRlGRQCaA4NmSnk5w+DCDqSmEZfQlwpfYsrIIentpiNbNwvcV/jc11ftnVqvgOBnqWtjQQOOf/9QiMZFIg5tutxB5/eMfGtxyiyfkzkd/dshyNWrRDlk0FIsmwohlhCIKcq5Et0YgTghFDrHgXVxcjPLy8qALuNDmGb1XiT/I6yVFRUWYmpqKaZ3GX51DLmXiO6wYDiIpyttsNhw/fhxmsxlnnLEV+/bRuPFGF+bmOKSk0NBogp8Lk8mEjz4y47XXtEhI4JGd7YLD4UJdHY3bbpvHXXcNo6wsBRkZGYq2fYsWz2azOWoDsVAhr72I5znYUKVcEiYxMRG1tbVYt24d3nvPge98x4CuLhoMQ2HDBha33cZi2zbdgntvfl5o4fY9dTqdIPnvdFKQk0Co8CWUCy5gcewYg/FxoYbCccDQkGCHfOaZwv36/vsMnnxSg95eGjqd0J12ww2eRb1Pjh1j4HDAq7iv0wlNGG+/zeCWWzxBtcUCwTf1KLdDFr10QrFDDgS1KB8YcUMo8gU8HM+OcG2AQ4HvfInovRFL+EYRMzMzOH78ONLT07F+/fqobmB/RljBIPi716KwsBCrV68GICyQGg2P9PTQO7lefJE5MU9BAUiA2ZyAjAygrc2IxkYXNJpuNDU1ITk5GRkZGcjMzIxY8wkApqamUFdXh9zcXKxevTqmLwCjozjx5g4UF/NSak5c/AINVfpGL+Ib+PR0Ou6/Px9jYxRSUjiwLIsPPzTgK1+x4847j6OyMtFLMn7NGh4pKQSTkyedEQkBJiZoVFZyXm6JvpicpPD++wxsNqCsjGD7dk6KcnwJ5bzzOPT3e/D3v2vQ1UWDpoGcHIJvfMON/HyCDz+k8ZOf6GC3U0hPFxwm//53LQYGaPzP/7gQaXZYvF2VGGyM1A45ENQaSmDEBaG4XC58+OGH4DgO1dXVYQmjKR2hyE25xHrJ/Px8zNuT5W+3YpSmhJcLEF7Kq6+vD+3t7ZIumnwxDLcteGiIgu+lZBhAo2Gg0+Vg164sOJ1OTE5OYnJyEt3d3dDpdFJhPy0tLWQiHR0dRXNzM1avXo2CgoKQjzFcEAK89RaN11+nJZn9lBQa+/fzfmdl/KXGxPNJCIHT6QQA/OMfNMbGhAl7hqEAaJGWBgwMJKO9fSMqK3vQ3t4Ot9stvV2ff34+/vEPI2w2QWJ/dlaQzr/uOjag5Mv77zO4914dxsaEY9dqBTOw73/fhaSkhYRC08AXv+jBhReyaGqiodMB27ZxknvlP/+pwdwchdWrxaK9YAhWU8Pg2DEaO3cGvu+2buVgNGoxNUVJagAej6CScNZZrHTOlIwG/Nkhi7UXXztk0VDMF7GMUEQHTZVQokRycjLWrFkT9oVSklDECXzfqfNoHRtDAUVR4DgObW1tGBgYULwteTFCEYdGx8bGvCbf5TIT4RJbWRlBf7/333gETyopzZGQkID8/HxJsVYs7Le2tsLtdiMtLQ2ZmZnIyMjwm/IjhKC3txc9PT3YtGmTJK0eK7S3U3jpJQZGI7BunfAdRkcpvPwyg/x8EtT617cteXJyEm1tbSgqKkJLCwONBqAoQSBTUC4W1JcHBsyoqKiQ8usWiwUTExOoqOjAxRcXoqYmH7OzJlRXU7jsMi7gIj41Bdx3nyC3X1rKg2EAux04dIjBE09o8aUvBU4x5ecT5Od7PwMcB3R0MEhJ8a71GI1Cq3lfX3BC2bSJx6c+5cHTT2thtQrfleOAjRt5XH75SUKJZTSg0Wi8ohe5HXJHRwcSEhKk6EW0Q45lE9D8/DwIISqhRIOEhASsXbs2or8N5NoYDsR02/DwsN+FfCkseimKQk9PDziOU9xZcbGUl8fj8UrxJSQkeE2+i3My4eLSSzl8/DGN7m4hLePxAGNjNCoqeFRXLzyfcr8NsbA/OTmJkZERtLa2wmQySeSSnJwMQghaWlpgsViwY8eOJSlktrTQcDqB0tKT5zMnh6CpiUJrK43Vq0N78RgdHUVTUxPWrl17YpCPklqPAXJiqJOA4yhkZnLS8KhoeFVYWAiWZbF58xQuvLAbk5MW8DwHozENw8PCAug7l3H0KIOxMQrFxbwUwZhMQlv4a69p8P/+nycs/xGaFgrzfX3enxcfx+Tk4GlWihI65rZs4fHOO0I95bTTeBw4wEoNBUup5eVrh8yyrGQoJrdD5jgORqMxJvNvdrsdAFRCiQbR2vNG6/cuX0z9hbixKvyLsNvtmJubC2tYMRwES3nZ7XYcO3YMiYmJ2Llzp0SeSugV7djB45vf9ODPf9ZgcFDwGTnjDA5f/jKLxWYg5Q+3aPMrpsZE4TqR6LZu3bpkD6DoGe8LjUb4XSjo6+tDV1cXNm/eLEVUn/oUj1dfBcbHaWRmCoQyNia4Hl5wgVu6/+SFfY1GIynKymsDYmeTyWTymstwODQn9Mi8j0enE1qOBQn+0BdJigIuvJDFL3+pxeSkILHv8QiRSX4+j127Fn9mGAbYt4/Dvn2BxVeXS8vL9/yKhmJ9fX2YnZ3F1NTUonbI4cJms4FhGEXbnJcScUEo0SCaorxYL0lJSQk6XyKmvGLxRiIukHq9Hvn5+TERugw0hyIqEOTn52PNmjUA/Hu+R4NzzuFxxhluDAxQSEgQUl2RbFar1UozHaK1sajz9MEHHyAlJUUq7Pta0SqJoiKC99+HJMECQFIYXmwAU9RfGx4exrZt27xmq3bv5nH77R48+KBAvoA42Mlixw4GhJz0l/HXlgzAqzbg8XhgtVoxOTmJhoaGE+cqHxrNGkxPM0hNpU4ck9Duu2cPB6MxfHHISy5hMTRE4dVXNWhvp6HRCOKYt93mVkTzK17UhuXR4czMDEwmE8xmc8h2yKFCnJKPh+8cCeKGUJRwbQwHgeolgfYBKKvEKub+Ozs7sW7dOkxMTMTEBAvwH6H09/dLciSi6qtSkYkvdDqhnqIEZmdnUVNTg6ysLFRUVICmaczPz0vRS1dXF/R6vUQugqKwcg/npk08Pv5YSG+lpQkL8tQUsG4dj40bA6dFxXkicVDXXyR8/fUczj9fSBMCwM6d/InW2/C8XgQVZC14fhX6+3ORmkpQUTEFq9WCjRtHcehQGkZHKZhMNOx2PTIzCa67znPCbTK8e1yrBb72NQ8uuYRFZ6cw/HnaaRzC7MQNiHghFDl4nodWq42JHfJKbhkG4ohQIkW4hCKvl2zZsiWkIq58Il+Jm1uc4hZz/ykpKbBYLDGr08iL8jzPo7W1FaOjo4oV35cKExMTaGhoQGlpKYqKiqTjNBgMKCgoQEFBATiOk4qqTU1NYFkW6enp0sMfrd6T2QzccAOHI0cI6uqEe+H004WaUKCsmyjm6fF4sGPHjqDHkJkJXHBB8PsgmNcLx3FgWeDuu4147LEEaQK9tDQBf/hDKh54gMff/gY8/zwwOcli7dpxnH32CAwGDcbHM8KqochRXExQXKx8WjiSOZRYw986oJQd8nJ4oSiJTxShuFwu1NbWwuPxBKyX+IN483AcF3VKyul0oqamBgC8hhVj5aoobpsQIhXfXS4Xdu3aBYPBoEjxfSnQ39+Pzs5OrF+/HtnZ2QE/xzDMgrrCxMSEl96TWNiPVK02LQ246CIeF14oyq0E/qw4nKrT6bB9+3bFZXv8tSU/+KAGDz+cAIoS7AYIAbq6aFx9tQEffDCHz32Oxg03AIQwANIxM6OBxWKRmkJaW1uRlZUVlRe8UojXCCVYvcSfHbIoarmYHbJIKPH6HC6GuCGUaFJeLpdr0c/J6yXbtm0L68EW39qjXfCDDStG0ppstwONjcKNt2EDQaAXG3HbH3zwAYxGI3bt2iURsfhGGm8PrQhBDr4dIyMj2Lp1a1jSM/KZg9LSUrjdbik11t/fD5qmvcQsw13sF3vmRWVouf9KLCG8lAC//70QAen1J+skFEUwPk7h2WdpXH2120sSRvQjKS8vx1tvvYWMjAzMzMygp6cn4tSNUog0Yoolwm0bNhgMUmt8MDvk8fFxzM3NLWmE0tvbix/96Ed48803MTo6itzcXFx//fW48847I5IsihtCiRShtA2HUy8JhGhnURYbVgw3Qnn9dQq//S2D4WFhO7m5BF/6Eof9+xeS8uzsLDweD/Ly8lBRUQFA+eJ7LMBxHBoaGmC32wPWHcKBTqfz8tqYnp6W6i4NDQ2SmGVGRkbU+5qenkZtbS3y8vIWlRBSEg6HYIQlX+8oCmAYChwHDAxoQNNswNoLIQSrVq1CSUmJlLoRbZDFwrNIwNGeo1AQrxFKpMcUyA65q6sLV111FXQ6HZKTk/Hkk0/ivPPOC1shO1y0traC53n87ne/Q3l5ORobG3HzzTfDbrfjvvvuC3t7pwShBPN7b21txcjISMj1kmD7iSRCEd+wFxtWDGeeprmZwr33MrDbBXtcQJhKv/deBnl5HNauPUkqAwMDaGlpAUVRqKys9BIxjGcyEdOTDMOgqqoqJq3U4oO9Zs0aOBwOTE5OYmJiQpLjEAv7KSkpYS0gYq2nvLwchYWFih73YjAagexsguFhykvni+eFfxUVNPR6vV+nSjFDIN4f8tQMAGmoUiQYf0N/SiMeCUXJwUa5HXJfXx9++MMf4vXXX8f//M//4Prrr0dVVRUOHjwYs6jlwIEDOHDggPTfpaWlaGtrw0MPPbSyCSXShS0QoYgLEsuyYdVLAiGSCMXj8aC+vh4Oh2NRD5VwIpSDB2lYrRQqKk624BYXE7S1UTh4kMbatcLi0NraiuHhYWzYsEGS9F4JxXebzYaampqwUkVOJ3D4MI2BAQppacK8SzjCzEajEYWFhdJAm1jYF8+bvLAfLBUgmnlt2LAhaK0nVqBp4NZbWdx5pxYulzAfQ4gwgZ6XR3DJJSevv7z2wrIsmpqaYDQaodFopJcb8T6hKEoqPIvND6LgYmtrKzwejyQXn56ertgcRbwSSiyOSa/Xw2w2Y+fOnXjssccwPDyM999/f8mL9DMzMxFHRnFDKJHC3xxKNPWSQAi3m0zurLhr165F37DDIZSREdGG9uTPKEr42ciI0FVUW1sLp9OJ3bt3A4BUlJcvEPEIi8WCI0eaYbeXg+NyMTlJsJhO6MgI8J//qUNDAw2eF96yCwsZ3HILi54eGjYbsG0bj717+QVDff7gK8cxNzeHiYkJyYY2KSlJIhez2Sylirq7u9Hf3x+RmZeS+NKXWExPAw8+qIXDIZDMpk08/u//3H7beXmeR0NDAziOQ1VVlVd9LZDXi1zVYM2aNbDb7V6Ci0rJxccjocRSy0vu1pibm4srr7wyJvsJhM7OTvzqV7+KKDoBTgFC8V3oxXqJUsKK8v2EuuBPTEygrq4OBQUFWLNmTUjHEA6hlJYSvPGGWGwVfsbzwoBdfr4LH3zwARISErBz505oNBq43W4kJCTg3XffRXp6ulQn0Ol0sNmA8XFhylmJQbRoMDQ0hL/9bQKHD1djZsYIQoThvquv5vDpT3MBi+C/+Y0Wx48L3iAJCcKQYV0djWuv1UOvFxZUigL27uXwhz+4FwhWBoNcCl30MREL+729vdBoNEhPT4fT6YTNZsP27TswP5+I6WmEFSEpCZoGvvc9Fl/5iiDomJpKsHat/4FSt9uNmpoaaDQar+HecLxeAEiqBkVFRX7l4uXRSzit2/HWNiwSbKwIxWazSSnGaPDd734XP/3pT4N+pqWlBZWVldJ/Dw0N4cCBA7jyyitx8803R7TfuCGUaFNeStZL/CGUlJd8WFFU6w1n+6ESyvnn83jxRRrt7RRWrTopUJiR4UZa2lHJ5EoUnKQoCnv27JFaaPv7+1FX14J33qnEe+/lwunUwmymccklgiyKUkNpoYIQgq6uLnz4oQXvvrsLHo8W5eU8aBoYGaHwyCMa5OcTVFUtPD8TE0KqKyNDIBNAcDOcnBSK0GlpBAkJQkrs7bcZPPigBt/6VuTab3q9Hnl5ecjNzQMhPCwWC9ra2uB0OtHenoKHHuIwOgokJGiwZw/whS9wyMmJzcDqYkhJAfbsCXxPOZ1OHD9+HCaTCRs3bvS7cPsKWoY6VOkb4VksFgwPD6OtrW2BVW+gZ19cvOMpmhaf0ViRnN1uR1FRUdTbuf3223HTTTcF/Uxpaan0/4eHh3HWWWehuroa//d//xfxfuOGUCIFwzDweDz46KOPFKuXBNpPsAVfPqwYyLI4GMIhlKIi4L/+i8Nvf0ujvV24sSsrbdizpxann16IgoICv8V3+Zv2/fcTPPecFhqNGzrdLCwWLf7v//SYnPTgxz9mluytUJwgn56exvz8bszO6rBu3Un/8rw8gtZWCu+8Q/slFIeDgscjDByKGB2lJMVesRNdIBWCp56KnFAcDuCvf9XgxRcF6fqtWz3Ytm0cZWV6JCbuwn33JWBigoPZPI/paQ5/+1sC6us9uP9+J/LylPc4n5kRvl8kkZCYkk1LS8O6devCEIQMPlTp+zmapr3MrkSrXovFgrq6OlAU5RW9yFPDYpPAUpikhQrxOy5FyisaiLNYoWBoaAhnnXUWtm3bhkceeSSq+3TFE4rD4QDLstDr9YrVS/whWA0l0LBiOAi36L95M8GDD3Lo72fR3d0NjuvF1q2nIS0tbVEZlakp4LnnEpCcDGRlGUBIAjweDyYmPHjxRWDLlqOoqDip7Kt0h9XYmNDampXlQk9PHXieR1VVFerrE6T0lBx6PcHEhP8FLzeXIC+PoKeHgtksLEAsS4EQoSCt1QqLrtMp/Hx8XJCHD/eZ4TjgP/9Ti9dfZ6DTAVoth2ee4XHoUAV+9zsGL76oxdSUBuvX06AoLXieh83mRmenHk880Y2qqhqp5hDtOa2ro/Ctb+nw/vvCorZrF4d77/Vg69bQXkjm5uZw/Phx5ObmRtXSvJjXi7/oRW7Vy/M85ubmpLmglpYWaSZDXtiPpwhFLtIZCyz1pPzQ0BD27duHoqIi3HfffZiYmJB+t0p0jQsDcUMokVygwcFBNDc3AwA2bdoU07fqQAv+9PQ0ampqonZWDNdVEQB4noXFUget1oGdO3fBaDRKD7S4TX/ndXCQgs1GST7e4oOenS20Hycnb4bROIze3l40NTV5CS9Gc7NPTQH33qvFm2/ScDoJGMaNAwcK8YMfZECvZ1BYKKjssuxJRV+eF6KQigr/ZKvVAjfeyOK//1uLri4KSUmAy0VACAUxVT86SsHtFutMFD7zGR0efNCNnJzFj3l2FvjnPxn84x8aHDtGIyuLIDPTA7t9FsXFOoyOmvGXv3AYHhYITTzdwpt5AvR6GmbzRmzdmoeJiQn09fVF5VLZ20vhvPMSMD9/8mcffUTjvPP0+OADJ8rLg99DU1NTqK2tRXFxMUpKSkLaZygIlBqTtyXLPyv+S05ORnJyslSfEtuS+/r6pG1ZLBZkZGQs+VClP4j1k1gSylJK1x88eBCdnZ3o7OxEfn6+1+8iGTRf/isUAeT1ks2bN6Ompibm3SD+Ul5iA8Dq1au9tKUiQbgRiqi4q9frsWvXLqnbTbwJgp2LjAwCvZ7A4QDkwZT438XFJpSXl6O8vFwSXpyYmEBnZycMBoMUTofTvUOI8Ib/5psMzGYWDGOD223As88WobiYxc03szj9dA4vvcSgtZVGdjYBTROMjdHIyyM499yT5350FHjuOQ2OHKGh1wNnnsnhe9/z4IUXGHR00Ni2jSApiUdfH43RUUry59BohO/+8ccM/vM/dXj4YXfQY56dBf7f/9Ph2DEaDgcFhwPo76dgtfKorEyAyWRAcjLBxx/T2LyZR0+P9/XneeF7p6ZCWjjFYbZIXSp/8xsN5ucBjju5L46j4HYT/PrXGvz8556Afyu2Qa9Zs2bB4qE0/EUv4v0ZKHrR6/Veg6eiHltvby9aWlokEo5GzTdanGr2vzfddNOitZZwsOIIxXe+RAyLBc/z2H0decqLEIK2tjYMDg4q1gAQTg1lamoKNTU1WLVqFSorK6Xie6jDijk5wFln8fjXvxhoNASJiQKZTExQOOsszst1UC68yLIsLBYLJicnUVdXB0KI9Jbtm//2RWMjhQ8+YJCc7AZF2WA2G6DX6zA6Cjz5JIPPflYwVbrzTg/+8hfBPpbjKJx+OodrruEkafjxceB739OhtZVCYqKQimps1KC6msd993mg0wnprOlp4I47tPjLXzSgaWHgLzOTwGgENBqC99+n0ddHoago8FvYU08JUUlGBoHNJhT7KYqDzaaHzaaDySREPKmpBAcOcDh2TCCwrCwCjhPIJyuLYO9e7+sajUvl0aO0F5mI4DgKR44EXuhGRkbQ3Ny8LPMxoUYvYju7SEZiS/auXbskPSxRzVen0ynuRRIKYm3/63A4Vqy5FrDCCEVML6WlpWHDhg3ShRUX1FhCjCA8Hg/q6uowPz+/6LBiOAi1LVmMiioqKlBYWOj1thfOsOLtt3tgswFHjjCYnAQMBuD00zl8//uegO25Go0G2dnZyM7OBiEEMzMzmJiYQHd3NxobG4NKlwwMUJibY5GWZkNioglarTAcaDYTzMxQmJgQFvf8fILvfIfF7KxAFikp3jWVl15i0NZGYfVqIqXFHA5hoT18mMbZZwvnMCUFuOoqDi+9pEF6OvGaGtfphOjDYglOKG+8QYOihM/r9W5QlAYAA0IoWK2C0+H8PHDxxRzOPZfH0BCLp57SoKNDsLPNzSX4xjdY5OUF3ke4LpVZWQQMQxaQCsMQBOKJgYEBdHR04LTTTlOkJTVaBIpe5LU/ANLcFM/zXnpYckmY9vZ2yUlRjF4MMWxTPNUiFKURN4Sy2EI4ODiIlpYWv/MlsXZUFPcxPz+PI0eOwGQyhTSsGA4Wi1DkEi5btmxBenq6VwE03Mn31FTggQc8aG1lMThIISeHYP360M2vKIpCSkoKUlJSJEXViYkJSbrEaDRKqTGz2Qy7vRcUVQitNgla7ck3PIcDMJkI0tK8F91Ajo4ff8wgIcHbNVH0MG9pOUkoALBmDYHRKKT25E13NpvQFVZSwmN2Fnj+eQZHj9IwGoGzz+ZwzjnCAKS4bjidLvC8Bzk5GoyPC11lc3MCqZx1Fofrr2dB08C//RuHCy7g0dREQacDtmzhEY4rcSgulWefXY6XXlqz4G85jsJNN3l3rxFC0NPTg76+vrCFNZcKwdqSLRaLNLXvO1QpV/MVJWFEH3iDweAlCaMkAcQyQgFUQok5QpkvUcJXfjHMz89jfHwcxcXFIQ8rhoNghMKyLOrr62Gz2bBr1y6YTKaQiu+LgaKAtWuJl/ZXpDAYDF7SJeIDXlNTc2KwjcHGjQVobNSAoggMBiFKsNspXH01G/LCazAsfDsXa4e+iih5eQRXXMHhz39mwHFCfcjhEBbfz37WA0KAm2/WSb4mhAjk8pnPcPjhDz04+2wWhw7RcDg4pKQYQdMUaJrAYqFwxRUsrr6aw65dvBe55eQQxeZO5C6VPM9jZmYGubmTuOaaXjz5ZDFoWtgPz1P42tc8+PSnT75UiS8go6Oj2LFjx4pZpMTopaenB4ODg9i8ebMUvQcq7ItOinIfeIvFgpaWFrAsi9TUVMUkYWIZofA8r6a8YolQ9bhiGaGIw4ojIyMwm82SWq/SCEQo8/PzOH78OHQ6nRQVhVp8Xy6IqbHk5GTMzs6CYRgkJyfjc5+rxW9/W4ze3nTwvAZmM43PfIbHrbeG/jJw5pk8jh6lMTsrRDGECJP+iYlAVdXCe+D73/cgJYXgySc1mJsTivKf+xyLL32JxUMPaVBbSyMnh0hkNDMDPPMMg/373Viz5hjWrVuN9vYMjIwIv2cY4FOfYvGzn3kWEFgsIZeZf/hh4N//fQpPP83CZrNjw4YerF7tQVtbhtQs0draiunpaezYsWNJVIGVgihhMzAwgO3bt8Mse9MIZajS1wfeZrPBYrFgdHQU7e3tMJlMXkOV4T4/SgpD+sLhcIAQohKKEvB9ww5UL/GHaHzlg0E+rFhSUoLZ2VnF9yFCbBuWW7CKxffs7GysXbtW8mSJd6VgQJDMr62tRUZGBiorK0HTNCorgbPPtuODD0bR3T2HxMRxlJTQGBoSFoBQDK/OO49DXR2FN95gMDIiEIrZDFx3HYtNm05GBvPzwDvv0Dh+nAbDAP/1X26sXUuQm0ukduKDB4WZEjkxJCcDU1MEf//7KG66ieCppxLw4osevPuu4Jd+9tk8LrqIW1Iy8YdNm/TYtEkPwASOS/dyqXS5XGAYBqWlpXE1FLgYCCHo6OjAyMgItm/fvmBhjWSoUvTDEVOI4lBlQ0MDCCFeQ5Wh+H/EMuVlt9sBQCUUpRGsXuIPsYhQfIcVLRYLpqamFN2HHPIHhWEYyT9lzZo1kgT6SpCdB062p5aUlCy4fomJJuzfbwKwCh5PsVQjOH78OETDK7FrzN+Dq9MB3/0ui3PP5dHYSEGjAbZv5720qhwO4Cc/0eLwYVqalj94kME553C4/faT0ZC/NnuO4+B2c9DpdDjttNNA0zSuvZbDtdfGtkYXDUSXytTUVNjtdmi1WmRmZmJ8fBydnZ2KuFTGGmLn5MTEBLZv375os0skQ5VardarqUQcqhwcHERrayvMZrNELmKHmS9imfISr120NtXLibgiFEIIWlpaJHe+UDtSlCYUMTrKyMjA+vXrQdN0xH4ooUK8SVmWRVdXF/r7+yX/lMUm3+MJYkfRunXrFp209a0RTE9PS0V9l8uFtLQ0iWDkuW+GAaqqeFRV+d/uW28xOHyYRmEhkXTJ5uaAN99ksGcPL7Xxnn02h9/8RgOPRxiQZFkW4+NO/P/2zjssqjN9//cwdKRIGRCkCCpioYpEExNNjGKjJJZkYxLTY1Z3s7qbmM1+YzbZFKObaIrGrFk1UX9foyAYayzYYmwUERFQpEidGcoAA0w77+8Pvu/JDAJSZuac0fO5Lq8rAZx5GWfOfd73eZ77trOzR0KCJ1ujsATUajV7NBodHc2KsbFTKk0BIQT5+floaGjA+PHj+9yl1d+hSmoJQ9M8aVvy7du3IRKJWHFxd3dnG3BMvUPhar7GWHD/bvo/GIbBxYsX++XHZUxB6W5Y0dSdZPRDcfXqVbS2thoU3y0hw2QgUb1A14FXMpkMNTU1rKGgftdYT6/DpUsiiEQwMLl0dgYqKoDsbCtWUJ55RovTp8W4dk0EQAeVSgdbWwckJ4vw4IP83ZF0pr29HZmZmXB2dsbYsWMN7qDNmVLZH6iXW1NTE8aPH2+UHJXetiXrRznY2toa3Nw0NTWhrq4OpaWlbGSBh4cH2traTCbCLS0tZs8+MTa8ERQrKysEBgbCy8urz3cAxujyYhgGRUVFqKys7LKbrD8BW31Bre6Y2tZoNBZTfKfodDrk5eWhpaXFKFG9IpGI7dwJCgoyuMsuKyuDtbU1u3PpbrK8O73R/7qXF7B5swr//W8zTp7UwMfHBQkJYsycqe1VbgofoCaPHh4ebJ2tO0yZUtkfaA5La2srxo8fb5Kjnru5JXeV9WJlZcW2xIeEhLAxvfQPrXfSoUpjCQxtGebrTWNv4I2gAGDvovrKQHcPGo2GDaSiO4OunsNUR170iE0kEmHMmDGwsbGxmCMu2olnZWWF2NjYXhU2+0rnu+yGhgbIZDJ2spymKXp5ecHOzg5xcQzOnBFDqQToP2VTU8exVmTk7/+GhBA0NNxCTEw5XnopEoMHWwOwnJ1JU1MTsrKyMHToUISEhPT5fWKslMr+oNPpkJubC5VKhZiYGJO8b7qip91Ld1kv+jG9165dY2dhiouL0dbWBjc3N/a1cnBw6Pfn1VhOw1zCK0HpLwPp8mppaWEzISZOnNjt3Yapjryqq6uRl5eHESNG4ObNmxaT+Q78HtXr5ubG1ppMjZWVFXu2TSfLZTIZqqqq2MJqYKAEEyYE4uLFjjMvQjrqLtOm6TBxYoeg0PkmuVxuUXMalPr6ely5coVtfBgo/Ump7C86nQ45OTnQ6XSIiYkxupt1b+lP1gvDMHB1dUVAQIDBUCW1hLGzszMYquzLaYtw5MUTxGIxe2TUF2iyIn1z3O24wJiCQgjBzZs3UVZWxhbfS0pKoNVqLUJM6AXN39+/X3fHxkB/spxmbchkMsjlcjzyyGlIJN6oqvKBs7MjHnrIHpMnd1iw6HQ69qhlwoQJRss/NxdSqRR5eXkIDQ2Fn5+f0R+/NymV+oX9vlw0tVotuxvXT4jkA71pS6YiQz+jjo6OcHR0hL+/P+vLVldXh4KCAmg0GoOhyrs1G5jbut4U8OdfEwNPbewt1JKiuLi418mKYrH4jjmR/kIvaAqFAnFxcRg0aBAYhoG9vT3bXSaRSHjThdOZqqoqNj7UFBe0/mJra8seTYwdq8P48Q2QyWogl8uh0WiQn99x5l1VVQWxWIzY2FjO7o77C33tzWnySFMq/fz82CNHuVzOduPpF/Z7umhqNBpkZWXBxsaGnYDnK53FBeho2FEoFAgKCupy96Lvy6Zfo5JKpbhx4wYcHR1ZcenKqbulpcXidsqd4d/Vqh/0RVBoAbmhoaFPyYr0H3+grsY0dlUsFmPixIkGxfeYmBj2qIF24bi7u0MikXTpPGtu6BQzbWnmg9Fgd+h/uOnEdFVVFW7cuAGNhoFU6oesrCb4+w/CI4/YwsmJv7tBSnl5OW7evMnpa69/5Kh/0aytrUVhYSHr4UbNLOnnhrY129vbmzy7yNhYWVmhurqaNdgcPHhwr4YqaWNJYGAgW6Oqq6vDtWvX/s+O6PehSjs7O05qKAkJCcjJyYFUKsXgwYMxbdo0rF69uk/x5fqISH9SVEyEVqvt17FSZWUlKioqEBcX1+PP0Yu5lZUVoqKi+tRVotPpcPToUTz66KP9LiAqFApkZWWx8y13s52n9QGZTAaFQgFnZ2d4eXlBIpH0KZTJGDAMw84KREVFWdydFE0pdHT0wfbto3DhggitrTowjBa+vu148806xMU5Y/Dgwby72OnbkURFRfU5Xtpc0El0euxI4w3c3NxQXl7eZVuzJVBdXY3r168jIiLiDiHvKuuFXlI7d45R6A2OXC5HXV0dcnNz8fXXXyMoKAiurq7YtWuX2XZvX3zxBSZOnIghQ4agsrISf/3rXwEA586d69fj8UpQdDpdv9p/a2pqcOvWLUyaNKnbn+lqWLEvEEJw5MgRPPLII/2yx66pqcHVq1fZ6X+gb5PvtHVWKpWirq4OdnZ27FyGqVs8qWW/TqdDZGSkxU3y0npPUFAQUlNH4P/9P2v4+XU4AatUBMXFBP7+LVi27BLEYq1Ju5v6Cp0gl0qliI6Othghp/EGNTU1qKioACEErq6u7HvW3DdE/aUnMemKzkOV+pdX/d2LPnV1dUhNTcWOHTuQn58PR0dHxMfHIyEhAQsXLjT679QT+/btQ1JSElQqVb+Og++LIy9q5TKQZEV6l9HXHRQhBMXFxSgpKUFERAQkEkm/Jt/1W2d1Oh3q6+shlUpZTyJ9yxJj1l1aW1uRnZ0NJycnREVF9enOSaMBLl/uCJ3y9iYYP54xuwdWTU0Nrl27hrCwMDg7++L4cTEGDyasu7GdnQjBwSJUV7vByelhjBnTkfFSXl6O/Px8g4uguaeY6dCfQqFAbGysSXM+jA0dFpTJZPD19cWwYcPYcLa+plRyRV/FBOjfUKWHhwdeeeUV/Pbbb0hISMD06dNx8OBBZGRkmFVQ6uvrsWPHDkyaNKnftcV7QlC6axtmGAaFhYWoqqrqk5VLd/R1FoUW3xsbG/HAAw+wxfeBTr5T7ybqqEqDroqLi5GXl8cm/tG5jP7S2NiInJwcDBkypM+W/dXVIrz/vjXy862g03W07YaFMVi1qufAqYFSUwPI5SJ4eBCo1WUoLi5GREQEPD07HINVKsDR0fD57ewAjYagudmwu6m9vZ09vikuLjbrrlB/TiM2NtbidoVKpRKZmZmQSCQIDQ2FSCTqd0olF/RHTDrT16FKal0/ceJETJw40Ti/SC94++238fXXX7MOHfv37+/3Y/HqyIthGGg03Wdid0dTUxMuXbqExx57jP2aWq3GlStXoFKpEB0dbRRbiYyMDLYodzeouaRIJEJUVBRsbW0N7lDo3Ymx6Vx3cXFx6dcxQ21tLa5du4bhw4ez5pS9hRDg7bdtcOqUFQIDO/y02tqA0lIrTJ6sw9q13adC9pfWVmDrVmucPWuFlhaAYVowfHgV3nrLHb6+HWldWi3wwgu2uHVLhGHDfn/b19cDKpUI332nRkhI1x8HnU7HZrzI5XIwDMPeYXt6ehq1W4wO2gJAZGSkxXWi0XqVr68vhg8f3uN7jhDCvmflcjkUCsUdKZXmPhozhpjcjc67F41Gg/DwcCxYsABfffXVgB575cqVWL16dY8/Q7s0AUAul6O+vh5lZWX45z//CVdXV+zfv79/Jzn3gqAolUr8+uuvmD59OgDDYcWIiAijHQGdPn0aY8aMueubjE4wU+t9/eJ75wKdKaFzGTKZjK27SCQS9g67qzcMIQRlZWW4desWxo4dC4lE0ufnLSsT4eWXbeHoSKBv6aVQAC0tImza1P2Fu79s2mSN1FQxJBIGOl09GhsZaDQeSEwEli79vS53+LAVPvnEBhoN4OZG0NoqQlsbkJSkwzvv9K5+RwhBU1MT+9oqlUq4ubkZHI31F5VKhezsbNjZ2SE8PJyXR0E9Qd/7AQEBGDZsWJ8vSvoplXK5HCKRyGDmxdTiag4x6YxWq8XLL7+MCxcuYPfu3ZjQnetpL6Gf954IDg7usj5YUVEBf39/nDt3rl+7pHviyIseRTEMA7lcjtzc3F4NK/bnee5WQ6mtrUVubi5CQkIwbNgwANzZzuvPZejfYV+5cgUADOZd6GtIC8Djx4+HS3c5vHehqanjaMnd3fDr9vYdu4Hm5oH+ZobIZMDp01bw9GQAyCAS6TBypBfq60X49VcR5s0DqPFxVBSDadN0OHPGCkqlCF5eBHPn6vDUU72vjYlEIri6usLV1RXDhw9n44/lcjk7b0BrWl3NG3QHDVNzcXExm/OAMaGNLwOZ3u8qpVIul6OkpAR5eXlsdrwpalpciIlOp8Mbb7yB3NxcXLhw4a4O3b2B3tj0B3qColKp+vX3eSUoAxlsBIDi4mKUlpZi7NixGDJkiDGXBqDnaXna2nnr1i2Eh4ezmQt8sVERi8UG1hoKhYIduKKus+3t7WAYBhMmTBhQATgwkMDdHairExnUS+rqRBg8GAgKMu7upL5ehOZmBnZ2MtjbiyCReMPKSgQXF6C8XIS6OhF8fAhSU8VYv94aDQ0iENKRZT9lCoPnntMN6AiOxh/7+wcgK4vB5cutIKQRQUF5sLfX9aphgu6q9WsOlkR9fT1ycnIwYsQI+Pv7G+Ux9VMqR4wYgba2NtbMkta06Gs70HZvLsSEYRj8+c9/xvnz55GRkWEUMekLFy5cwKVLl/DQQw9h8ODBKC4uxv/8z/8gJCSk3zUcXgnKQKmoqOjTsGJf6a4orz8sGRcXB2dnZ15nmIhEItZNdeTIkaivr2cNAbVaLa5evTqg9k4XF2DePC02bbJGaakIzs4dBW+dDli0SIs+OtvfFUdHJVQqLQhxgL//726tCoUIgwYReHkR5OWJ8O9/W0OlEiEgoCOMq64O2LLFGqGhDB5/fGDGn62twN/+ZoOMDDFUKkeIRJ7w9Q3B++/Xw86uih1UFYu9cO5cMLKy3GBnJ8aMGTpMn16PwsLsfps8cg09FTCVFQzFwcEB/v7+rM2JfkqlVmvY7t2XJgauxGTFihXIyMhARkaG0US4Lzg6OiI1NRWrVq2CUqnEkCFDEB8fj3/84x/9bgLhVQ2FENJnTy46rNjU1IS4uLheFcz7S2ZmJry8vAyK1PTMmxCC6OhosxXfjUVzczOys7NZ+3N6hi2VSlFfXw97e3uDzqbe/i4MA/z8sxipqWLIZCJ4ehIkJ+uQkKAzqjU87UT79ddxOHNmCDw9ARcXgqYmEWQyEZKTdXj9dS3Wr7fGf/5jjeBgYrAbKSkRYdo0HT7/vO+1O33WrrXGxo02cHVl4OTU0QAglYrg60tw8KAKzs5AZWUbFi+2Q0GBDQDm/94bVhg9Wop165oRGho4sBeDA2jr+ujRo01yKtAb6KAgPXZsamrqdUolV2LyzjvvID09HRkZGQgJCTHL85oDi96h0Mx1iUSC1tZWkxcwOx950QLk4MGD2QlgS8kwAX6/s9SP6tX3beqq7kLF5W6mgFZWQGKiDnPm6NDaCjg6wugZI9Rqffjw4YiL84CPjw4ZGWJUVVnByYngySd1WLSoo9BeX99xQel8XbGx6WgzHghqNZCaKoadHQGdO7SxAby9CaqrRThxQozERB3S0pxRXGwNPz8Ca2sClUqFlhYV8vI8sGePFElJ19iMFz56uHWmtrYWeXl5ZvUV6wqRSMRmx9P0xd6kVHIlJu+99x5SUlJw8uTJe0pMAJ4JSl/u5OmwIs1cl8vlJg3AAgyPvKRSKa5cuYLg4GAEBwcDACsmfN+VAB2vX1FREcLCwrq9s+xcd6ERvbTuQn3GvLy8up0oF4vBDhEae/2FhYUGF7OXXtIhOVkHmaxjDkU/Iy00lIGVlRhaLUCv1QzT0TwwbtzAjrva2gClUgRbW8PNvljc0UJdX9/x/xkZVhCLO8RGrdZCrdbAzc0B7e02qK0dARubYty4cQPt7e2s4WLn+GO+QOMCwsPD+10ANhW9Sam0tbWFVCo1qy8aIQQfffQRduzYgYyMDIwcOdIsz2tOeCUoQIeo9HQK192wojFSG++GlZUVtFotbt26heLiYowbNw4+Pj4GXj58FxNCCG7cuIGqqipERUX1+ohQJBIZFEjp7EBlZSWuX78OFxcXVlxMaXCnb1AZHR19x/rd3QF39zvfP/HxOuzZI0ZRkRXc3DqOvRoaRBgypGMnMxCcnTsaDa5dE8HRsaNe1NracewFdDQpAB1CwjAd7dwqlQqOjo6wtu7Ytjk52WPkyJEYOXIk+9rqxx/T4nNPxzfmgt6MmPPOvr90lVJ569YtVFdXQyQSoaCgwCwplYQQfPbZZ9i8eTNOnDiB0aNHm+R5uIZ3gtIT+sOKnXPnTZ35DnS8OaVSKbRaLSZMmAAXFxdeF987Q5sHmpubERsb2+8Lf+ccEpVKxc5kFBcXs3UXiURi1MG0gYRiubsD69ZpsGmTNc6csQLDAI8+qsOrr2oRHDywMqKVFfDqq1qsWGGD4mIriET4v4CmjtpRTo4VJk1iMH26DufOETQ3a+Dm5gSxuGMI08YGmDLl9/eufvwxrWnJZDLW2JTWBvqaRWIMysvLUVxc3KebET5Buxujo6Ph6upqlpRKQgjWr1+Pr776CseOHcO4ceOM8rh8hFdFeaBDNLpaEi0eDxo0COHh4XecMV+4cAFDhw41WZeJWq3Gr7/+CkIIJk2aBDs7O4sqvqvVaoPpa1OZHtK6i1QqhVwuB9D7usvdHpeGYkVHRw/oGKilBdDpAGM3A37wgTX++19r9lht1CiC6Ggdqqqs8NprGtjZFeDdd71RWOgNQkQQiTp+LjFRh08/1dy1xqSfRSKTyaBSqcxqWVJSUoLS0lL2Ymxp9FQzocOqtPbS3NxslJRKQgg2bNiAjz/+GEeOHBnw0CLf4Z2gaDSaO1pzab0iKCioWyuHrjqwjAW1khCLxXB2dkZ4eLhFFd+VSiWys7PZgTlz3dXSwTSpVMpeAD08PFiB6a2oUTEUiUS8tiL56itr5OZ2dHbZ2IA1wszLE2Hs2FI8+GApRo+OxsmTg/Drr1awtu7YmTz+ONPnhoWuLEtoZ5OXl9eAY3o7P1dxcTEqKioQExMDZ1MUxUwMFZPw8HB46hfXukE/pbKurq5fKZWEEGzevBnvvfceDh061KMb+r0CrwVFf1iQ1iu6IycnB66urux0urGQSqXIzc1FUFAQrKysoFAoMG7cOIs44gJ+t24fOnToXX2VTIn+BVAmk6GpqekOO/OuoNPjgwYNwtixY3ltRfL992KcPWuFsLDfP1IMQ/Drr0146KEa/OUv/ibbGdbVqVFU1AidTgq1Wgpra2t25zIQN19ac6uurkZMTIzF2Ofr01cx6UxXO8O7pVQSQvDDDz/g7bffxs8//4xHHnnEGL8K7+FtDUXfqTcuLu6uNiDGrqEQQlBaWoqbN2+yk/dlZWVob29He3s77O3teS8m1dXVyM/PR2hoKIYOHcrpWu5Wd3FwcGDFhdZd6M7Q29vbIqbHIyMJzp0Toa6OwMMD0OkY5OXJYW8vRkLCMNjaGn8nq1YDO3aIceDAIDQ1OcPR0R/TpmmRlCRDS4uUdfOlO8O+DP3RLBaZTIbx48dbZN75QMUE6DqlUiaT3ZFS6ebmBldXV9jY2GDnzp146623kJ6eft+ICcDTHQo9ohGLxb0OdMrPz4dYLEZoaOiA10DTCWUyGXtezDAMmpubkZeXh5aWFri5ubFdTXzLqSCEoKSkBGVlZQgPD+d9J45WqzVw8qVzBQ0NDQgKCkJwcDDvxQToqMukpIiRkWGF5maC+vp6uLoCixa5YPZs0zzn99+LsXWrNQYNAlxdOzrMFArgiSd0WL5c2+XQH60NeHl5YdCgQV2+toQQNqEzJiaGd+/x3lBTU4P8/PwBicnd0E+pPHDgAD7//HNERETg8uXL+PHHHzF//nyTPC9f4Z2gSKVSNkdh9OjRva5PFBYWQqfTDbgdT61WIzs7GzqdDtHR0V0W31UqFVsXaGhowKBBg9h5Da6T6PSjeiMjIy3uvJthGNy6dQslJSWwsbGBTqeDh4cHJBIJLxIU7wYhQH6+Cr/8cgvOzk54/HF/BAaa5v2gUAAvvGCH9nZgyJDfP8ZyOaDTddjx+/oafrxpbYA60tra2rI7Q+qHRYO9mpqaEBMTw8s5mLthDjHpjFarxfr167F9+3ZoNBqUl5dj4sSJWLBgAZYtW2aWNXAN7468pFIpQkJCEBAQ0KcLs1gs7rdDJqWlpQWZmZlwcXFBeHh4t5Pv9vb2CAgIQEBAADQaDXt0U1JSwlrEG7tltjfQqF6tVovY2FiLvBDcvn0b5eXliIqKgoeHB5RKJaRSKW7fvn1HgiIfj2CUyhbI5ZmYOdMboaH+Jv33r6kRoakJkEgMRcPVFSgrA6qqRHcISmcnhPr6esjlctYPy93dnTUJHT9+vMUFewHciAkAHD58GJ9++il+/PFHPPHEE6ioqMDBgwdRTydb7wN4t0PRarX9qoWUlJSgsbERUVFR/Xpeai8SGBiI4cOHA/g9Ya23xffOLbMikYidx3B3dzdpN1hbWxuys7Ph4OCAcePGWYR1hz6EEBQVFaG6uhpRUVFdtqW2t7cb+IzRs2v9uguXUF8xf39/sxzTyWTAiy/aQSQi0B9Wb2zsmNzfuFFtECTWE9SB+tq1a6yg6FvFc73z7i1cicmRI0fw7LPP4vvvvzd7Djyf4N1VZyAW9v0RIhoodePGDYwZMwa+vr79tp3Xtyqhlg9SqRTXr1+HVqtlP5yenp5GveArFArk5ORYTPG6M/rZ6RMmTOg2oMre3p6NkdWvu2RnZ7MDf+7uXpDLPUGIFUaOJDDXDXZdXR2uXLnSr4TL/uLl1dF2nJIihrU1gYtLx4xNdbUI06YxfYoJYBgGxcXFsLGxwYQJE6DT6dijsVu3bpk1/ri/cCUmGRkZePbZZ7Fx40YsWLDAbM/LR3i3Q9HpdP2yUKmqqsLt27cRFxfX679D6w10ctbNzc0kk+/6CX9SqRStra1s141EIhlQXUAqlSIvL69fx4R8QKvV4sqVK9BoNIiKiurXEQsV71OnWvDtt26oqnKAWGwNPz9g2TKC+HjTXvyoSSIXjrvNzcD69db49VcxlErAwQEYP57B8uUa9LYXQ6vVsnHVkZGRd9zs0J03FRg6UU5vjvgwF1RTU4Nr164hIiLCrGJy5swZzJs3D+vWrcOLL75ocZ8/Y3PPCEptbS2Ki4t7PTxEh+U0Gg07eU13JoBpJ9/pPIZUKmXnMejOprfdNIQQ1gajv1G9XEOt/21tbbt0P+gLFRUivPKKLWpqAC8vHXQ6FWpqRLC1VeNvf7uFBx90GnA8b9fP2+FrNW7cOM5MEgnpiF2uru6wehk+3NCivyc0Gg2ysrJgY2ODiIiIu86rdBd/rH80Zm64EpPffvsNycnJWL16NV5//fX7XkyAe+zIq7dCRNPxnJ2dER0dzR6XUW01tY2KvldTe3s7++G8ceMGnJycWHHprqWTYRgUFRWhtrYWMTExFmmDoVQqWev/vnTzdceRI2JUV4sQEsL832M5YPBg4OZNe2RnB2HUqAI2npe2ew/UaLG0tBQlJSWc+1qJRB3mlH1NwlSr1cjKyoK9vT3bhHL35zKMPy4qUuHAARXq61vg55ePsWPVkEg6di7mOBqjx1zmFpPLly/jySefxL/+9S9BTPTgnaD0l97WUORyOXJyctjMeQCcmjva29uzKXT64VZlZWVsS6dEImHDrWiiYltb24CjermCFq/9/PyMNr1fWSmCSESgf/0SiQB7exHq690QHR0NrVbbpdEizSDp7TQ5IQQ3b95EZWUlYmJi7jp0y0dUKhUyMzNZB4L+XPi3bxdjzRpXtLQAgAS2tsF47LFmvPLKDeTm5oIQYhB/bOyjMa5qJjk5OUhMTMQ//vEPLFu2TBATPe4ZQbG2tr6roJSVlaGoqAijR4+Gn58frzLfAcDGxgZDhgzBkCFD2JZO6mMGAO7u7mhqaoK9vT1iY2N5cXbdV/RDsYxZvO5ojxWBYX4XFUKA9nYRAgM7Zoisra3h4+MDHx8fg6aJgoICaDQaA5+x7l5bQgiuX7+Ourq6ATk2c0lbWxsyMzPh5ubW793htWsirF5tA42mYwZGJOpoCDhyxBkTJ47DH/6ghUKhYNvp8/LyMHjwYFZgBnr0yNUxV15eHubOnYu//e1vWLFiBefXDL7BuxpKf2KAAaC1tRVnzpzBjBkz7vgetT2vqalhjycsyXaeYRhUV1ejsLCQ/Zp+x5ilCEtXoVjGory8o4Yik3Vc4KysOuY0HB2BdevUiIrq/m1Op8npsCp1QqDiQi9+DMOwTgkDdTzmitbWVmRmZrKRz/193//739bYsMEavr6G9ZqqKhGiohjs3m34GW5ra2OPdhsaGgbU8s2VmFy/fh0zZ87EkiVL8P777/P6msEV98wORSwWgxDCCgRFo9EgJyeHzVCxt7dn50sA8F5MgI6o46KiIgQFBSEoKIgd9istLcW1a9cMkhP5OIh2t1AsYxAQQPCvf2nw739bo6xMBIYB/PwIlizR9igmgGGEbEhISJd1LQ8PDzQ0NIAQgvHjx/N+Yr8rlEolMjMz4e3tjZEjRw7ofd/cLAIhXUcqNzTc+bgODg7sMLB+yzeNVNA/GuupOYOrmklRURHmzJmDF198URCTHrhndiharRbHjh3DY489xt6x0w8QzVAxd/HdGNC7+u5aUltbW9k7a4VCwSYnSiQSo3c09Qf9UKzo6GiTu9VqNEBBgQhaLRAWRjDQTYRGo4FUKsWNGzeg1WphY2PDireph1WNCTXa9PX1NUrdKiVFjLfftoGnJ2Ft+hmmY4eycKEOn3yi6dXj0IgD6jXW2toKd3d3VmD0a4Rc7Uxu3bqF+Ph4LFiwAGvXrrWYf3Mu4J2gAOiXhQohBEeOHMGUKVNgb2+Puro65OTkYOjQoWx2M62XiEQi3r8paOG3oqICkZGRvbqr13fwraurYzuaJBKJUfMxeosxQ7G4or29nXUgGDNmjEHLLK27UJ8xvh49NjU1ISsrCwEBAQgODjbKYyqVwDPP2CI31woODoCVFUFLiwgSCbBtmwqjRvXvsqJUKtnGicbGRjg5dbR7W1lZ4datW4iIiDBre3ZZWRni4+Mxd+5cfPnll7y/bnDNPSMoAPDLL79g0qRJqK+vR2FhIcLCwjB06FDeFd/vhk6nY835oqKi+lX4pR1N1AbGxsbGoGPM1B8MSwnF6onW1la2tTksLMzgNeuu7sI3B+rGxkZkZ2dj2LBhCAoKMupjy2TAhg02OHhQDLUaeOABHZYs0SI83DiXFNr1WFFRgcbGRlhbW7OvrznijysrKzFjxgw8/vjj2LhxoyAmvYCXgtJdDPDdOHbsGDw9PVFXV8ee1VuamJgiqpdhGLZjTCaTgRBilFje7rCkUKzuoEdEPj4+vao3dC460ztrY8y79Jf6+nrk5ORgxIgR8Pf3N9nz6HQdf0xRVqqtrcW1a9cwduxYWFtbs68xjT+mR2PG3v3W1NRgxowZeOihh7B582aLfA9zwT0jKBqNBhkZGbCzs0NsbCwcHBzMNvluLGgOjLOzs8kuxNQEUCqVQiqVQqVSsR/Kntple4ulhWJ1Bb2rp00Qff0d6J01PXoUi8UG8y7muNOVy+XIzc1FaGgo/Pz8TP58poBa2oSHhxsccxFC2JArWjs0ZvyxVCrFzJkzER0djW3btlmc0SqX3BOCQqeu29vbMW7cOHh7e9+RYcL3C1tDQwOuXLli1GG/u6EfviSVStHS0oLBgwezxwp9veujccP9vRDzAXohNtZdPY2Ppa9xZ5NQUxwFSqVSXL16lRNvMWPRnZh0hVqtZvPf5XI5m//e14FVoOPff/bs2Rg1ahR27txpkUe1XMJLQdHPlb8btPju5+eH+vp6DBs2DF5eXndkmPAZvkT10mMbqVSKxsZGODs7GwSH9QTtwAkLC4Ovr6+ZVmxc6O8wZswY+Pj4GP3xCSFobm5mX2OlUslmkxur7kJ/B1PM+piLvohJZ/QFXCaTQa1Ww93dnX2Ne2qrb2howJw5cxAYGIiffvrJIlvDucaiBeX27dsoKChgi+8XL15kJ6EtoV5Co3pLS0vNbh9xN9RqNXvhq6+vZzPfJRLJHTWBsrIyFBcX8+536AvU5NGcv0NXdRe6O+zPsU1VVRUKCgo4NaocKAMRk84QQlgjVplMhqamJjg7O7Piou+Vp1AoMHfuXHh7eyM1NZWX81yWgEUKCiEEBQUFqKqqQlRUFNzd3UEIwdWrVyGXyyGRSODt7c3b3Aag406KWnhERUXxOqqXDqLRjjGa++Lp6Qm5XM46EFiiSSUhBKWlpSgtLUVUVBTc3Nw4WYd+3YUe21ABp9G8PUEFMSIiAh699a3nGcYUk66gN0lyuRx1dXVoampCWloapk+fju+//x7Ozs7Yt28fZ+3tn3zyCVJTU1FQUAAHBwdMmjQJq1evRmhoKCfr6Q+8FJSeUhtpfkZraytiYmLY4jvDMNBqtWzBWb+bSSKRwMPDgzfiotFokJubC41Gg8jISIuaz6BHCrW1taiurgbDMPDy8sKQIUPg6elpUd0whBDcuHED1dXViI6O5o2o0648emet0+l6zB+hMQa9nVfiI6YWk87Q1vy1a9ciIyMDCoUCs2fPRnJyMmbPns3JDi8+Ph5PPfUUYmNjodVq8fe//x15eXnIz8+3GM84ixIUOhdgb2+PiIgIWFtbd1t8J4Sw5n/6xVB6Z83Vhc/So3oBw1CskJAQ9nVub283GPTj8xk03SHW19cjJiaGF64CXUHrLvQmqXPdpaamBqWlpYiOjrbIHSJgfjGhtLW1Yf78+VCpVFizZg1OnDiBffv2obi4GLW1tZx/NmUyGSQSCU6dOoWHH36Y07X0FosRlPr6emRnZ8PX15dtR9W3Uelp90FDgai4tLe3G4iLuTo5aFSvRCJBaGgob3ZMfUGlUiErKwt2dnYGoVj659VSqRTNzc28HPQDOu5O8/LyoFQqLW6CX79xoqGhAQDg5+eHoUOHcuKGMFC4EpP29nY8/fTTUCgUOHLkiIEYNzU18SKS4ObNmxgxYgSuXr2KsWPHcr2cXmERglJRUYHr168jNDQUAQEBAxpWpBe+2tpattOG3lV7eXmZ7K6aRvUGBwcjMDDQ4j74QN9Csdrb29m76oaGBgwaNMigY4yr35/urnQ6HaKioiyyLZQe1VVVVSEwMBDNzc0GbgheXl69qrtwDVdiolarsWjRItTU1ODo0aO8PCZkGAYJCQlobGzE2bNnuV5Or+GloNAYYEIICgsLUVlZicjISHh4eIAQwiYzGmO+hJor0jheNzc3eHt7G3X6try8HDdv3sSYMWMstpVzIKFYGo2Gvauuq6uDnZ0dKy59tS4fCGq1GtnZ2bC2tmaPTC0N2pBCzTbp2Xp3dRdaP+SbcHIlJhqNBs8//zxKSkpw4sQJ3jYwLFmyBIcOHcLZs2c5HSXoK7wVlPb2drb4Hh0dDUdHR7b4biobFXpXTecwqHOvt7d3v45sqCBachcUYNxQLJ1Ox3aMyWQyNjVRIpGYdIq8vb0dWVlZcHJywrhx43h/994VhBDk5+ejoaGBbUjp7uc6574PZGDV2HAlJlqtFi+99BKuX7+OEydOQCKRmO25+8LSpUuRnp6O06dPY9iwYVwvp0/wUlCam5tx8eJF2NnZITIyssfiu6lQq9WsuNTX1xsc2fTGgl3faTcyMpK3Rd+7YcpQLP3URKlUCp1Ox9a27paL0RfoUZ27uztGjx5tkceNDMOwhqExMTF9EgV9m5LGxkbWpoS+l835enAlJjqdDq+//jqysrKQkZFhksHVgUIIwbJly7B3716cPHmSjSi3JHgpKDU1NaiursaoUaP6VHw3FZ2PbBwcHHq0hVepVAZHK3w7bugN+qFY5mhH1b+rlkqlaGtrMwgO629ty9g5IFzAMIxBDMBAhu6oTQn1GTNn3YVLMfnTn/6Es2fP4uTJk7z1NnvjjTewc+dOpKenG8yeuLq68qqppSd4KSgMw0Cj0bBHXDqdjjeT73TIr7a2li2E0mMxV1dX1uCxN4VrvmLuUKyuoKmUdMLZ1dWVFfHefrgaGhqQk5ODoKAgizs6oOh0OuTm5kKlUiE6OtqoTSM6nc6g7sIwjIHPmDFrTFyJCcMwWL58OY4dO4aMjAwEBgaa7bn7SnfXty1btmDx4sXmXUw/4a2gqNVq3tvO0w8kvfABHYLj4+ODsLAwixryo9ALWFtbG29aamkkL22VpRYlPR3Z0LrPyJEjLaqoqY9Op0NOTo5ZOtI67xBpciLdvQzkfcClmKxcuRL79u3DyZMnjRYuJtA9vBSU48ePAwBiYmJgY2PDSzHpTEVFBQoKCuDm5galUsnbKf2esIRQLGpRQo8fbW1tDYLDRCIRa7ZpyQaJWq0W2dnZ7L+FuTvSuqq70OPHvtRduBST9957D7t27UJGRgab2ipgWngpKB988AE+//xzODk5ISEhAUlJSZg4cSIv2zwJISguLsbt27cRERHB+oopFAp21kWj0bAXPb7ak1hiKFbnHaJIJIKDgwOam5vNfgEzJhqNBllZWbCxsUFERATn/xZd1V2ouPTkl8eVmBBC8K9//QtbtmxBRkYGwsLCzPbc9zu8FBSg45jj2LFjSE1NRXp6OqytrTF37lwkJSVh8uTJvLh7pp03CoUCkZGRXdYa9K0zamtrWXsSb29v3uSQ3wuhWDqdDgUFBaiuroaNjQ3bMWbK3BFToFarkZmZCQcHB4SHh/NuZ9td3aVzZx7NZBk3bpxZ23MJIfjss8+wYcMGnDhxAuPGjTPbcwvwWFD00Wg0OHnyJPbs2YO0tDRotVrMmTMHSUlJmDJlCidW02q1GleuXAEhpE9RvTSHnAZa0U4miUTCiffVvRCKRQhBUVERampqEBMTAycnpztyR/Q7xvhqTa5SqZCZmcnuEvkmJp2hO3EqLrTuYm9vj6qqKoSHh5tdTNatW4d///vfOHbsGKKjo8323AIdWISg6KPVanH27Fns3r0baWlpUCqVmD17NhITE/HYY4+Zpb2utbUV2dnZAz4e6mpKn4qLOYrh90IoFsMwyM/PR2NjIzsA2xn6OtO4WDqwKpFIeDMf1NbWhszMTLi5uWHMmDEWKexKpRIlJSWorq4GALi4uHSZPWIKCCH45ptv8Mknn+DIkSOYMGGCyZ5LoHssTlD00el0+O2339idS319PWbMmIGkpCRMnz7dJJbP1ILE19cXI0aMMNqHpLspfVNd9O6FUCw6PEo70nqz81CpVAbBYU5OTmx9iytzxdbWVmRmZsLT05OdvbJE9I+53NzcDJon7OzsWHExdk4RIQT/+c9/sGrVKhw6dAiTJk0y2mML9A2LFhR9GIbBpUuXsGfPHuzduxfV1dV4/PHHkZSUhPj4eKO4h9bU1CA/P99oeePdQYOAamtr2YsenXUZqLEiPR6qrq62aDsYrVaLnJwcMAzT75ZarVbLXvT0zRVpx5g5jpyUSiUyMzPh7e2NkSNH3hNi0vmYq3PdhRDC1rcG6ohACMG2bduwcuVK7N+/32Js3u9V7hlB0YdhGOTk5CAlJQWpqakoKSnBtGnTkJiYiNmzZ/fZkJCm+pWUlJg9XlW/TVYul8Pe3p4Vl77eUes3EXR3PGQJqNVqZGVlwdbW1mhdUNRcsXM4G73omaLTijZD+Pn5ISQk5J4Uk850V3fpT32LEIKdO3di+fLlSE9Px6OPPjrQX0VggNyTgqIPIQTXrl3Dnj172HjNqVOnIjExEXPmzIGHh0ePH2T9qfHIyEhOcxJ0Oh0rLjKZjG3f1J/B6A5q267VahEVFcXr8KueoCaPpixc04sePYJUqVRGz89pampCVlYWAgICLHrgbqDdXPqZ7wqFAs7Ozqy49LQbJ4Rg9+7dWLp0Kfbs2YP4+PiB/ioCRuCeFxR96HEP3blcuXIFkydPRmJiIhISEiCRSAzewFqtlrW9iIqK4sXUOIVhGAPXXpFIxIpLZ0+m7kKxLA1q8ujh4YGwsDCz3NETQtjOPJlMhpaWlgE79zY2NiI7OxvDhg1DUFCQ8RdtJozdGkyPeum8S091l7S0NLz66qv43//9X8yZM2fAzy1gHO4rQdGHmh+mpKRg7969uHTpEiZNmoSEhAQkJiaira0Nb775JlauXIkHHniA1xdhfdfe2tpagyl9e3t75OTkWLS3GPD7Hf3QoUM5PR5qa2tjdy76d9Q0OOxu1NfXIycnx+R1OFNj6jkTGnNABQYATp8+jcDAQDg5OWHJkiXYvn07kpOTjf7cfeH06dNYs2YNMjMzUV1djb179yIpKYnTNXHJfSso+hBCcPv2baSmpiI1NRW//vorBg0ahOjoaKxfv96izrf1j2uqq6uhVqvh6OiIkJAQoxv+mQs6K8O3O3p6R007xhwcHFghd3FxueM9I5fLkZubi9DQUN463vYGcw8t0vf0xx9/jLS0NFRXVyMiIgJLlizB3LlzObWiP3ToEH799VfExMTgiSeeEARFEBRDfv75Zzz99NN4/PHH2fjN8PBwJCUlITEx0WLERSaTITc3F/7+/rCysmIt4fXjji1hepyaPPL9IkxdqGnzhFgsZl/nwYMHQy6X4+rVqxg9ejSGDBnC9XL7DVcT8ACQkZGBhQsXYtWqVWAYBvv27cOFCxfw7bff4uWXXzbrWrpCJBIJgiIIyu9cuHABjz32GLZs2YL58+eDEAKZTIa0tDSkpKQgIyMDo0aNYsWFrzMD3YVi8W1K/25UV1fj+vXrFhedzDAMGhoaDILDdDodgoKCEBwczLk3V3/hUkzOnDmDefPmYf369XjhhRfYz11tbS3EYjEvZqkEQREExQAa2Ttq1Kguv9fQ0ID09HSkpKTg2LFjCA4ORmJiIpKSkjBmzBjO6xN9CcVqa2tjzStp3oi3t7fZpvTvRnl5OW7evImIiAje5n73hsrKShQUFMDT0xMtLS2slxvtGOOjkHcFl2Ly22+/ITk5GatXr8brr7/Oy5s4QBAUQBCUfqNQKPDzzz8jNTUVhw8fhp+fHysukZGRZheXgYRidc4boYVmb29vs8+qUFG8ffu2RQ9eAh07xaKiIlYUCSEGwWHNzc2s3Y6XlxdvU/m4FJNLly4hMTERH3zwAZYtW8ZbMQEEQQEEQTEKzc3NOHjwIFJTU3Hw4EF4enpi7ty5SE5ORmxsrMnFxZihWPqF5rq6ul6FWRkLukOUSqWcJUUai7KyMty6davHnSK125HJZGhoaGAzR2jHGB8unlyKSXZ2NubMmYN3330XK1as4MXr0ROCoAiCYnRaW1tx5MgRpKSkYP/+/Rg0aJBBpouxz89NGYrV3ZR+d11MA0Hf5DEmJoa3d+u9oaSkBKWlpYiOju71DotmjlAhp6+1l5dXn50djAWXYnL16lXMmjULK1aswDvvvMN7MQEEQQEEQTEpNNMlJSUF+/btg42NDZvp8tBDDw344m/OUCw6F0DvqK2trXs9pd+bx9YfIOWrvfzdoGFrFRUViImJgbOzc78ep/NrbWVlxbYju7u7m+U4lUsxyc/Px6xZs/DGG29g1apVvBaTlpYW3Lx5EwAQFRWFzz//HFOnToW7uzsCAgI4Xp35EQTFTGg0GmRkZGDPnj1IT0+HTqczyHTpa3GWy1Asfd8rqVQKkUgELy8veHt73zGlfzc0Gg1ycnIAgLexw72BEIIbN26guroaMTExRjuuox1j9BiSBod1DrQyJlyKSVFREWbOnInFixfj448/5rWYAMDJkycxderUO77+/PPPY+vWreZfEMcIgsIBWq0WZ86cwe7du5Geno7W1lbMmjULiYmJmDZt2l1rIHwKxdKf0qcXPHo3fTdTRWrySC1hLLWdlhDCNkTExMSYrJGBEIKmpiZWXNra2gyMFY3RMcalmBQXF2PmzJlYuHAh1qxZw3nXpEDfEQSFY3Q6Hc6dO8dawDQ2NhpkunS+OPE5FKuzqaJarTYwVdS/m6bHdS4uLrxoue4vhBDk5+ejoaHB7LUf/Y4x2vpNjyH7sw4uxaS0tBQzZ87E3Llz8eWXX1rs++F+RxAUHsEwDC5evMiKS01NjUGmy+eff46qqip89NFHvBjk6glqqkhnXejdtLe3NxwcHHD16lVIJBKLzbAHfo8DaG5uHnB33UDp3Prd1+486qzQeRjWHFRWVmL69OmYPn06Nm7cKIiJBSMICk+hmS579uxBSkoKG6v6l7/8Ba+99hpnnT/9hd5NV1VVobW1Ffb29ggKCoJEIrHIIjzDMLh69SpaW1t7nRZpLjp351HX3u4aKLgUk+rqasTHx2Py5Mn4z3/+Y7HHngIdCILCc9RqNRYvXowzZ84gOTkZJ0+eRGFhoUGmi7u7u0WIC639+Pv7w8bGhnXsHehRjbnR70qLjo7m9bQ7TUvUjznQDw6rq6vjTEykUilmzpyJ6Oho/PDDD4KY3AMIgsJz/vjHP+LChQs4cOAAvL292eE/mumSm5uLyZMnIykpCXPnzr0j04UvSKVS5OXlYdSoUQa1H5VKxdZc9Kf0e2sHb250Oh1ycnKg0+n6HT3MFbSBgh6NqdVqMAyDgIAAhISEmNWJWi6XY/bs2QgLC8POnTst0gVb4E4EQeE51dXVcHZ27rINVT/TJTU1FZcvX8akSZPYwDBfX19eiEtVVRUKCgowduzYHou9dLivtrYW9fX1cHR0NNuUfm/QarXIzs5mh0gt+SIolUqRm5sLLy8vtLa2QqlU9juKt680NDRgzpw5CAwMxE8//cTrHZ45IIRw/t42FoKg3CMQQlBeXs5muvz222+IjY1FYmIiEhMTERAQwMmbllqQREREwN3dvdd/T6vVGtQBbG1tWfNKY0/p9waNRoOsrCzY2NgYLceeK7qqmbS2trI7xaamJri4uLBibsw2aIVCgblz58Lb2xupqam8qj2Zm4yMjC5nWCwZQVDuQQghqKqqwt69e5GSkoKzZ88iIiKCtd0PDg42+QVZf2o8OjoaLi4u/X6szpPjNGuExh2b+ndRq9XIzMyEg4MDwsPDLboLqTcFeJVKZRAc5uTkxBb1nZ2d+/16Nzc3IzExES4uLti3bx8vXK25orq6GkFBQZgxYwb27dsH4N7YqQiCco9DCIFUKmUzXU6ePImwsDBWXEzRtksH/WQyGWJiYoxaC9Gf0pfJZCCEsOJiClsSlUqFzMxM1t7mXheTznTeKdrY2LDHYp1z3ntCqVTiiSeegLW1Nfbv38/L+pg5IYTg2LFjWLx4McaPH4/09HT265YsKoKg3EcQQlBfX4/09HSkpqbi2LFjCAkJQUJCApKTk42SOc8wDPLy8tjZDFN2bRFC0NjYyM669GVKvze0tbUhMzMTbm5uGDNmjEV/0I3RGswwjEHOOyHEoGOsu9e7ra0N8+bNg1arxaFDhyzaRdrYnDp1Ck8//TQiIiJw6NAhAJYtKoKg3KfQqXaa6XLkyBH4+fkhKSkJSUlJiIiI6LO46HQ6XLlyBWq12uzttNSWRCqVora2FiqVCp6envD29r5jSr83tLa2IjMzE56enrxN5uwtppgzoWKu3zGmHxxGu9/a29vx1FNPobm5GYcPH+ZFvs0333yDNWvWoKamBhEREfjqq68wYcIETtbCMAzOnTuHhQsXYvTo0fjll18gEoksVlQEQREA8HumS0pKCg4dOgRPT0925zJ+/Pi7igs1eeRDBxSd0qdF5tbW1j55XimVSmRmZsLb2xsjR460yA82xRxDi/qvt0wmQ11dHb744gs89thjuHz5MmQyGY4ePdpjgqi52LVrF5577jl8++23iIuLw7p167B7924UFhaaxW5Gp9NBLBaDXnbpe+v8+fOYP38+QkJCcOzYMVhbW1ukqAiCInAHra2tOHz4MFJSUnDgwAE4OzuzmS4PPPDAHUcbKpUKWVlZsLe356XJI53Sl0qlaG5uxuDBg9m6S+cuI+ri7Ofnh5CQEIv7QOvD1QS8TCbDN998g7S0NNy8eRPR0dGYN28ekpOTERoaarZ1dEVcXBxiY2Px9ddfA+jYIfj7+2PZsmVYuXKlSZ+biklJSQm+/fZbXLlyBVOmTMH48eMxbdo0XL58GU899RS8vb1x4sQJ2NnZWZyoWG6FUcBkODo64oknnsCOHTtQU1ODDRs2QKlUYuHChRg5ciTefPNNnDx5EhqNBgUFBXjjjTfg5OTE23ZaJycnDBs2DHFxcXjwwQfh5eWFmpoanDlzBpcuXUJZWRna2trQ1NSEzMxM+Pv7Y/jw4Rb1Qe4Ml3YqgwcPxq1bt2Bra4u8vDwsWbIEZ8+eRXh4OLKzs826Fn1ot960adPYr1lZWWHatGn47bffTPrchBCIxWKUlZXhgQceQFVVFSIiIpCZmYk//OEPuHTpEsaPH49du3ahsbERkZGRaG1ttbj34H25QyktLcWHH36IEydOoKamBr6+vli0aBHefffd+37IqifUarVBpotWqwUhBA8++CC2bdtmEbYp+nRujyWEwMPDA6GhoRbdhcSlmOh0Orz++uvIyspCRkYGfHx82O81NzfDycmJs065qqoq+Pn54dy5c5g4cSL79bfeegunTp3ChQsXTPr8arUazzzzDFxdXbF582YAQHh4OIYNG4YdO3awzQrZ2dl45plnsH37dkRHR5t0TcbGckd9B0BBQQEYhsGmTZswfPhw5OXl4ZVXXoFSqcTatWu5Xh5vsbW1xYwZMzBjxgw8//zzmDVrFsaMGYPMzEwMHz4cs2fPRlJSEh599FGLmDGws7PD0KFD4ejoiIaGBvj4+ECr1eL8+fNwcHCARCKBt7c3L6b0ewvXYrJs2TJcvHgRJ0+eNBATAP1OsLyXqKmpwTPPPAMAmDx5Mtzc3PDDDz9g0KBBOHPmDDw9PREVFYVLly5Z5E3NfSko8fHxiI+PZ/8/ODgYhYWF2LhxoyAoveD8+fOYNWsWPvroIyxbtgw6nQ6//vorUlJSsHz5cigUCsTHxyMpKQmPP/64yQKnjIFcLkdubq5Bvoz+7MWlS5dga2vL1lz47PLMpZgwDIPly5fj9OnTyMjIgJ+fn1mfvzd4enpCLBajtrbW4Ou1tbV3iJ+xoDUQhmGgVqvh6uoKsViMOXPmQKfTYf/+/XB1dYVcLsfu3bvxwAMPYNSoURYpJoBQQ2FRKBR9sga5nxk9ejR27NiBZcuWAQDEYjEefvhhrF+/HqWlpThy5Aj8/f3xj3/8A0FBQVi0aBH27NmD5uZmjlduiFQqxZUrVzB69GgDw0pra2v4+PggPDwcjzzyCEJDQ6FWq5GdnY0zZ86goKAA9fX1YBiGw9UbIpPJcPXqVc7E5O2338aRI0dw7NgxBAYGmvX5e4utrS1iYmJw/Phx9msMw+D48eMGR2ADhRACnU4H4PcuLisrKwwaNAhhYWFITExEaWkpjh49yl5zDh8+jJ9//hnDhg3j7Q1Lb7gvayiduXnzJmJiYrB27Vq88sorXC/nnoFhGGRnZ2PPnj1ITU1FeXk5pk2bhqSkJMyaNYsTTy4KTb7sSzohzXevra01GOzz9vY2yZR+b6FiMmbMGE7E5H/+53/w008/4eTJkxgxYoRZn7+v7Nq1C88//zw2bdqECRMmYN26dfjpp59QUFAw4NeupaXFYGizvb0dGzZsgFgshqurKxYvXgwAePXVV7Fz505s3LiRHTZeuXIlvvvuOzz33HMDWgPX3FOCsnLlSqxevbrHn7l+/TpGjRrF/n9lZSUeeeQRTJkyhS2UCRgfQgjy8vJYcSkqKsKjjz6KxMREzJ4926yZLtT9ODw8vN/Jl3Swj7Yja7VadpDSGFP6vYVLMSGE4MMPP8TWrVuRkZGBsLAwsz5/f/n666/ZwcbIyEh8+eWXiIuLG9BjymQyvPjii0hMTMTLL78MABg+fDgcHR2h0WjQ2NiIwMBApKamws3NDW+99RZ++eUXqNVqjBo1Cs8++yxbW7Fk7ilBoUNVPREcHMx2clVVVWHKlCl44IEHsHXrVov2abIkaKYLFZe8vDyDTBcvLy+TiUtFRQWKiooQGRlptCNO/Sl9qVSK9vZ2eHp6soOUphry5LJmQgjB6tWrsXHjRpw4cQLjxo0z6/PzjWvXruHtt99Gc3MzXnjhBYhEIqSnp2PXrl1obm5GRUUFu0PJysoCAJSXl7MNH3wY+jQG95Sg9IXKykpMnToVMTEx2L59Oy/nJ+4HqCsxzXTJysrCxIkTkZSUhISEBAwZMsRo4kKt9KOiouDm5maUx+wMIQRKpZL1F1MqlawlSW+m9HsLbSYYPXq0yQrK3UEIwRdffIEvvvgCx48fR2RkpFmfn6/k5eVh9erV7I71wQcfxAcffMB+v7S0FI899hhmzpyJr7/+mi3YW9rwYk/cl4JSWVmJKVOmIDAwENu2bTMQE3N/OAV+h2a6UHE5f/48JkyYwGa6+Pv79/uDV1JSgtLSUkRHR5vVT6pzzgid0vfy8up3azXXYvL111/j008/xS+//ILY2FizPj/fuXbtGj777DOkpaVhzpw52LFjB4COWpOVlRXeeOMNlJWV4cCBAxyv1DTcl4KydetWvPDCC11+7z58OXgJzXShgWFnz55FZGQka7vf224Y/VyWmJgYTmch2tvbWXFpbGxkQ6y8vb17PRTKtZh89913+Oc//4lDhw4ZtTPKUulqd3Hjxg18/PHHOHr0KFasWIG//OUv7Pfef/99nDx5krXwv1d2JpT7UlAELAtCCGpra5GWlobU1FScPHkSo0ePRmJiIpKSkro1cCSE4MaNG6iurkZMTAyvbNPVajUrLvX19Rg0aJBB3HFXyOVyXLlyBWPGjOFETLZu3Yp33nkH+/fvx8MPP2zW5+cj1JsLABobG2Fvbw9ra2tYW1vjxo0bWL16NS5duoTp06fjySefRE1NDRYtWoRVq1bhb3/7G8erNw2CoAhYFPqZLikpKTh27BhGjBjBOiOHhYXBysoKOp0Ohw8fhouLC2JiYng9XKnRaFgLmLq6OnZKXz8hkeudyY4dO7BixQrs27fvnout7Q/6YrJ06VLk5uaCYRg88sgjWL58OTw8PHDz5k2sWbMGP/74I1xdXZGUlISwsDD86U9/4nj1pkMQFAGLRT/TJSUlBb/88guGDh2KuXPnIi8vDzdu3MD58+d5tTO5G1qtFnV1daitrYVcLoetrS2cnZ0hl8sxevRoDBkyxKzrIYRg9+7dWLp0KVJSUjBjxgyzPj/fSUxMxK1bt/Duu++ipKQEW7duRVhYGDZs2ABfX1/cvn0bH330Ec6ePYuvvvrqnhdjQVB4xEcffYQDBw4gJycHtra2aGxs5HpJFkVzczPS09Px97//HY2NjfD398fjjz+OpKSkXmW68A2dTofS0lKUlJTAysoKYrGYrbn0JX53IOzduxevvvoqdu3ahTlz5pj8+SyJNWvWYM+ePTh48CA8PDzw4YcfYu3atQgKCoK3tze2bNkCPz8/FBcX49q1a0hISOB6ySbnvvTy4itqtRrz58/HxIkT8f3333O9HIvD1tYWqampGDx4ME6dOoWsrCykpKQgMTERrq6uSEhIQGJiYpeZLnykoaEBZWVlGDt2LCQSCRoaGiCVSnH16lV2Sp/GHZtCXPbv349XX30V27dvF8SkC3x8fJCYmAgPDw+sWbMGGzduRHp6OoqKivCXv/wFixcvxoYNGzBixAiEhIRwvVyzIOxQeMjWrVvx5ptvCjuUPnL58mUsX74caWlpBkOLbW1tOHr0KFJTU7Fv3z7Y2dmxgWEPPvggp+mS3dFTzYQe9dFZF41Gw4oLNUAcKIcPH8azzz6LLVu2YMGCBQN+vHsVhUKBhoYGJCcnY+XKlVi4cCHKysrYo8ElS5bgz3/+M8erNB/8+yQJCPST8ePH49SpU3d0fDk4OCAhIQEJCQlQq9U4fvw4UlNT8dxzz0EkEmH27NlITk7Gww8/zIs8nLsV4EUiEdzc3ODm5oaRI0eiubkZUqkUN2/eRF5eHjulr5/t3hdOnDiB5557Dps2bcL8+fON8SvdE3TVIuzq6orc3FxUVFRg9OjRADpMR6OiorBs2TJMmjSJi6VyhrBD4SHCDsU8aLVanD59Grt370ZaWhpUKhWb6TJ16lROMl0G0s1Fp/RpO3JLSwvc3d3ZjrHeiOXp06cxf/58fPnll1i8ePE9NyfRV44cOYLm5mYkJSV1m/NeWFiI5557DsHBwUhMTMR7772H6dOnszHD9xOCoJiY/hhWCoJifmimy549e5CWlgaFQoGZM2ciKSkJ06ZNM0vbsbFbgztP6bu5ubHi0pVYnjt3Dk888QQ+++wzvPbaa7wUE3M1rlAL+ocffhjNzc348MMPMXv2bNjY2NwhKjqdDhs2bMCuXbsglUrx4IMPYsuWLSZZF98RBMXE9NWwEhAEhWsYhsGFCxdYcamtrcWMGTOQmJiI+Ph4k7Qhm3rOpKspfS8vL6hUKowaNQqXLl1CYmIiPvzwQyxdupSXYgIAq1atgpubGyoqKvD999+b/DOiVCoxf/581NbWYuXKlUhISICdnd0dPlzNzc1ob28HwzBmN+rkE4Kg8BBBUPgDwzBst1hqaipu376NadOmITEx0WiZLuYeWlSr1axT8VNPPYWhQ4eipaUFzz//PD777DOLaK82x2dEq9XC2toaarUaSUlJqKqqwsqVK5GUlGSww7tx4wb++te/4s0337zn50zuBv/fOfcR5eXlyMnJQXl5OXQ6HXJycpCTk4OWlhaul3bfYmVlhfHjx+OTTz5BQUEBzp8/j8jISHzxxRcICgrCvHnz8MMPP6C+vr5fPnBcTMDb2trCz88PM2fOxMGDB+Hq6gpvb29s2LABYWFheOedd1BVVWWWtfAF+m+nf5pgbW0NnU4HW1tb/PzzzwgMDMTHH3+MlJQUtLe3A+hwEJ43bx7Ky8vvezEBBEHhFe+99x6ioqKwatUqtLS0ICoqClFRUbh8+TLXSxNAR3dVeHg4PvjgA1y9ehU5OTmYNGkSNm3axBZk//vf/7Jpjnejrq6OMzsVAMjPz8czzzyD5ORkXL16FTKZDJ988gnKy8uh0WjMvh4uEYlEuHr1KqKiolBTU8N+XSwWszYr6enpGDFiBD755BOkpKSgqKgI8+fPh6OjI7KzszlcPX8QjrwEBAYIdTSmgWHZ2dmYNGkSm+ni4+Nzx7FYXV0drly5grCwMLPbqQAdnUkzZ87Eiy++iI8++ojTmglfGlfOnTuHhQsXIjc3947AK33vrqeeego5OTlQKBTw8/MTbvj0EARFQMCIEEJQVlaGlJQU7N27F+fPn0dcXByb6TJ06FCkpaUhLy8PL7/8MidiUlxcjPj4eDz11FNYs2YN5zUTvjSuqNVqjBgxAv/+978xb968O76vLyrz5s1DTU0Nzp49a7TnvxcQjrwEDPjmm28QFBQEe3t7xMXF4eLFi1wvyaIQiUQICgrCihUrcObMGZSWlmLhwoU4ePAgxo4diwcffBAvv/wy7O3tOTnmKi0txZw5c/DEE0/wQkwAwMvLC6NGjerxj7EHThmGueP/CSEYMmQISkpKuvw79PgLAPbs2SOISRdw/24S4A27du3C8uXLsWrVKmRlZSEiIgIzZsyAVCrlemkWiUgkwtChQ/GnP/0JGRkZ+PHHH1FQUIDw8HB89NFHeOihh/DZZ5+hsLDQLMFuFRUVmD17NmbOnIn169fzQkz6irEaV6ysrHDz5k3s3r0bFRUVaG5uhp2dHZ544gk2852Khz5isfgOMRL4HeHIS4AlLi4OsbGx7IQvwzDw9/fHsmXLsHLlSo5XZ9kcPXoUycnJ+O677/D000+jvr4eaWlpSElJwfHjxzFixAgkJiaymS7GrmlUV1cjPj4ekydPxn/+8x+LMMfsisWLF2Pbtm13fD0jIwNTpkzp1WMQQtDa2oqEhARkZWXBy8sLCoUCEydORE5ODhwcHJCZmQlHR0eDYy6BuyMIigCAjvNjR0dH7NmzB0lJSezXn3/+eTQ2NiI9PZ27xd0DXL58GTdv3sRTTz1l8HVq9Lhv3z420yUgIIAVl3Hjxg14J1FbW4uZM2di/Pjx2LZtm3CB/D/q6urg6uqK/Px8XL58GfX19Th+/DjKysowbtw4bN68Gc7OzoKo9AFBUAQAAFVVVfDz88O5c+cMssLfeustnDp1ChcuXOBwdfcPTU1NOHDgAFJSUnD48GFIJBI26jgmJqbP4iKXyzFr1iyMGTMGO3bs4KWzMlcwDHPH66lSqZCSkoJ169bBz88P27Ztg4uLS5c/K3AnwiskIMAjXFxc8PTTT2PPnj2ora3FZ599htraWiQkJGDMmDF4++23ce7cuS7P9ztTX1+PhIQEjBgxAtu3bxfEpBNUIOg9NcMwsLOzw7x587Bs2TJWjBUKhSAmvUR4hwkAAJujUVtba/D12tpaTrqRBAAnJyfMmzcP8+bNYzNdUlJSsGDBAtjb22Pu3LlITk7GpEmT7hCLxsZGtk35f//3f/tlY3+/QOtVVlZWIITA1tYWf/jDH6BWq3Hw4EGhCN8HhCMvAZa4uDhMmDABX331FYCOO7aAgAAsXbpUKMrzCJVKhRMnTiAlJQXp6ekQiUSYM2cOkpOTMXnyZLS3tyMpKQmurq5IT0/nxIbfkqGGjwzDQKVSwcHBgeslWQyCoAiw7Nq1C88//zw2bdqECRMmYN26dfjpp59QUFBwXzuo8hmtVotTp05h9+7dSE9PR3t7O2xtbREaGorDhw+bxXb/XqSr3BOBuyMICsfQl58vb96vv/4aa9asQU1NDSIjI/Hll18iLi6O62UJ9AKdTofjx49j1apVOHToENzc3LheksB9hiAoHKJUKuHk5MT1MgQEBASMgtC6wCEvvfQSXn75ZahUKvZrtAAo6LyAgIClIQgKh/zxj3/ETz/9xGYrEEJgZWWFmpoa3hyBCQgICPQWQVA4xM/PD/7+/jh48CAAoKWlBevXr0dwcDA2btzY7d+733Yvp0+fxty5c+Hr6wuRSIS0tDSulyQgINAFgqBwBMMwCA4OhpubG/Lz86FQKPDMM8/g22+/xdq1a7FkyRIAXYvH/bZ7USqViIiIwDfffMP1UgQEBHpAKMpzzM6dO/Gvf/0Lzc3NCAgIwDfffIPIyEgAhtYQ1E/oyJEjKCoqwrPPPntfdvGIRCLs3bvXwG9MQECAHwg7FA6ghffq6mpcu3YNBQUFmDJlCvbv38+KCQADuwf637t378aPP/6IiooKs65ZQKC3lJaW4qWXXsKwYcPg4OCAkJAQrFq1Cmq1muulCZgYwXrFzNCdRmlpKebPnw9PT08AQGxsLAYPHgyNRtOlTYZIJEJzczOKiorwyCOPYPTo0eZeuoBArygoKADDMNi0aROGDx+OvLw8vPLKK1AqlVi7di3XyxMwIcIOxcyIxWKcPn0aDz/8MNzc3LBlyxa8+OKLOHbsGHQ6XZdiQnc0p06dQktLC8LDw1nfoa4ghECr1d53xXsBfhAfH48tW7Zg+vTpCA4ORkJCAv76178iNTWV66UJmBhBUMyIVqvFa6+9hkWLFmHWrFk4ePAgfHx88OSTT+L06dNQKpU9/v2jR4/Cy8sL0dHRBl+nwtHU1ASZTAaRSARra+sui/f79+/HoUOHjPdLCQj0AoVCAXd3d66XIWBiBEExIyKRCOPGjcMXX3yBDRs2wMbGBoQQhIaGwsfHh20f7oyVlRVaW1uRnZ2NUaNGITQ0lH08fX766SckJiYiLCwM77zzDiorKwH8HmVaV1eHH374AX//+99N+FsKCBhy8+ZNfPXVV3jttde4XoqAiREExYyIxWIsXboUTz75pEHBPTg4GO7u7jh16hQAw1Zhetx1+vRptLS0IDIyEtbW1gY/Q4UlICAA69atw9tvv41Lly7h9ddfR0NDA5s2V1hYiIqKCjzzzDMAgPb2douw5m5paWGzwwGgpKSEzRUXMB8rV66ESCTq8U9BQYHB36msrER8fDzmz5+PV155haOVC5gLoSjPMVQMPvjgA3Zgr6ujqqNHj8LDwwMxMTEAunZDnTRpEpycnDBhwgTMmTMHUVFROHr0KBYsWAAAyMnJQXNzM6ZOnQoAFmNrfvnyZXbNALB8+XIAHfHEW7du5WhV9x8rVqzA4sWLe/yZ4OBg9r+rqqowdepUTJo0Cd99952JVyfABwRB4QnTpk3DtGnT7vi6lZUVVCoVLl68iLFjx2LMmDHs1ymtra1YtWoVsrKyUF5ejtGjR2P27NmIjY1FdnY2FixYgLq6OuTm5kKpVGL//v1YtGgRHnroIbz77rsICgq643n5ZN89ZcoUocGAB3h5ecHLy6tXP1tZWYmpU6ciJiYGW7ZsERIP7xOEf2UL4NatWygrK8PmzZuxfPlyHDt2DAqFgv3+1q1bsXHjRiQnJ2PdunUIDQ3Fp59+irS0NEyYMAEAUFxcjIyMDADAoEGDsG7dOuTk5OD9998HcOdEPhUTnU53x/dkMpmpflWBe4DKykpMmTIFAQEBWLt2LWQyGWpqalBTU8P10gRMDRGwCDQaDdm+fTuZMmUKsbW1JS4uLuTvf/87qaqqIq+99hqJjY01+PlPP/2UuLm5EaVSSQghZNOmTWTw4MHk/Pnz7M9s27aN+Pv7k3PnzrFfa2xsJIcPHyYnTpzoch1VVVVEJBJ1+30BgS1bthAAXf4RuLcRdigWgrW1NZ555hlkZGSgvb0dGzduhI2NDRwcHBATE4OGhgYcO3YMlZWV+PLLL7Fu3TpMnDgRjo6OqK+vx+XLlzFixAiDsKy5c+eipqaG7QL75ZdfMGfOHHzwwQdYtGgRJBIJNm3axH4f6KjluLu7C4OVAD755BPExsbC2dkZEokESUlJKCws5HpZnLN48WIQQrr8I3CPw6WaCRiHmpoa8uqrr5JBgwaRqVOnkrlz5xKRSER27dpFCCHk0qVLZOTIkeT1118nhBCiUqkIIYScPn2a2Nraktu3bxOFQkF8fX3Jhg0b2O/v3LmTjB07luTm5rLPNX36dDJ//nwz/4b8ZMaMGWTLli0kLy+P5OTkkFmzZpGAgADS0tLC9dIEBDhBEJR7jOvXr5OLFy+SoKAg0tjYSAghZOPGjcTHx4fMnz+faLVa9mcXLlxIJk+eTBiGIRs3biQikYhERUWRtWvXksrKSkIIIbNmzSLr168nhBAil8uJvb092b17t/l/MQtAKpUSAOTUqVNcL0VAgBOELq97jFGjRgHomNUAOjrAysvLYWtrC5FIhJSUFMTFxWH9+vU4cOAAtm/fDpFIhM2bN2PBggWYOHEifvrpJ/zzn//E0KFD0dDQgICAAADAgQMHYGdnh4ceeoiz34/P0EYJYSJc4H5FsK+/T7h9+zYKCwsxf/58AB3zAosXL8ayZcvAMAwmTpyIWbNmYdWqVezPHzp0CGlpaVi+fDmmTZuGGTNmwMnJSfBk6gKGYZCQkIDGxkacPXuW6+UICHCCICj3Ifn5+XByckJgYCCAjpbhDz/8EN9//z3OnTsHPz+/O/6OQqGAr68vNm/ejKefftrcS+Y9S5YswaFDh3D27FkMHTqU6+UICHCCICgCADqyWV577TUolUq8+OKLGDlyJBQKBcaOHQsfHx/s3r0bL774IgoLC+Hr68v1cnnF0qVLkZ6ejtOnT2PYsGFcL0dAgDMEQRFgp+LLy8uxfv16pKenw87ODo8//jhef/11jBo1Ck8++SS0Wi3S09O5Xi5vIIRg2bJl2Lt3L06ePIkRI0ZwvSQBAU4RBEWgS6qqqqBWqxEUFISmpia4ubnhu+++w8svv8z10njDG2+8gZ07dyI9PZ11gAYAV1dXODg4cLgyAQFuEARF4K60t7fju+++w8KFC+Ht7c31cnhDd15nW7ZsuauJooDAvYggKAICAgICRkGwXhEQEBAQMAqCoAgICAgIGAVBUAQEBAQEjIIgKAICAgICRkEQFAEBAQEBoyAIioCAgICAURAERUBAQEDAKAiCIiAgICBgFARBERAQEBAwCoKgCAgICAgYBUFQBAQEBASMwv8HoNXfli4Cy0wAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import numpy as np\n",
    "\n",
    "# Enable interactive mode\n",
    "plt.ion()\n",
    "\n",
    "# Generate random data\n",
    "np.random.seed(0)\n",
    "n = 100\n",
    "x = np.random.standard_normal(n)\n",
    "y = np.random.standard_normal(n)\n",
    "z = np.random.standard_normal(n)\n",
    "\n",
    "# Create a 3D scatter plot\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "ax.scatter(x, y, z, c='b', marker='o')\n",
    "\n",
    "ax.set_xlabel('X Label')\n",
    "ax.set_ylabel('Y Label')\n",
    "ax.set_zlabel('Z Label')\n",
    "\n",
    "plt.title('3D Scatter Plot')\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7783990-f2a9-4c95-bec6-b847b63e9775",
   "metadata": {},
   "source": [
    "### R-5.9 \n",
    "Explain the changes that would have to be made to the program of Code\n",
    "Fragment 5.11 so that it could perform the Caesar cipher for messages\n",
    "that are written in an alphabet-based language other than English, such as\n",
    "Greek, Russian, or Hebrew\n",
    "\n",
    "Need to shift the order and find the encoder/decorder for the letters in their alphabets. As well shifting the ord('A') to accomdate the letters in those languages"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42fe8058-3085-42c5-9522-5965b121ce84",
   "metadata": {},
   "source": [
    "### R-5.10 \n",
    "The constructor for the CaesarCipher class in Code Fragment 5.11 can\n",
    "be implemented with a two-line body by building the forward and backward strings using a combination of the join method and an appropriate\n",
    "comprehension syntax. Give such an implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0d09fd83-a8e5-4869-a5c1-609ebf74c73a",
   "metadata": {},
   "outputs": [],
   "source": [
    "class CasarCipher:\n",
    "\n",
    "    def __init__(self,shift):\n",
    "        self._forward = ''.join([chr((k+shift) % 26 + ord('A')) for k  in range(26)])\n",
    "        self._backward = ''.join([chr((k-shift) % 26 + ord('A')) for k in range(26) ])\n",
    "\n",
    "    def encrypt(self,message):\n",
    "        return self._transform(message,self._forward)\n",
    "\n",
    "    def decrypt(self,secret):\n",
    "        return self._transform(secret,self._backward)\n",
    "\n",
    "    def _transform(self,original, code):\n",
    "        msg = list(original)\n",
    "        for k in range(len(msg)):\n",
    "            if msg[k].isupper():\n",
    "                j = ord(msg[k]) - ord('A')\n",
    "                msg[k] = code[j]\n",
    "        return ''.join(msg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "730e9f3b-2be0-4e8c-b691-1084832d9f01",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Secret: WKH HDJOH LV LQ SODB; PHHW DW MRH'V\n",
      "Message: THE EAGLE IS IN PLAY; MEET AT JOE'S\n"
     ]
    }
   ],
   "source": [
    "cipher= CasarCipher(3)\n",
    "message = \"THE EAGLE IS IN PLAY; MEET AT JOE'S\"\n",
    "coded = cipher.encrypt(message)\n",
    "print(f'Secret: {coded}')\n",
    "answer = cipher.decrypt(coded)\n",
    "print(f'Message: {answer}') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7e97a3c3-11c2-448d-9427-d715f67ce32f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'X'"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chr((0-3) % 26 + ord('A'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "59998f90-267f-45e8-883a-8a3d7ac9cc8a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "65"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ord('A')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b350881-71c4-4551-ba29-cca8b2119913",
   "metadata": {},
   "source": [
    "### R-5.11 \n",
    "Use standard control structures to compute the sum of all numbers in an\n",
    "n×n data set, represented as a list of lists."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b5ed410c-4be3-4a70-abbd-f5e8aa65c214",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sum_data(dataset):\n",
    "    total = 0\n",
    "    for array in dataset:\n",
    "        for i in array:\n",
    "            total+=i\n",
    "    return total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a6b0964b-d338-4aaf-8b5e-1c012287a6e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "l1 = [[i for i in range(0,10)],[i for i in range(0,10)]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b9a2df13-baaf-44d6-aee3-e05196a880bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "90"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_data(l1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b235794c-14e6-4cd6-b5a9-9ad1e271e0b8",
   "metadata": {},
   "source": [
    "### R-5.12 \n",
    "Describe how the built-in sum function can be combined with Python’s\n",
    "comprehension syntax to compute the sum of all numbers in an n×n data\n",
    "set, represented as a list of lists."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "75f8cfd7-88fc-414e-bb3a-ab10110685e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sum_list(dataset):\n",
    "    return [sum(array) for array in dataset] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "095cd913-9a45-4ec9-a478-259b1b257732",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[45, 45]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_list(l1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04ab1d0e-a3d7-42f7-b08b-00afbafc5dd1",
   "metadata": {},
   "source": [
    "### C-5.13 \n",
    "In the experiment of Code Fragment 5.1, we begin with an empty list. If\n",
    "data were initially constructed with nonempty length, does this affect the\n",
    "sequence of values at which the underlying array is expanded? Perform\n",
    "your own experiments, and comment on any relationship you see between\n",
    "the initial length and the expansion sequence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "073c1422-8f2c-4511-94d2-14bf89683d04",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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     ]
    }
   ],
   "source": [
    "import sys\n",
    "data = [] \n",
    "for k in range(10*100):\n",
    "    a = len(data)\n",
    "    b = sys.getsizeof(data)\n",
    "    print(f'Length {a}; Size {b}')\n",
    "    data.append(None)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9d6b811-79de-4bff-86b1-ef518cabfe58",
   "metadata": {},
   "source": [
    "### C-5.14 \n",
    "The shuffle method, supported by the random module, takes a Python\n",
    "list and rearranges it so that every possible ordering is equally likely.\n",
    "Implement your own version of such a function. You may rely on the\n",
    "randrange(n) function of the random module, which returns a random\n",
    "number between 0 and n−1 inclusive"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "57d5ea06-8753-4d71-8a89-90bc336de0cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "def okie_dokie_shuffle(iterable):\n",
    "    new_iter = iterable.copy()\n",
    "    random_iter = []\n",
    "    while new_iter:\n",
    "        index = random.randrange(len(new_iter))\n",
    "        random_iter.append(new_iter.pop(index))\n",
    "    return random_iter\n",
    "    \n",
    "iterable = [i for i in range(10)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "38a7656a-b6fc-420c-8f86-d5c91dc95461",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9, 5, 0, 1, 8, 2, 7, 6, 3, 4]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "okie_dokie_shuffle(iterable)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3ce723e-b1cf-4c02-85ff-349637ed9700",
   "metadata": {},
   "source": [
    "### C-5.15 \n",
    "Consider an implementation of a dynamic array, but instead of copying\n",
    "the elements into an array of double the size (that is, from N to 2N) when\n",
    "its capacity is reached, we copy the elements into an array with \n",
    "[N/4]\n",
    "additional cells, going from capacity N to capacity N +\n",
    "[N/4]. Prove that\n",
    "performing a sequence of n append operations still runs in O(n) time in\n",
    "this case.\n",
    "\n",
    "This is O(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "add933be-3ea0-4a54-b413-b5ddf1956b27",
   "metadata": {},
   "outputs": [],
   "source": [
    "import ctypes\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "class DynamicArray:\n",
    "\n",
    "    def __init__(self):\n",
    "        self._n = 0\n",
    "        self._capacity = 1\n",
    "        self._A = self._make_array(self._capacity)\n",
    "\n",
    "    def __len__(self):\n",
    "        return self._n\n",
    "\n",
    "    def __getitem__(self,k):\n",
    "        if not k < self._n:\n",
    "            raise IndexError('invalid index')\n",
    "        return self._A[k]\n",
    "\n",
    "    def append(self,obj):\n",
    "        if self._n == self._capacity:\n",
    "            self._resize(self._capacity//4)\n",
    "        self._A[self._n] = obj\n",
    "        self._n += 1\n",
    "\n",
    "    def _resize(self,c):\n",
    "        if int(c) == 0:\n",
    "            c = 1\n",
    "        c = self._capacity + c\n",
    "        B = self._make_array(c)\n",
    "        for k in range(self._n):\n",
    "            B[k] = self._A[k]\n",
    "        self._A = B\n",
    "        self._capacity = c\n",
    "\n",
    "    def _make_array(self,c):\n",
    "        return (c * ctypes.py_object)()\n",
    "\n",
    "    def __str__(self,):\n",
    "        return f\"Array  {[self._A[i] for i in range(self._n)] }, Number of items {self._n}, Capacity {self._capacity}\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "4a8eebb7-a448-4abb-94f1-6640f56f263b",
   "metadata": {},
   "outputs": [],
   "source": [
    "da_list = [DynamicArray() for i in range(0,6)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "03e68da6-4cf6-477f-9418-19db3bffbf01",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Array  [], Number of items 0, Capacity 1'"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(da_list[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "93f5c62c-191c-46db-8c59-2512f26d2203",
   "metadata": {},
   "outputs": [],
   "source": [
    "array_sizes = [1,10,100,10000,100000,1000000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "0ac0afbb-d7bc-460c-b3f4-5a8e310432be",
   "metadata": {},
   "outputs": [],
   "source": [
    "durations = []\n",
    "for size,da in zip(array_sizes,da_list):\n",
    "    start = time.perf_counter()\n",
    "    for i in range(0,size):\n",
    "        da.append(i)\n",
    "    end = time.perf_counter()\n",
    "    durations.append(end-start)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "c6b97bc7-1298-4428-8aaa-327d59bc849e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2.0899999071843922e-05,\n",
       " 0.00013949999993201345,\n",
       " 0.00030250000418163836,\n",
       " 0.021457499999087304,\n",
       " 0.2377972999966005,\n",
       " 2.35065370000666]"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "durations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "646a6c78-04a7-4177-a26c-5d720754d8e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "index = ['append to last item']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "2e402828-d3c0-45c5-81c0-cbf898f8ecfa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Array Size  Duration in Secs\n",
      "0           1          0.000021\n",
      "1          10          0.000139\n",
      "2         100          0.000303\n",
      "3       10000          0.021457\n",
      "4      100000          0.237797\n",
      "5     1000000          2.350654\n"
     ]
    }
   ],
   "source": [
    "df = pd.DataFrame({'Array Size': array_sizes, 'Duration in Secs': durations })\n",
    "print(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "3823620d-f131-42e7-87a1-55158d3eb52f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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p00ewsLAQXF1dhQ8++EA4cOBApbfPt23bttJzHD9+XOjUqZNQr149wd3dXXjvvfeEP/74o8I5CgsLhbFjxwoODg4CANWt9JXdPi8IgnDw4EGha9euQr169QQ7OzshNDRUSE5OLndMVT9zVS0NQGQI+KwxInqisrIyuLu7IzQ0FGvWrBG7HCIireEcISJ6oj179iArKwvjx48XuxQiIq3iiBARVenUqVM4c+YM5s+fDycnp2oXKSQiqo04IkREVVq+fDmmTp0KFxcXbNiwQexyiIi0jiNCREREZLQ4IkRERERGi0GIiIiIjBYXVHwCpVKJtLQ02Nraqr0kPREREYlLEAQUFBTA3d0dJiZVj/swCD1BWloavLy8xC6DiIiINHDz5k14enpWuZ9BqAqRkZGIjIxULW9/8+bNck+/flpyuRz79+9Hv379YGZmprXz1kXsVc2wX+pjr9THXqmPvVKfLnuVn58PLy8v1YONq8IgVIXw8HCEh4cjPz8f9vb2sLOz03oQsrKygp2dHf+gPAF7VTPsl/rYK/WxV+pjr9Snj149aVoLJ0sTERGR0WIQIiIiIqPFIERERERGi0GIiIiIjBaDEBERERktBiEiIiIyWgxCVYiMjISPjw+CgoLELoWIiIh0hEGoCuHh4UhOTsbp06fFLoWIiIh0hEGIiIiI9E6hFHAqNQfx2RKcSs2BQimIUgdXliYiIiK92nc2HfN+SUZ6XjEAKTZcikNDe0vMCfXBAN+Geq2FI0JERESkN/vOpmPqpoT/QtD/u5NXjKmbErDvbLpe62EQIiIiIr1QKAXM+yUZlV0Ee7ht3i/Jer1MxiBEREREehGbmlNhJOhRAoD0vGLEpuborSYGISIiItKLzIKqQ5Amx2kDgxARERHphYutpVaP0wYGISIiItKLVq42MJNKqtwvAdDQ3hLBTR31VhODEBEREenczZwijPrhJOSKyidCP4xHc0J9IDWpOixpG4MQERER6dTZ23kYvvwErmTJ0NDeEh8/54OG9uUvf7nZW2L5uI56X0eICypWITIyEpGRkVAoFGKXQkREVGsdvpCJ8M0JKCpVwNvNFlETg+Fmb4kJXZrg5OVM7D92Cv26haBzCxe9jgQ9xBGhKvBZY0RERE8n+vQNvLI+DkWlCnRt0QA/vt4Zbv+NBElNJAhp6ogAJwEhTR1FCUEAR4SIiIhIywRBwOKDl/BdzCUAwPCOHvhieHuYmxre+AuDEBEREWmNXKHE7F3/Ykf8LQDAm71bIKJvK0gk4oz4PAmDEBEREWlFQbEcb2xOwLFL2ZCaSDD/eV+MDWkkdlnVYhAiIiKip5aRX4wJ607jfHo+6plJ8f1LHdHL20Xssp6IQYiIiIieysWMAkxYG4u0vGI42Zhj7YQgtPd0ELsstTAIERERkcZOXrmLVzfGoaC4DM2crBE1MRiNGliJXZbaGISIiIhIIz8npWHmj0koVSgR2Lg+Vo0PRH1rc7HLqhEGISIiIqoRQRCw8uhVLNibAgAY6OuGxaP9YWkmFbmymmMQIiIiIrUplALm/XIOG05eBwBM6toUHw5uI9qCiE+LQYiIiIjUcr9Ugbe2/YMDyRmQSIAPB7XBK92aiV3WU2EQIiIioie6W1iCyevjkHgzF+amJlg8yh+D2+v3Aam6wCBERERE1bqWLcOEdbG4drcI9vXMsDosEEFNHMUuSysYhIiIiKhK/9y4h8nr45AjK4Vn/XqImhiMFi42YpelNYb39DMd+PXXX9G6dWu0bNkSq1evFrscIiKiWuFAcgbGrPobObJS+HrYYdcbXepUCAKMYESorKwMEREROHz4MOzt7REQEIBhw4ahQYMGYpdGRERksDaevIY5P5+DUgB6tnZG5NiOsLaoe7Ghzo8IxcbGom3btvDw8ICNjQ0GDhyI/fv3i10WERGRQVIqBXyxNwUf//QgBL0Y5IXV4wPrZAgCakEQOnr0KEJDQ+Hu7g6JRII9e/ZUOCYyMhJNmjSBpaUlQkJCEBsbq9qXlpYGDw8P1WsPDw/cvn1bH6UTERHVKiVlCrzzYyJW/HkFADCjbyssGN4OplKDjwsaM/h4J5PJ4Ofnh0mTJmH48OEV9kdHRyMiIgIrVqxASEgIlixZgv79++PChQtwcan5U29LSkpQUlKiep2fnw8AkMvlkMvlmn8jj3l4Lm2es65ir2qG/VIfe6U+9kp9tbVX+ffleGNrIk6l3oOpiQSfDfXB8A4eKCsr09ln6rJX6p5TIgiCoPVP1xGJRILdu3dj6NChqm0hISEICgrCsmXLAABKpRJeXl548803MWvWLJw4cQJffvkldu/eDQB4++23ERwcjLFjx1b6GXPnzsW8efMqbN+yZQusrGrPQ+SIiIjUlVMC/HBeijv3JbCQCpjUSglvh1oTDypVVFSEsWPHIi8vD3Z2dlUeV6uDUGlpKaysrLBjx45y4SgsLAy5ubn46aefUFZWhjZt2uDIkSOqydInTpyocrJ0ZSNCXl5eyM7OrraRNSWXy3HgwAH07dsXZmZmWjtvXcRe1Qz7pT72Sn3slfpqW6/OpxdgysYEZBSUwNXWAqte7og2DW318tm67FV+fj6cnJyeGIQM/tJYdbKzs6FQKODq6lpuu6urK1JSHjwIztTUFF9//TV69eoFpVKJ9957r9o7xiwsLGBhYVFhu5mZmU5+oHV13rqIvaoZ9kt97JX62Cv11YZeHbuUhambElBYUoZWrjaImhgMd4d6eq9DF71S93y1Ogipa8iQIRgyZEiN3hMZGYnIyEgoFAodVUVERCSeHfG3MGvnGZQpBXRq5ogfXg6EfT3DDm66UKungTs5OUEqlSIjI6Pc9oyMDLi5uT3VucPDw5GcnIzTp08/1XmIiIgMiSAIWBpzCTO3J6FMKeB5f3esnxRslCEIqOVByNzcHAEBAYiJiVFtUyqViImJQefOnUWsjIiIyPCUKZSYvetffH3gIgBgas/mWDzKHxamUpErE4/BXxorLCzE5cuXVa9TU1ORmJgIR0dHNGrUCBEREQgLC0NgYCCCg4OxZMkSyGQyTJw48ak+l5fGiIioLpGVlCF8SwKOXMiCiQSYN6QtXu7cROyyRGfwQSguLg69evVSvY6IiADw4M6wqKgojB49GllZWfjkk09w584d+Pv7Y9++fRUmUNdUeHg4wsPDkZ+fD3t7+6c6FxERkZgyC4oxKeo0zt7Oh6WZCZaO6Yi+Pk/372RdYfBBqGfPnnjSHf7Tpk3DtGnT9FQRERFR7XE5sxAT1sXi1r37cLQ2x5qwQHRoVF/ssgyGwQchIiIi0szpazl4ZX0c8u7L0aSBFaImBqOJk7XYZRmUWj1ZWpciIyPh4+ODoKAgsUshIiKqsd/OpOOl1aeQd1+ODo0csHNqF4agSjAIVYG3zxMRUW21+thVTNuagNIyJfr6uGLLK53QwKbiYsHES2NERER1hlIp4H+/ncfa46kAgPGdG2NOaFtITSQiV2a4GISIiIjqgGK5Au9EJ2Lv2TsAgNkDvfFq92aQSBiCqsMgREREVMvdk5ViyoY4xF2/B3OpCb4a5Ychfu5il1UrMAhVgQsqEhFRbXAzpwhh62JxNUsGO0tTrBwfiE7Nqn64OJXHydJV4GRpIiIydGdu5WLY98dxNUsGd3tL7JjahSGohjgiREREVAsdTsnEG5sTcF+uQJuGdoiaGARXO0uxy6p1GISIiIhqma2xN/DRnrNQKAV0a+mE71/qCFtL43x6/NNiECIiIqolBEHA1/svYtnhBw8jHxHgiQXD28FMypkummIQqgInSxMRkSEpLVNi1q4z2JVwGwAw/dmWeLtPS94e/5QYIavAydJERGQo8ovlmBR1GrsSbkNqIsHCF9rhnb6tGIK0gCNCREREBuxOXjEmrItFyp0CWJlLEflSR/Rq7SJ2WXUGgxAREZGBunCnABPWxSI9rxhONhaImhgEXw97scuqUxiEiIiIDNCJK9l4bWM8CorL0NzZGlETg+HlaCV2WXUOgxAREZGB2fPPbby7IwlyhYDgJo5YOT4ADlbmYpdVJzEIVYF3jRERkb4JgoDlf17Bon0XAACD2zfE1yP9YGkmFbmyuot3jVWBd40REZE+lSmU+Pins6oQNKVbUyx9sQNDkI5xRIiIiEhkRaVleGvrPzh4PhMSCfDJcz6Y2LWp2GUZBQYhIiIiEWUXlmDy+jgk3cyFhakJvn3RHwN8G4pdltFgECIiIhJJarYMYWtjcSOnCA5WZlgTFoiAxo5il2VUGISIiIhEEH/9Hl5Zfxr3iuTwcqyHqInBaO5sI3ZZRodBiIiISM/+OHcHb239ByVlSrT3tMeasCA421qIXZZRYhAiIiLSo/UnrmHuL+cgCMCz3i5YOrYDrMz5z7FY2HkiIiI9UCoFfLEvBSuPXgUAjA1phE+HtIWplCvZiIlBqApcUJGIiLSlpEyBGT8m4dcz6QCAd/u3xhs9m/Pp8QaAMbQKXFCRiIi0Ia9IjpfXxOLXM+kwk0qweLQfwnu1YAgyEBwRIiIi0hKFUsCp1BzEZ0vQIDUHXg1sMHl9HC5nFsLWwhQrXg5A1xZOYpdJj2AQIiIi0oJ9Z9Mx75dkpOcVA5Biw6U4mEgApQC42VkialIQvN3sxC6THsMgRERE9JT2nU3H1E0JEB7brvxvw/Q+LRiCDBTnCBERET0FhVLAvF+SK4SghyQAvou5DIWyqiNITAxCRERETyE2Nee/y2GVEwCk5xUjNjVHf0WR2hiEiIiInkJmQdUhSJPjSL8YhIiIiJ6Ck416j8ZwsbXUcSWkCU6WJiIi0lBJmQIbT16r9hgJADd7SwQ35VPlDRGDEBERkQZkJWV4bWM8/rqcDVMTCcqUAiRAuUnTD5dMnBPqA6kJF1A0RLw0RkREVEP3ZKUYu/oU/rqcDWtzKdZPCsaKcR3hZl/+8pebvSWWj+uIAb4NRaqUnoQjQlXgs8aIiKgy6Xn38fKaWFzOLER9KzNETQyGn5cDAKCvjxtOXs7E/mOn0K9bCDq3cOFIkIHjiFAV+KwxIiJ63NWsQoxYfhKXMwvR0N4S21/vrApBACA1kSCkqSMCnASENHVkCKoFOCJERESkhrO38xC2NhZ3ZaVo5mSNja+EwMOhnthl0VNiECIiInqCv6/exSvr41BYUgZfDztETQxW+7Z5MmwMQkRERNU4mJyB8C0JKClTIqSpI1aHBcLW0kzsskhLGISIiIiqsDP+Ft7beQYKpYA+bVyxbGwHWJpJxS6LtIhBiIiIqBJr/krF/F+TAQAvdPTEwhfawVTKe4zqGgYhIiKiRwiCgG8OXMTSQ5cBAJOfaYoPB7WBCe8Aq5MYhIiIiP6jUAqY8/NZbPr7BgDg3f6t8UbP5pBIGILqKgYhIiIiAKVlSkT8mIhfz6RDIgHmP++LcZ0ai10W6RiDEBERGb2i0jJM3ZSAPy9mwUwqwTej/BHq5y52WaQHDEJERGTU8orkmLT+NOKv30M9MylWvByAHq2cxS6L9IRBiIiIjFZmfjFeXhOLCxkFsK9nhrUTghDQuL7YZZEeMQgREZFRun5XhnFrTuFmzn242Fpg4+QQtHazFbss0jOjWBBh2LBhqF+/PkaMGCF2KUREZADOp+djxIqTuJlzH40bWGHn1C4MQUbKKILQ9OnTsWHDBrHLICIiAxB3LQejfjiJrIISeLvZYvvrneHlaCV2WSQSowhCPXv2hK0tkz4RkbE7fCET49acQkFxGQIb10f0a53hYmspdlkkItGD0NGjRxEaGgp3d3dIJBLs2bOnwjGRkZFo0qQJLC0tERISgtjYWP0XSkREtdpPibcxZX0ciuVK9GrtjI2TQ2Bfjw9PNXaiByGZTAY/Pz9ERkZWuj86OhoRERGYM2cOEhIS4Ofnh/79+yMzM1N1jL+/P3x9fSt8paWl6evbICIiA7bx5DW8HZ2IMqWA5/3dsXJ8IOqZ8+GpZAB3jQ0cOBADBw6scv8333yDKVOmYOLEiQCAFStW4LfffsPatWsxa9YsAEBiYqLW6ikpKUFJSYnqdX5+PgBALpdDLpdr7XMenkub56yr2KuaYb/Ux16pr7b2ShAELDtyFd8dugIAeDnECx8N8gaUCsiVCp18Zm3tlRh02St1zyl6EKpOaWkp4uPjMXv2bNU2ExMT9OnTBydPntTJZy5YsADz5s2rsH3//v2wstL+ZLoDBw5o/Zx1FXtVM+yX+tgr9dWmXikFYPc1Exy98+DixwBPBQIkqdi3L1Uvn1+beiU2XfSqqKhIreMMOghlZ2dDoVDA1dW13HZXV1ekpKSofZ4+ffogKSkJMpkMnp6e2L59Ozp37lzpsbNnz0ZERITqdX5+Pry8vNCvXz/Y2dlp9o1UQi6X48CBA+jbty/MzHiNujrsVc2wX+pjr9RX23olVygxe/c5HL2TDgD4eLA3xndqpJ/PrmW9EpMue/Xwis6TGHQQ0paDBw+qfayFhQUsLCwqbDczM9PJD7SuzlsXsVc1w36pj71SX23oVbFcgTe3JSImJRNSEwm+HumHoR089F5HbeiVodBFr9Q9n0EHIScnJ0ilUmRkZJTbnpGRATc3N51+dmRkJCIjI6FQ6OYaMhERaV9+sRyvRMUh9loOLExNsHxcR/T2dn3yG8loiX7XWHXMzc0REBCAmJgY1TalUomYmJgqL21pS3h4OJKTk3H69Gmdfg4REWlHVkEJXvzhb8Rey4GthSk2Tg5hCKInEn1EqLCwEJcvX1a9Tk1NRWJiIhwdHdGoUSNEREQgLCwMgYGBCA4OxpIlSyCTyVR3kREREd3MKcLLa07h2t0iONlYYP2kILR1txe7LKoFRA9CcXFx6NWrl+r1w4nKYWFhiIqKwujRo5GVlYVPPvkEd+7cgb+/P/bt21dhArW28dIYEVHtcDGjAC+vOYWM/BJ41q+HTZND0MTJWuyyqJYQPQj17NkTgiBUe8y0adMwbdo0PVX0QHh4OMLDw5Gfnw97e/6vgojIEP1z4x4mRp1GbpEcrVxtsHFyCFzt+MgMUp/oQYiIiEgTxy5l4bWN8SgqVaBDIwesmxAEBytzscuiWoZBiIiIap3f/03H9G3/QK4Q0K2lE1aMC4C1Bf9Jo5oz6LvGxBQZGQkfHx8EBQWJXQoRET1ia+wNhG9JgFwhYHC7hlgdFsgQRBpjEKoCb58nIjIsgiDg+yOXMXvXvxAEYGxII3w3pgMsTPnwVNLcU0fokpKSSldiJiIi0hZBELBgbwpWHr0KAAjv1Rwz+7WGRCIRuTKq7Wo8IrR3716EhYWhWbNmMDMzg5WVFezs7NCjRw989tlnSEtL00WdRERkpMoUSry344wqBH00uA3e7e/NEERaoXYQ2r17N1q1aoVJkybB1NQU77//Pnbt2oU//vgDq1evRo8ePXDw4EE0a9YMr7/+OrKysnRZt85xjhARkfiK5Qq8sTkB2+NvQWoiwZcj2uOVbs3ELovqELUvjS1atAiLFy/GwIEDYWJSMT+NGjUKAHD79m0sXboUmzZtwjvvvKO9SvWM6wgREYmrsKQMr26Iw4krd2FuaoJlYzqgX1vdPmeSjI/aQejkyZNqHefh4YEvvvhC44KIiIjuFpZgYtRpnLmVBxsLU6wcH4AuzZ3ELovqIK3cNaZQKJCYmIh79+5p43RERGTE0nLvY+QPJ3HmVh4crc2xdUonhiDSGY2C0Ntvv401a9YAeBCCevTogY4dO8LLywtHjhzRZn1ERGRELmcWYsTyE7iaJYO7vSW2v94Z7Tw5PYF0R6MgtGPHDvj5+QEAfvnlF6SmpiIlJQXvvPMOPvzwQ60WSERExuHMrVyM+uEk0vKK0dzZGjumdkFzZxuxy6I6TqMglJ2dDTe3BxPWfv/9d4wcOVJ1R9m///6r1QLFwrvGiIj058SVbIxZ+TdyZKVo72mP7a93gbtDPbHLIiOgURBydXVFcnIyFAoF9u3bh759+wIAioqKIJXWjRU+ubI0EZF+/HHuDiasOw1ZqQJdmjfAlimd4GjNh6eSfmi0svTEiRMxatQoNGzYEBKJBH369AEAnDp1Ct7e3lotkIiI6q7tcTfx/s4zUApAPx9XfDemAyzN6sZ/qKl20CgIzZ07F76+vrh58yZGjhypesSGVCrFrFmztFogERHVTauPXcX/fjsPABgV6InPh7WDqZSPwCT90vhZYyNGjKiwLSws7KmKISKiuk8QBHz5xwV8f+QKAODV7s0weyAfmUHiUDsIfffdd2qf9K233tKoGCIiqtsUSgEf7TmLrbE3AADvD/DG1J7NRa6KjJnaQWjx4sXlXmdlZaGoqAgODg4AgNzcXFhZWcHFxaVOBKHIyEhERkZCoVCIXQoRUZ1QUqZARHQSfvs3HSYS4LNh7TAmuJHYZZGRU/tibGpqqurrs88+g7+/P86fP4+cnBzk5OTg/Pnz6NixI+bPn6/LevWGd40REWmPrKQMr6yPw2//psNcaoJlYzsyBJFB0GhW2scff4ylS5eidevWqm2tW7fG4sWL8dFHH2mtOCIiqv1yi0oxbs0pHLuUDStzKdZOCMKgdg3FLosIgIaTpdPT01FWVlZhu0KhQEZGxlMXRUREdcOdvGKMX3sKFzMK4WBlhnUTgtChUX2xyyJS0WhE6Nlnn8Vrr72GhIQE1bb4+HhMnTpVtaYQEREZt9RsGUasOIGLGYVwtbPAj691Zggig6NREFq7di3c3NwQGBgICwsLWFhYIDg4GK6urli9erW2ayQiolrmXFoeRq44gVv37qOpkzV2vN4FrVxtxS6LqAKNLo05Ozvj999/x8WLF5GSkgIA8Pb2RqtWrbRaHBER1T6xqTmYHHUaBSVl8Gloh/WTguFsayF2WUSV0nhBRQBo1aoVww8REakcSsnA1E0JKClTIripI1aHBcLO0kzssoiqpFEQUigUiIqKQkxMDDIzM6FUKsvtP3TokFaKExPXESIiqpk9/9zGjO1JUCgF9GnjgmVjO/K5YWTwNApC06dPR1RUFAYPHgxfX986uSx6eHg4wsPDkZ+fD3t7e7HLISIyaFHHUzH3l2QAwPAOHlg4oj3M+NwwqgU0CkLbtm3Djz/+iEGDBmm7HiIiqkUEQcCSg5fwbcwlAMDErk3w8WAfmJjUvf8gU92kURAyNzdHixYttF0LERHVIkqlgHm/nMP6k9cBABF9W+HN3i3q5FUCqrs0GrecMWMGvv32WwiCoO16iIioFpArlHg7OhHrT16HRALMf74t3nq2JUMQ1ToajQj99ddfOHz4MPbu3Yu2bdvCzKz8HQG7du3SSnFERCQ+hVLAqdQcxGdL0CA1B/6NGmDa1gQcuZAFUxMJvh7lh+f9PcQuk0gjGgUhBwcHDBs2TNu1EBGRgdl3Nh3zfklGel4xACk2XIqDmVQCuUKApZkJVowLQM/WLmKXSaQxjYLQunXrtF0HEREZmH1n0zF1UwIenwQhVzzYMq1XC4YgqvWe6t7GrKws/PXXX/jrr7+QlZWlrZqIiEhkCqWAeb8kVwhBj9p86gYUSs4VpdpNoyAkk8kwadIkNGzYEN27d0f37t3h7u6OyZMno6ioSNs1EhGRnsWm5vx3Oaxq6XnFiE3N0VNFRLqhURCKiIjAn3/+iV9++QW5ubnIzc3FTz/9hD///BMzZszQdo1ERKRnmQXVh6CaHkdkqDSaI7Rz507s2LEDPXv2VG0bNGgQ6tWrh1GjRmH58uXaqo+IiETgZKPeQ1JdbC11XAmRbmk0IlRUVARXV9cK211cXOrMpbHIyEj4+PggKChI7FKIiPQq774cP/x5pdpjJAAa2lsiuKmjfooi0hGNglDnzp0xZ84cFBf//5Do/fv3MW/ePHTu3FlrxYkpPDwcycnJOH36tNilEBHpzdWsQgz7/jiOXsqGmfTB4oiPL5H48PWcUB9I+SgNquU0ujT27bffon///vD09ISfnx8AICkpCZaWlvjjjz+0WiAREenHkQuZeHPrPygoLoO7vSVWjg/ErXtFj6wj9ICbvSXmhPpggG9DEasl0g6NgpCvry8uXbqEzZs3IyUlBQAwZswYvPTSS6hXr55WCyQiIt0SBAGrj6Viwd7zUApAYOP6WD4uAM62FvD1sEdfHzecvJyJ/cdOoV+3EHRu4cKRIKozNApCAGBlZYUpU6ZosxYiItKzYrkCH+z+F7sSbgMARgd64dOhbWFhKlUdIzWRIKSpI+6eFxDS1JEhiOoUjYLQggUL4OrqikmTJpXbvnbtWmRlZeH999/XSnFERKQ7mfnFeHVjPBJv5kJqIsHHg9sgrEsTPjiVjIpGk6V/+OEHeHt7V9jetm1brFix4qmLIiIi3Uq6mYvQZX8h8WYu7OuZYcOkYEzo2pQhiIyORiNCd+7cQcOGFSfJOTs7Iz09/amLIiIi3dnzz228t/MMSsuUaOlig9VhgWjcwFrssohEodGIkJeXF44fP15h+/Hjx+Hu7v7URRERkfYplAIW7D2Pt6MTUVqmRJ82Ltj1RheGIDJqGo0ITZkyBW+//Tbkcjl69+4NAIiJicF7773HR2wQERmg/GI5pm/9B4cvPHhAdniv5pjRtzVMOPGZjJxGQejdd9/F3bt38cYbb6C0tBQAYGlpiffffx+zZ8/WaoFERPR0UrNleGX9aVzJksHC1ASLRrTH8/4eYpdFZBA0CkISiQQLFy7Exx9/jPPnz6NevXpo2bIlLCzUezYNERHpx7FLWQjfnID84jK42Vli1fhAtPO0F7ssIoOh0Ryhh+7cuYOcnBw0b94cFhYWEARBW3UREdFTEAQBa/5KRdjaWOQXl6FjIwf8/GZXhiCix2g0InT37l2MGjUKhw8fhkQiwaVLl9CsWTNMnjwZ9evXx9dff63tOomISE0lZQp8tPsstsffAgCMCPDEZ8N8yy2SSEQPaDQi9M4778DMzAw3btyAlZWVavvo0aOxb98+rRVHREQ1k1lQjDEr/8b2+FswkQAfP+eDL0e0ZwgiqoJGQWj//v1YuHAhPD09y21v2bIlrl+/rpXCtOXmzZvo2bMnfHx80L59e2zfvl3skoiIdOLfW3l4ftlxJNzIhZ2lKaImBmPyM1wkkag6Gl0ak8lk5UaCHsrJyTG4CdOmpqZYsmQJ/P39cefOHQQEBGDQoEGwtua6GURUd/yclIZ3tyehpEyJ5s7WWB0WhKZO/HuO6Ek0GhHq1q0bNmzYoHotkUigVCqxaNEi9OrVS2vFaUPDhg3h7+8PAHBzc4OTkxNycnLELYqISEuUSgFf/pGCt7b+g5IyJXp7u2B3eFeGICI1aRSEFi1ahJUrV2LgwIEoLS3Fe++9B19fXxw9ehQLFy6s0bmOHj2K0NBQuLu7QyKRYM+ePRWOiYyMRJMmTWBpaYmQkBDExsZqUjbi4+OhUCjg5eWl0fuJiAxJQbEcr26MQ+ThKwCA13s0x6rxgbCzNBO5MqLaQ6NLY76+vrh48SKWLVsGW1tbFBYWYvjw4QgPD6/0GWTVkclk8PPzw6RJkzB8+PAK+6OjoxEREYEVK1YgJCQES5YsQf/+/XHhwgW4uLgAAPz9/VFWVlbhvfv371c98iMnJwfjx4/HqlWrqq2npKQEJSUlqtf5+fkAALlcDrlcXqPvrToPz6XNc9ZV7FXNsF/qq829un63CK9v/geX/1sk8bOhbfG8X0MoFWVQKrT/ebW5V/rGXqlPl71S95wSwYAW/5FIJNi9ezeGDh2q2hYSEoKgoCAsW7YMAKBUKuHl5YU333wTs2bNUuu8JSUl6Nu3L6ZMmYKXX3652mPnzp2LefPmVdi+ZcuWSudFERHp24U8CaIumKBIIYG9mYDJ3go0thG7KiLDUlRUhLFjxyIvLw92dnZVHqfRiNC+fftgY2ODZ555BsCDS1erVq2Cj48PIiMjUb9+fc2qfkxpaSni4+PLPbbDxMQEffr0wcmTJ9U6hyAImDBhAnr37v3EEAQAs2fPRkREhOp1fn4+vLy80K9fv2obWVNyuRwHDhxA3759YWbGYezqsFc1w36pr7b1ShAEbPj7Bn44dREKpQA/T3t8P9YfLra6v0mltvVKTOyV+nTZq4dXdJ5E42eNPZwL9O+//yIiIgIzZszA4cOHERERgXXr1mly2gqys7OhUCjg6upabrurqytSUlLUOsfx48cRHR2N9u3bq+Yfbdy4Ee3atav0eAsLi0rvfDMzM9PJD7SuzlsXsVc1w36przb0qqRMgU9+OofouJsAgOEdPfD5sHawNNPv+kC1oVeGgr1Sny56pe75NApCqamp8PHxAQDs3LkToaGh+Pzzz5GQkIBBgwZpckqdeeaZZ6BUKmv8vsjISERGRkKh0MHFdiKiGsgqKMHUTfGIu34PJhLgg0FtuD4QkZZodNeYubk5ioqKAAAHDx5Ev379AACOjo5qD0Wpw8nJCVKpFBkZGeW2Z2RkwM3NTWufU5nw8HAkJyfj9OnTOv0cIqLqnL2dh+eX/YW46/dga2mKtROC8Eq3ZgxBRFqiURB65plnEBERgfnz5yM2NhaDBw8GAFy8eLHCatNPw9zcHAEBAYiJiVFtUyqViImJQefOnbX2OUREhujXM2kYseIE0vKK0czZGnvCu6JnaxexyyKqUzQKQsuWLYOpqSl27NiB5cuXw8PDAwCwd+9eDBgwoEbnKiwsRGJiIhITEwE8uOyWmJiIGzduAAAiIiKwatUqrF+/HufPn8fUqVMhk8kwceJETUonIjJ4SqWAr/dfwLQt/6BYrkSPVs7Y/UZXNHfmrWFE2qbRHKFGjRrh119/rbB98eLFNT5XXFxcudWoH96xFRYWhqioKIwePRpZWVn45JNPcOfOHfj7+2Pfvn0VJlBrG+cIEZEYCkvK8E50Ig4kP5gS8Gr3Znh/gDekJrwURqQLagchmUxWo+dzqXt8z5498aSljKZNm4Zp06ap/dnaEB4ejvDwcOTn58Pe3l6vn01ExunG3SK8suE0LmYUwtzUBF8Mb4fhHbU33YCIKlL70liLFi3wxRdfID09vcpjBEHAgQMHMHDgQHz33XdaKZCIyBicuJKNIZF/4WJGIVxsLRD9aieGICI9UHtE6MiRI/jggw8wd+5c+Pn5ITAwEO7u7rC0tMS9e/eQnJyMkydPwtTUFLNnz8Zrr72my7p1jpfGiEgfBEHApr+vY+4vyapFEn94ORBu9pZil0ZkFNQOQq1bt8bOnTtx48YNbN++HceOHcOJEydw//59ODk5oUOHDli1ahUGDhwIqVS/C3zpAi+NEZGulZYpMefnc9ga++DmkGEdPLBguP4XSSQyZjWeLN2oUSPMmDEDM2bM0EU9RERG4W5hCaZuSkDstRxIJMCsAd54tTvXByLSN43uGiMiIs0lp+VjyoY43M69D1sLU3w3pgN6eXN9ICIxMAgREenR3n/TEfFjEu7LFWjqZI1V4wPRwoXrAxGJhUGoCpwsTUTapFQK+DbmEr6NuQQA6NbSCcvGdIS9FR/KSSQmjVaWNgZ81hgRaYuspAxvbE5QhaBXnmmKdROCGIKIDABHhIiIdOhmThGmbIhDyp0CmEtN8NkwX4wM9BK7LCL6j8ZBKDc3F7GxscjMzIRSqSy3b/z48U9dGBFRbff31bt4Y3MCcmSlcLKxwA8vByCgcX2xyyKiR2gUhH755Re89NJLKCwshJ2dXbnbPSUSCYMQERm9TX9fx9yfz6FMKaCdhz1Wjg9AQ/t6YpdFRI/RaI7QjBkzMGnSJBQWFiI3Nxf37t1TfeXk5Gi7RlFERkbCx8cHQUFBYpdCRLWIXKHER3v+xUd7zqJMKWCInzu2v96ZIYjIQGk0InT79m289dZbsLKy0nY9BoMrSxNRTeXISjF1UzxOpT5YJPG9/t54vQcXSSQyZBoFof79+yMuLg7NmjXTdj1ERLXS+fQHiyTeuncfNham+PZFfzzbxlXssojoCTQKQoMHD8a7776L5ORktGvXDmZm5W8BHTJkiFaKIyKqDfadvYOIHxNRVKpA4wZWWD0+EC1dbcUui4jUoFEQmjJlCgDg008/rbBPIpFwEUIiMgpKpYClhy5j8cGLAIBnWjhh2dgOcLAyF7kyIlKXRkHo8dvliYiMTVFpGWZuT8Lv/94BAEzs2gQfDmoDUynXqSWqTbigIhFRDd26V4QpG+JxPj0fZlIJPhvaDqOCuEgiUW2k8X9d/vzzT4SGhqJFixZo0aIFhgwZgmPHjmmzNlHx9nkiqkxsag6eX3Yc59Pz4WRjjq1TOjEEEdViGgWhTZs2oU+fPrCyssJbb72Ft956C/Xq1cOzzz6LLVu2aLtGUfBZY0T0uK2xN/DS6r9xV1aKtu52+GnaMwhs4ih2WUT0FDS6NPbZZ59h0aJFeOedd1Tb3nrrLXzzzTeYP38+xo4dq7UCiYjEJlco8b9fk7H+5HUAwOD2DfHVCD/UM5eKXBkRPS2NRoSuXr2K0NDQCtuHDBmC1NTUpy6KiMhQ3JOVYvyaWFUIerd/aywb04EhiKiO0GhEyMvLCzExMWjRokW57QcPHoSXF6+VE1HdcOFOAV7ZcBo3c+7D2lyKxaP90a+tm9hlEZEWaRSEZsyYgbfeeguJiYno0qULAOD48eOIiorCt99+q9UCiYjEsP/cHbwTnQhZqQKNHK2wanwgWrtxkUSiukajIDR16lS4ubnh66+/xo8//ggAaNOmDaKjo/H8889rtUAiIn0SBAGRhy/jq/0PFkns3KwBvn+pI+pbc5FEorpI43WEhg0bhmHDhmmzFiIiUd0vVeDdHUn49Uw6ACCsc2N89JwPzLhIIlGdxQUVqxAZGYnIyEg+LoTISNzOvY9XN8ThXNqDRRI/fd4XY4IbiV0WEemY2kHI0dERFy9ehJOTE+rXrw+JRFLlsTk5OVopTkzh4eEIDw9Hfn4+7O3txS6HiHQo/vo9TNuWhOzCUjSwNsfycQEIbsr1gYiMgdpBaPHixbC1tVX9urogRERUW5zMkGBnbBzkCgFtGtph1fgAeNa3ErssItITtYNQWFiY6tcTJkzQRS1ERHpTplBi/m8p2HZVCkDAoHZu+GqkH6zMOWOAyJhoNANQKpUiMzOzwva7d+9CKuUiY0Rk2HKLSjFh3Wls+PsGAGB67+aIHNuRIYjICGn0p14QhEq3l5SUwNyct5gSkeG6lFGAVzbE4frdIliZS/Fik1JM69Wcl/uJjFSNgtB3330HAJBIJFi9ejVsbGxU+xQKBY4ePQpvb2/tVkhEpCUHkzPwdnQiCkvK4Fm/HlaM9ceVhGNil0VEIqpREFq8eDGAByNCK1asKHcZzNzcHE2aNMGKFSu0WyER0VMSBAHL/7yCL/+4AEEAQpo6Yvm4ANiaS3BF7OKISFQ1CkIPH6jaq1cv7Nq1C/Xr19dJUURE2nK/VIH3d57Bz0lpAIBxnRphTmhbmElNIJfLRa6OiMSm0Ryhw4cPa7sOIiKtS8+7j1c3xOPf23kwNZFg7pC2GNepsdhlEZEB0fgWiVu3buHnn3/GjRs3UFpaWm7fN99889SFERE9jfjr9/DaxnhkF5bA0doc37/UEZ2aNRC7LCIyMBoFoZiYGAwZMgTNmjVDSkoKfH19ce3aNQiCgI4dO2q7RiKiGtkedxMf7j6LUoUS3m62WDU+EF6OXCSRiCrSaB2h2bNnY+bMmfj3339haWmJnTt34ubNm+jRowdGjhyp7RpFERkZCR8fHwQFBYldChGpqUyhxPxfk/HujjMoVSgxoK0bdk7twhBERFXSKAidP38e48ePBwCYmpri/v37sLGxwaeffoqFCxdqtUCxhIeHIzk5GadPnxa7FCJSQ16RHBOjTmPNXw9u6pj+bEt8/1JHWFtwkUQiqppGf0NYW1ur5gU1bNgQV65cQdu2bQEA2dnZ2quOiEgNlzMLMGVDPFKzZahnJsU3o/wwsF1DscsiolpAoyDUqVMn/PXXX2jTpg0GDRqEGTNm4N9//8WuXbvQqVMnbddIRFSlwymZeGvrPygoKYOHQz2sGh8IH3c7scsiolpCoyD0zTffoLCwEAAwb948FBYWIjo6Gi1btuQdY0SkF4Ig4IejV7FwXwoEAQhu4ojvx3WEk42F2KURUS1S4yCkUChw69YttG/fHsCDy2RcTZqI9KlYrsCsnWewJ/HBIoljghth3pC2MDfVaNojERmxGgchqVSKfv364fz583BwcNBBSUREVbuTV4xXN8bhzK08SE0kmBvqg3GdGvOhqUSkEY0ujfn6+uLq1ato2rSptushIqrSPzceLJKYWVACByszfP9SR3Rp7iR2WURUi2k0jvy///0PM2fOxK+//or09HTk5+eX+yIi0rad8bcweuXfyCwoQWtXW/wc/gxDEBE9NY1GhAYNGgQAGDJkSLnhaEEQIJFIoFAotFMdERk9hVLAF3vPY9WxB+sD9fVxxeLR/rDh+kBEpAV86CoRGay8+3K8tfUf/HkxCwDwZu8WeKdPK5iYcD4QEWmHRkGoR48e2q6DiKicK1mFmLI+DlezZbA0M8FXI/3wXHt3scsiojpGoyB09OjRavd3795do2KIiADgyIVMvLn1HxQUl8Hd3hIrxwfC18Ne7LKIqA7SKAj17NmzwrZH5wpxjhARaUIQBKw+looFe89DKQCBjetj+bgAONtykUQi0g2N7hq7d+9eua/MzEzs27cPQUFB2L9/v7ZrfCq5ubkIDAyEv78/fH19sWrVKrFLIqJKFMsVmLE9CZ/9/iAEjQ70wuYpIQxBRKRTGo0I2dtXHKLu27cvzM3NERERgfj4+KcuTFtsbW1x9OhRWFlZQSaTwdfXF8OHD0eDBg3ELo2I/pORX4zXNsYj8WYupCYSfDy4DcK6NOEiiUSkc1q9/9TV1RUXLlzQ5imfmlQqhZWVFQCgpKQEgiBAEASRqyKih5Ju5uLVjXHIyC+Bfb0HiyR2bcH1gYhIPzS6NHbmzJlyX0lJSdi3bx9ef/11+Pv71+hcR48eRWhoKNzd3SGRSLBnz54Kx0RGRqJJkyawtLRESEgIYmNja/QZubm58PPzg6enJ9599104OfEvWSJDsOef2xj5w0lk5JegpYsNfp7WlSGIiPRKoxEhf39/SCSSCiMrnTp1wtq1a2t0LplMBj8/P0yaNAnDhw+vsD86OhoRERFYsWIFQkJCsGTJEvTv3x8XLlyAi4uLqp6ysrIK792/fz/c3d3h4OCApKQkZGRkYPjw4RgxYgRcXV1rVCcRaY9CKWDRHyn44c+rAIA+bVyweLQ/bC3NRK6MiIyNRkEoNTW13GsTExM4OzvD0tKyxucaOHAgBg4cWOX+b775BlOmTMHEiRMBACtWrMBvv/2GtWvXYtasWQCAxMREtT7L1dUVfn5+OHbsGEaMGFHpMSUlJSgpKVG9fvjIELlcDrlcrtbnqOPhubR5zrqKvaoZQ+9XQbEc72z/F39ezAYATO3eFG8/2wImJvqv2dB7ZUjYK/WxV+rTZa/UPadEMKAJMxKJBLt378bQoUMBAKWlpbCyssKOHTtU2wAgLCwMubm5+Omnn554zoyMDFhZWcHW1hZ5eXno2rUrtm7dinbt2lV6/Ny5czFv3rwK27ds2aKaa0REmsm8D6y+IEXGfQnMJALGtFAiwMlg/goiojqkqKgIY8eORV5eHuzs7Ko8rsYjQkqlElFRUdi1axeuXbsGiUSCpk2bYsSIEXj55Ze1epdHdnY2FApFhctYrq6uSElJUesc169fx6uvvqqaJP3mm29WGYIAYPbs2YiIiFC9zs/Ph5eXF/r161dtI2tKLpfjwIED6Nu3L8zMeDmgOuxVzRhqv45dzsbH0WeQX1wGNzsLLB/bAb4e2vszpQlD7ZUhYq/Ux16pT5e9Uvch8DUKQoIgYMiQIfj999/h5+eHdu3aQRAEnD9/HhMmTMCuXbsqnewspuDgYLUvnQGAhYUFLCwqrltiZmamkx9oXZ23LmKvasZQ+iUIAtYev4bPfkuGUgA6NnLAipcD4GJb80vpumIovaoN2Cv1sVfq00Wv1D1fjYJQVFQUjh49ipiYGPTq1avcvkOHDmHo0KHYsGEDxo8fX5PTVsnJyQlSqRQZGRnltmdkZMDNzU0rn1GVyMhIREZGcpVsoqdQUqbAh7vPYkf8LQDAyABP/G+YLyxMpSJXRkT0QI1un9+6dSs++OCDCiEIAHr37o1Zs2Zh8+bNWivO3NwcAQEBiImJUW1TKpWIiYlB586dtfY5lQkPD0dycjJOnz6t088hqqsyC4oxZuXf2BF/CyYS4JPnfLBoRHuGICIyKDUaETpz5gwWLVpU5f6BAwfiu+++q1EBhYWFuHz5sup1amoqEhMT4ejoiEaNGiEiIgJhYWEIDAxEcHAwlixZAplMprqLjIgMz5lbuXh1Qzzu5BfDztIUy8Z2RPdWzmKXRURUQY2CUE5OTrXr77i6uuLevXs1KiAuLq7cCNPDicphYWGIiorC6NGjkZWVhU8++QR37tyBv78/9u3bp/N1gHhpjEgzPyXexns7zqCkTInmztZYHRaEpk7WYpdFRFSpGgUhhUIBU9Oq3yKVSitd2LA6PXv2fOIjL6ZNm4Zp06bV6LxPKzw8HOHh4cjPz6/02WpEVJ5SKeCr/Rfw/ZErAIDe3i5Y8qI/7LhIIhEZsBrfNTZhwoRK76oCUG4hQiIyHgXFcry9LRExKZkAgNd7NMe7/VtDasKHphKRYatREAoLC3viMdq6Y4yIaodr2TK8siEOlzMLYWFqgoUvtMfQDh5il0VEpJYaBaF169bpqg6DwzlCRE/216VshG9JQN59OVztLLDy5UD4eTmIXRYRkdo0evq8MeDt80RVEwQB646nImxdLPLuy+Hv5YBfpj3DEEREtY5GD10lIuNVUqbAJ3vOITruJgBgeEcPfD6sHSzNuD4QEdU+DEJEpLasghJM3RSPuOv3YCIBPhjUBpOfaarVZwwSEekTg1AVOEeIqLyzt/Pw6oY4pOUVw9bSFEvHdEDP1i5il0VE9FQ4R6gKnCNE9P9+PZOGEStOIC2vGM2crbEnvCtDEBHVCRwRIqIqKZUCvjlwEcsOP3gMTo9WzvhuTAfY1+MiiURUNzAIEVGlCkvK8E50Ig4kZwAAXu3eDO8P8OYiiURUpzAIEVEFN+4W4ZUNp3ExoxDmpib4Yng7DO/oKXZZRERaxyBEROWcuJKNNzYnILdIDhdbC/zwcgA6NKovdllERDrBIFQF3jVGxkYQBGz8+zrm/ZIMhVKAn6c9fng5EG72lmKXRkSkM7xrrAq8a4yMSWmZEh/s/hef/HQOCqWAYR08EP1aZ4YgIqrzOCJEZOSyCx8sknj62j1IJMCsAd54tXszLpJIREaBQYjIiJ1Ly8OrG+JxO/c+bC1M8d2YDujlzfWBiMh4MAgRGanf/03HjB+TcF+uQFMna6waH4gWLjZil0VEpFcMQkRGRqkUsCTmEr6LuQQA6NbSCcvGdIS9FRdJJCLjwyBUBd41RnWRrKQMET8m4o9zDxZJfOWZppg10BumUt43QUTGiUGoCuHh4QgPD0d+fj7s7e3FLofoqd3MKcKUDXFIuVMAc6kJPhvmi5GBXmKXRUQkKgYhIiNw8spdvLE5HveK5HC2tcCKcQEIaMxFEomIGISI6hCFUsCp1BzEZ0vQIDUHnVu4YEvsDcz7+RzKlALaedhj5fgANLSvJ3apREQGgUGIqI7YdzYd835JRnpeMQApNlyKg5W5FEWlD+a5DfFzx6IR7WFpJhW3UCIiA8IgRFQH7DubjqmbEiA8tv1hCBrq74HFo/24SCIR0WN4qwhRLadQCpj3S3KFEPSoU6l3oazuACIiI8UgRFTLxabm/Hc5rGrpecWITc3RU0VERLUHL41VgesIkaG7mlWIQymZ2Hb6hlrHZxZUH5aIiIwRg1AVuI4QGRq5QonTqTmIScnEoZRMpGbLavR+F1s+SZ6I6HEMQkQGLEdWiiMXMhGTkomjF7JQUFKm2mcmlaBTswbo2doZK45cRXZhSaXzhCQA3OwtEdzUUW91ExHVFgxCRAZEEARcyChAzPkHoz4JN+5BeCTdNLA2Ry9vFzzr7YJurZxhY/Hgj7CHQz1M3ZQACVAuDD28R2xOqA+kJrxjjIjocQxCRCIrlivw99W7OJSSiZjzmbide7/cfp+Gdni2jQt6e7vAz9MBJpUEmgG+DbF8XMdH1hF6wM3eEnNCfTDAt6HOvw8iotqIQYhIBJn5xQ+CT0om/rqUjfvy/5+Ub2Fqgq4tnNDb+0H4cXdQbxXoAb4N0dfHDScvZ2L/sVPo1y0EnVu4cCSIiKgaDEJEeqBUCjiXlo+YlAwcSsnEmVt55fa72lmgt7cr+rRxQZfmTqhnrtnqz1ITCUKaOuLueQEhTR0ZgoiInoBBiEhHikrLcPzyXcScfxB+MgtKyu3383LAs/+N+rR1t+Oqz0REImAQItKiW/eKcPi/S14nrtxFaZlStc/KXIpuLZ3wrLcreno783Z2IiIDwCBE9BQUSgGJN3NxKCUDMeczkXKnoNx+z/r10KeNK3p7uyCkmSMsTPnAUyIiQ8IgRFRD+cVyHLuYjZiUDBy5kIUcWalqn4kECGhcH729XfFsGxe0dLHhJS8iIgPGIESkhmvZsv9WdM7Aqas5KHvkCaa2lqbo0coZz7ZxQc9WLqhvbS5ipUREVBMMQlXgs8aMm1yhRNy1ew8ueaVk4mpW+cdZNHO2/m+isysCm9SHmZTPLyYiqo0YhKrAZ40Zn3uyUvx5MQsxKZn480Im8ov//3EWpiYSBDd1RG9vFzzbxhVNnaxFrJSIiLSFQYiMliAIuJxZiIPnH1zyir9+D49c8UJ9KzP0av0g+HRr5QQ7SzPxiiUiIp1gECKjUlKmwKmrOf+t6pyBmznlH2fh7Wb736iPC/y96nNBQiKiOo5BiOq8rIISHL6QiZjzGTh2KRtFpf8/78tcaoLOzRvg2TYu6NXaBV6OViJWSkRE+sYgRAZNoRRwKjUH8dkSNEjNUevZWYLw4HEWD5/llXQzt9x+Z1sL1YrOXVs4wdqCfwyIiIwV/wUgg7XvbPojT1OXYsOlODSs4mnq90sVOHEl+8Et7uczcSe/uNz+dh72qktevu72lT7BnYiIjA+DEBmkfWfTMXVTAoTHtt/JK8bUTQlYPq4j2ns64FBKJg6lZOL45WyUPPI4C0szEzzT4sHaPr29XeBqx8dZEBFRRQxCZHAUSgHzfkmuEIIAqLZN2/JPuUUNAcDd3hLPtnFF7zYu6NysASzN+DgLIiKqHoMQGZzY1Jz/LodV7WEI6tjI4UH48XaBt5stH2dBREQ1wiBEBiezoPoQ9NBnQ33xUqfGOq6GiIjqMj4XgAyOi61683maOdvouBIiIqrrGITI4FiYmkBazSUuCYCG9pYIbuqov6KIiKhO4qUxMhhKpYBVx67iyz8uQCFUNlX6QQgCgDmhPlz1mYiInhqDEBmErIISzNiehKMXswAAA33d0KeNK77af6HcxGm3KtYRIiIi0oTRBKGioiK0adMGI0eOxFdffSV2OfSIoxezEPFjErILS2BhaoI5oW0xJtgLEokEQzt44OTlTOw/dgr9uoWotbI0ERGRuowmCH322Wfo1KmT2GXQI0rLlPj6wAX88OdVAEBrV1ssHdsBrVxtVcdITSQIaeqIu+cFhDR1ZAgiIiKtMoogdOnSJaSkpCA0NBRnz54VuxwCcONuEd7c9o/qOWDjOjXCR4N9uAgiERHpleh3jR09ehShoaFwd3eHRCLBnj17KhwTGRmJJk2awNLSEiEhIYiNja3RZ8ycORMLFizQUsX0tH5KvI1B3x1D0s1c2FmaYsW4jvjf0HYMQUREpHeijwjJZDL4+flh0qRJGD58eIX90dHRiIiIwIoVKxASEoIlS5agf//+uHDhAlxcXAAA/v7+KCsrq/De/fv34/Tp02jVqhVatWqFEydOPLGekpISlJSUqF7n5+cDAORyOeRyuabfZgUPz6XNcxo6WUkZ5v+egp0JaQCAgEYO+GZkO7g71Ku2D8bYq6fBfqmPvVIfe6U+9kp9uuyVuueUCEIV9ymLQCKRYPfu3Rg6dKhqW0hICIKCgrBs2TIAgFKphJeXF958803MmjXrieecPXs2Nm3aBKlUisLCQsjlcsyYMQOffPJJpcfPnTsX8+bNq7B9y5YtsLKy0uwbI9ySAesvSpFZLIEEAvp5COjvpYSUU36IiEgHioqKMHbsWOTl5cHOzq7K4ww6CJWWlsLKygo7duwoF47CwsKQm5uLn376qUbnj4qKwtmzZ6u9a6yyESEvLy9kZ2dX28iaksvlOHDgAPr27QszMzOtndfQCIKADX/fwMI/LkKuEOBqZ4GvR7RDSA0WQzSWXmkL+6U+9kp97JX62Cv16bJX+fn5cHJyemIQEv3SWHWys7OhUCjg6upabrurqytSUlJ08pkWFhawsLCosN3MzEwnP9C6Oq8hyJGV4r0dSTh4PhMA0KeNCxaN8IOjtblG56vLvdIF9kt97JX62Cv1sVfq00Wv1D2fQQchbZswYYLax0ZGRiIyMhIKhUJ3BdVhJ6/cxdvR/yAjvwTmUhN8MMgbYV2a8OnwRERkUAw6CDk5OUEqlSIjI6Pc9oyMDLi5uen0s8PDwxEeHo78/HzY29vr9LPqkjKFEt/GXMKyw5chCEAzZ2ssHdMBbd3ZQyIiMjyi3z5fHXNzcwQEBCAmJka1TalUIiYmBp07dxaxMqrMrXtFeHHl31h66EEIGhXoiV/ffIYhiIiIDJboI0KFhYW4fPmy6nVqaioSExPh6OiIRo0aISIiAmFhYQgMDERwcDCWLFkCmUyGiRMnilg1PW7f2XS8t+MM8ovLYGNhis+G+eJ5fw+xyyIiIqqW6EEoLi4OvXr1Ur2OiIgA8ODOsKioKIwePRpZWVn45JNPcOfOHfj7+2Pfvn0VJlBrG+cIqadYrsD8X5Ox+dQNAICflwOWvtgBjRpwqQEiIjJ8ogehnj174kl38E+bNg3Tpk3TU0UPcI7Qk13MKMC0LQm4mFEIAHi9R3PM6NcKZlKDvuJKRESkInoQotpHEARsib2BT39JRkmZEk42Flg82g/dWjqLXRoREVGNMAhVgZfGKpdXJMesXWew9+wdAED3Vs74eqQfnG0rrr1ERERk6BiEqsBLYxXFXcvB9G2JuJ17H6YmErw3oDVeeaYZTEy4NhAREdVODEL0RAqlgO8PX8aSmEtQKAU0bmCF717sAD8vB7FLIyIieioMQlStO3nFeCc6ESev3gUADPV3x/yhvrC15LLxRERU+zEIUZVizmdg5vYk3CuSw8pcik+f98ULHT34mAwiIqozGISqYMyTpUvKFFjwewqiTlwDALR1t8PSMR3QzNlG3MKIiIi0jEGoCsY6WfpKViHe3PIPktPzAQCTujbF+wNbw8JUKnJlRERE2scgRAAerA20I/4W5vx8DkWlCjham+Orke3R21u3K3gTERGJiUGIUFAsx0d7zuKnxDQAQOdmDbDkRX+42lmKXBkREZFuMQgZuaSbuXhz6z+4kVMEqYkEEX1b4fUezSHl2kBERGQEGISqUNcnSyuVAlYdu4ov/7iAMqUAD4d6+G6MPwIaO4pdGhERkd4wCFWhLk+WzioowYztSTh6MQsAMKidGxYMbw/7elwbiIiIjAuDkJE5ejELET8mIruwFJZmJpgT2hYvBnlxbSAiIjJKDEJGorRMia/3X8APR68CAFq72mLZ2A5o6WorcmVERETiYRAyAjfuFuHNbf8g6WYuAGBcp0b4aLAPLM24NhARERk3BqE67qfE2/hw91kUlpTBztIUi0a0xwDfhmKXRUREZBAYhOooWUkZ5v58DtvjbwEAgprUx5IXO8DDoZ7IlRERERkOBqEq1Obb58+l5eHNrf/gapYMJhJgWu+WeKt3C5hKTcQujYiIyKAwCFWhNt4+LwgCok5cw4LfU1CqUMLNzhJLXvRHp2YNxC6NiIjIIDEI1RE5slK8tyMJB89nAgD6tHHBlyP8UN/aXOTKiIiIDBeDUB1w8spdvB39DzLyS2AuNcEHg7wR1qUJ1wYiIiJ6AgahWqxMocS3MZew7PBlCALQzNkay8Z0hI+7ndilERER1QoMQrXUrXtFeHtbIuKu3wMAjAr0xNwhbWFlzt9SIiIidfFfzVpo77/peH/nGeQXl8HWwhSfDW+HIX7uYpdFRERU6zAI1SLFcgU+/TUZW07dAAD4eznguxc7oFEDK5ErIyIiqp0YhKpgaOsIXcwowLQtCbiYUQgAeL1Hc8zo1wpmXBuIiIhIYwxCVTCUdYQEQcCW2Bv49JdklJQp4WRjgcWj/dCtpbNoNREREdUVDEIGLK9Ijlm7zmDv2TsAgO6tnPH1SD8421qIXBkREVHdwCBkoOKu5WD6tkTczr0PM6kE7/X3xuRnmsLEhGsDERERaQuDkIFRKAV8f/gylsRcgkIpoHEDKywd0wHtPR3ELo2IiKjOYRASgUIp4FRqDuKzJWiQmoPOLVwgNZHgTl4x3o7+B39fzQEADPV3x/yhvrC1NBO5YiIiorqJQUjP9p1Nx7xfkpGeVwxAig2X4tDQ3hLDOnhga+wN3CuSw8pcivnP++KFAE+xyyUiIqrTGIT0aN/ZdEzdlADhse3pecX4/sgVAEBbdzssHdMBzZxt9F8gERGRkWEQ0hOFUsC8X5IrhKBHWZtLsf31znxMBhERkZ5wNT49iU3N+e9yWNVkpQok3czTU0VERETEIKQnmQXVh6CaHkdERERPj0FIT1xsLbV6HBERET09BqEqREZGwsfHB0FBQVo5X3BTRzS0t0RVyyFKADS0t0RwU0etfB4RERE9GYNQFcLDw5GcnIzTp09r5XxSEwnmhPoAQIUw9PD1nFAfSLlyNBERkd4wCOnRAN+GWD6uI9zsy1/+crO3xPJxHTHAt6FIlRERERkn3qetZwN8G6KvjxtOXs7E/mOn0K9biGplaSIiItIvBiERSE0kCGnqiLvnBYQ0dWQIIiIiEgkvjREREZHRYhAiIiIio8UgREREREaLQYiIiIiMFoMQERERGS0GISIiIjJaDEJERERktBiEiIiIyGgxCBEREZHR4srSTyAIAgAgPz9fq+eVy+UoKipCfn4+zMzMtHruuoa9qhn2S33slfrYK/WxV+rTZa8e/rv98N/xqjAIPUFBQQEAwMvLS+RKiIiIqKYKCgpgb29f5X6J8KSoZOSUSiXS0tJga2sLiaT8M8GCgoJw+vTpardV9To/Px9eXl64efMm7OzstF53ZbVp6z3VHVfVPvZK/X1P0ysAOu0Xe6U+TXql7vt01avHt+mrV9XV/bTv0VevHn1dF3tV3X5D/ftdEAQUFBTA3d0dJiZVzwTiiNATmJiYwNPTs9J9Uqm0wm/c49ue9NrOzk4nf1Aqq01b76nuuKr2sVfq79NGrwDd9Iu9Up8mvVL3fbrq1ePb9NWrqj5LG+/RV68qe12XelXdfkP++726kaCHOFn6KYSHhz9x25Ne64omn6Pue6o7rqp97JX6+9gr9ffVtV6p+z5d9erxbfrqlaafZUi9UrcebRCjV9XtN+Q/h+rgpTGR5Ofnw97eHnl5eTpJwXUJe1Uz7Jf62Cv1sVfqY6/UZwi94oiQSCwsLDBnzhxYWFiIXYrBY69qhv1SH3ulPvZKfeyV+gyhVxwRIiIiIqPFESEiIiIyWgxCREREZLQYhIiIiMhoMQgRERGR0WIQIiIiIqPFIGSgfv31V7Ru3RotW7bE6tWrxS7HoA0bNgz169fHiBEjxC7FoN28eRM9e/aEj48P2rdvj+3bt4tdksHKzc1FYGAg/P394evri1WrVoldksErKipC48aNMXPmTLFLMWhNmjRB+/bt4e/vj169eoldjsFLTU1Fr1694OPjg3bt2kEmk2n9M3j7vAEqKyuDj48PDh8+DHt7ewQEBODEiRNo0KCB2KUZpCNHjqCgoADr16/Hjh07xC7HYKWnpyMjIwP+/v64c+cOAgICcPHiRVhbW4tdmsFRKBQoKSmBlZUVZDIZfH19ERcXxz+D1fjwww9x+fJleHl54auvvhK7HIPVpEkTnD17FjY2NmKXUiv06NED//vf/9CtWzfk5OTAzs4OpqbafToYR4QMUGxsLNq2bQsPDw/Y2Nhg4MCB2L9/v9hlGayePXvC1tZW7DIMXsOGDeHv7w8AcHNzg5OTE3JycsQtykBJpVJYWVkBAEpKSiAIAvh/xqpdunQJKSkpGDhwoNilUB1y7tw5mJmZoVu3bgAAR0dHrYcggEFIJ44ePYrQ0FC4u7tDIpFgz549FY6JjIxEkyZNYGlpiZCQEMTGxqr2paWlwcPDQ/Xaw8MDt2/f1kfpeve0vTIm2uxVfHw8FAoFvLy8dFy1OLTRq9zcXPj5+cHT0xPvvvsunJyc9FS9fmmjVzNnzsSCBQv0VLF4tNEriUSCHj16ICgoCJs3b9ZT5eJ42n5dunQJNjY2CA0NRceOHfH555/rpE4GIR2QyWTw8/NDZGRkpfujo6MRERGBOXPmICEhAX5+fujfvz8yMzP1XKn42Cv1aatXOTk5GD9+PFauXKmPskWhjV45ODggKSkJqamp2LJlCzIyMvRVvl49ba9++ukntGrVCq1atdJn2aLQxs/VX3/9hfj4ePz888/4/PPPcebMGX2Vr3dP26+ysjIcO3YM33//PU6ePIkDBw7gwIED2i9UIJ0CIOzevbvctuDgYCE8PFz1WqFQCO7u7sKCBQsEQRCE48ePC0OHDlXtnz59urB582a91CsmTXr10OHDh4UXXnhBH2UaBE17VVxcLHTr1k3YsGGDvkoV3dP8XD00depUYfv27bos0yBo0qtZs2YJnp6eQuPGjYUGDRoIdnZ2wrx58/RZtii08XM1c+ZMYd26dTqs0nBo0q8TJ04I/fr1U+1ftGiRsGjRIq3XxhEhPSstLUV8fDz69Omj2mZiYoI+ffrg5MmTAIDg4GCcPXsWt2/fRmFhIfbu3Yv+/fuLVbJo1OkVPaBOrwRBwIQJE9C7d2+8/PLLYpUqOnV6lZGRgYKCAgBAXl4ejh49itatW4tSr5jU6dWCBQtw8+ZNXLt2DV999RWmTJmCTz75RKySRaNOr2QymernqrCwEIcOHULbtm1FqVds6vQrKCgImZmZuHfvHpRKJY4ePYo2bdpovRbtzzqiamVnZ0OhUMDV1bXcdldXV6SkpAAATE1N8fXXX6NXr15QKpV47733jPJuFXV6BQB9+vRBUlISZDIZPD09sX37dnTu3Fnf5YpKnV4dP34c0dHRaN++vepa/caNG9GuXTt9lysqdXp1/fp1vPrqq6pJ0m+++abR9QlQ/88gqderjIwMDBs2DMCDOxOnTJmCoKAgvddqCNT9t/Dzzz9H9+7dIQgC+vXrh+eee07rtTAIGaghQ4ZgyJAhYpdRKxw8eFDsEmqFZ555BkqlUuwyaoXg4GAkJiaKXUatM2HCBLFLMGjNmjVDUlKS2GXUKgMHDtT53Yi8NKZnTk5OkEqlFSZeZmRkwM3NTaSqDBN7pT72Sn3slfrYK/WxVzVjSP1iENIzc3NzBAQEICYmRrVNqVQiJibG6C7nPAl7pT72Sn3slfrYK/WxVzVjSP3ipTEdKCwsxOXLl1WvU1NTkZiYCEdHRzRq1AgREREICwtDYGAggoODsWTJEshkMkycOFHEqsXBXqmPvVIfe6U+9kp97FXN1Jp+af0+NBIOHz4sAKjwFRYWpjpm6dKlQqNGjQRzc3MhODhY+Pvvv8UrWETslfrYK/WxV+pjr9THXtVMbekXnzVGRERERotzhIiIiMhoMQgRERGR0WIQIiIiIqPFIERERERGi0GIiIiIjBaDEBERERktBiEiIiIyWgxCREREZLQYhIiIiMhoMQgRET0liUSCPXv2iF0GEWmAQYiIRHXy5ElIpVIMHjxY7FIqlZWVhalTp6JRo0awsLCAm5sb+vfvj+PHj6uOSU9Px8CBA0Wskog0xafPE5Go1qxZgzfffBNr1qxBWloa3N3dqzxWEAQoFAqYmpb/q6u0tBTm5uY6qe+FF15AaWkp1q9fj2bNmiEjIwMxMTG4e/eu6hg3NzedfDYR6R5HhIhINIWFhYiOjsbUqVMxePBgREVFldt/5MgRSCQS7N27FwEBAbCwsMBff/2Fnj17Ytq0aXj77bfh5OSE/v37AwC++eYbtGvXDtbW1vDy8sIbb7yBwsJCAIBMJoOdnR127NhR7jP27NkDa2trFBQUVKgvNzcXx44dw8KFC9GrVy80btwYwcHBmD17NoYMGaI67tFLY3PnzoVEIqnw9fB7UyqVWLBgAZo2bYp69erBz8+vQk1EpD8MQkQkmh9//BHe3t5o3bo1xo0bh7Vr10IQhArHzZo1C1988QXOnz+P9u3bAwDWr18Pc3NzHD9+HCtWrAAAmJiY4LvvvsO5c+ewfv16HDp0CO+99x4AwNraGi+++CLWrVtX7tzr1q3DiBEjYGtrW+FzbWxsYGNjgz179qCkpESt72nmzJlIT09XfX311VewsrJCYGAgAGDBggXYsGEDVqxYgXPnzuGdd97BuHHj8Oeff6rfOCLSHoGISCRdunQRlixZIgiCIMjlcsHJyUk4fPiwav/hw4cFAMKePXvKva9Hjx5Chw4dnnj+7du3Cw0aNFC9PnXqlCCVSoW0tDRBEAQhIyNDMDU1FY4cOVLlOXbs2CHUr19fsLS0FLp06SLMnj1bSEpKKncMAGH37t0V3nvy5EnB0tJSiI6OFgRBEIqLiwUrKyvhxIkT5Y6bPHmyMGbMmCd+P0SkfRwRIiJRXLhwAbGxsRgzZgwAwNTUFKNHj8aaNWsqHPtwNOVRAQEBFbYdPHgQzz77LDw8PGBra4uXX34Zd+/eRVFREQAgODgYbdu2xfr16wEAmzZtQuPGjdG9e/cq63zhhReQlpaGn3/+GQMGDMCRI0fQsWPHCpfxHnfjxg0MHToUM2fOxKhRowAAly9fRlFREfr27asabbKxscGGDRtw5cqVas9HRLrBIEREolizZg3Kysrg7u4OU1NTmJqaYvny5di5cyfy8vLKHWttbV3h/Y9vu3btGp577jm0b98eO3fuRHx8PCIjIwE8mEz90CuvvKIKMevWrcPEiRMhkUiqrdXS0hJ9+/bFxx9/jBMnTmDChAmYM2dOlcfLZDIMGTIEnTt3xqeffqra/nC+0m+//YbExETVV3JyMucJEYmEQYiI9K6srAwbNmzA119/XS4QJCUlwd3dHVu3bq3xOePj46FUKvH111+jU6dOaNWqFdLS0iocN27cOFy/fh3fffcdkpOTERYWVuPP8vHxgUwmq3SfIAgYN24clEolNm7cWC5k+fj4wMLCAjdu3ECLFi3KfXl5edW4DiJ6erx9noj07tdff8W9e/cwefJk2Nvbl9v3wgsvYM2aNXj99ddrdM4WLVpALpdj6dKlCA0NLTeJ+lH169fH8OHD8e6776Jfv37w9PSs8px3797FyJEjMWnSJLRv3x62traIi4vDokWL8Pzzz1f6nrlz5+LgwYPYv38/CgsLVaNA9vb2sLW1xcyZM/HOO+9AqVTimWeeQV5eHo4fPw47OzuNQhkRPR2OCBGR3q1ZswZ9+vSpEIKAB0EoLi4OZ86cqdE5/fz88M0332DhwoXw9fXF5s2bsWDBgkqPnTx5MkpLSzFp0qRqz2ljY4OQkBAsXrwY3bt3h6+vLz7++GNMmTIFy5Ytq/Q9f/75JwoLC9GlSxc0bNhQ9RUdHQ0AmD9/Pj7++GMsWLAAbdq0wYABA/Dbb7+hadOmNfp+iUg7JIJQyb2qRER12MaNG/HOO+8gLS1NZwsxElHtwEtjRGQ0ioqKkJ6eji+++AKvvfYaQxAR8dIYERmPRYsWwdvbG25ubpg9e7bY5RCRAeClMSIiIjJaHBEiIiIio8UgREREREaLQYiIiIiMFoMQERERGS0GISIiIjJaDEJERERktBiEiIiIyGgxCBEREZHR+j9zjDAr3MnZIwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(array_sizes, durations, marker='o', linestyle='-')\n",
    "\n",
    "# Labeling\n",
    "plt.title('Array Size vs Duration')\n",
    "plt.xlabel('Array Size')\n",
    "plt.ylabel('Duration (seconds)')\n",
    "plt.xscale('log')  # Use logarithmic scale for better visualization of the large range of array sizes\n",
    "plt.yscale('log')  # Use logarithmic scale for better visualization of the range of durations\n",
    "plt.grid(True)\n",
    "\n",
    "# Show plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8fe4339-852f-44c1-9214-73e160a3a01f",
   "metadata": {},
   "source": [
    "### C-5.16\n",
    "Implement a pop method for the DynamicArray class, given in Code Fragment 5.3, that removes the last element of the array, and that shrinks the\n",
    "capacity, N, of the array by half any time the number of elements in the\n",
    "array goes below N/4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "id": "e58859dc-8ad9-4a33-a6ac-2faa99adad1c",
   "metadata": {},
   "outputs": [],
   "source": [
    "class DynamicArray:\n",
    "\n",
    "    def __init__(self):\n",
    "        self._n = 0\n",
    "        self._capacity = 1\n",
    "        self._A = self._make_array(self._capacity)\n",
    "\n",
    "    def __len__(self):\n",
    "        return self._n\n",
    "\n",
    "    def __getitem__(self,k):\n",
    "        if not k < self._n:\n",
    "            raise IndexError('invalid index')\n",
    "        return self._A[k]\n",
    "\n",
    "    def append(self,obj):\n",
    "        if self._n == self._capacity:\n",
    "            self._resize(self._capacity//4)\n",
    "        self._A[self._n] = obj\n",
    "        self._n += 1\n",
    "\n",
    "    def pop(self):\n",
    "        value = None\n",
    "        if not self._n > 0:\n",
    "            return value\n",
    "        end_split = (len(self._A)//4)\n",
    "        if end_split > 0:\n",
    "            removal_indices = end_split*-1\n",
    "            value = self._A[removal_indices:self._n-1]\n",
    "            self._A = self._A[:removal_indices]\n",
    "            self._n -= removal_indices\n",
    "            self._capacity -= removal_indices\n",
    "        else:\n",
    "            self._A = self._A[:-1]\n",
    "            self._n -= 1\n",
    "            self._capacity -= 1\n",
    "            value = self._A[:self._n-1]\n",
    "        return value\n",
    "        \n",
    "    def _resize(self,c):\n",
    "        if int(c) == 0:\n",
    "            c = 1\n",
    "        c = self._capacity + c\n",
    "        B = self._make_array(c)\n",
    "        for k in range(self._n):\n",
    "            B[k] = self._A[k]\n",
    "        self._A = B\n",
    "        self._capacity = c\n",
    "\n",
    "    def _make_array(self,c):\n",
    "        return (c * ctypes.py_object)()\n",
    "\n",
    "    def __str__(self,):\n",
    "        print(self._n,self._capacity)\n",
    "        return f\"Array  {[self._A[i] for i in range(self._n)] }, Number of items {self._n}, Capacity {self._capacity}\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "id": "aab9f81c-2bc3-4546-a904-3e157a32a0be",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Array Size  Duration in Secs\n",
      "0           1          0.000006\n",
      "1          10          0.000002\n",
      "2         100          0.000006\n",
      "3       10000          0.000243\n",
      "4      100000          0.002885\n",
      "5     1000000          0.036664\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "da_list = [DynamicArray() for i in range(0,6)]\n",
    "array_sizes = [1,10,100,10000,100000,1000000]\n",
    "\n",
    "durations = []\n",
    "for size,da in zip(array_sizes,da_list):\n",
    "    for i in range(0,size):\n",
    "        da.append(i)\n",
    "    start = time.perf_counter()\n",
    "    da.pop()\n",
    "    end = time.perf_counter()\n",
    "    durations.append(end-start)\n",
    "\t\n",
    "index = ['append to last item']\n",
    "\n",
    "df = pd.DataFrame({'Array Size': array_sizes, 'Duration in Secs': durations })\n",
    "print(df)\n",
    "\n",
    "plt.plot(array_sizes, durations, marker='o', linestyle='-')\n",
    "\n",
    "# Labeling\n",
    "plt.title('Array Size vs Pop Method')\n",
    "plt.xlabel('Array Size')\n",
    "plt.ylabel('Duration (seconds)')\n",
    "plt.xscale('log')  # Use logarithmic scale for better visualization of the large range of array sizes\n",
    "plt.yscale('log')  # Use logarithmic scale for better visualization of the range of durations\n",
    "plt.grid(True)\n",
    "\n",
    "# Show plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64d1f9ae-1f23-429f-8f8c-08a0d3aa7f93",
   "metadata": {},
   "source": [
    "### C-5.21 \n",
    "In Section 5.4.2, we described four different ways to compose a long\n",
    "string: \n",
    "(1) repeated concatenation\n",
    "(2) appending to a temporary list and then joining\n",
    "(3) using list comprehension with join\n",
    "(4) using generator comprehension with join. Develop an experiment to test the efficiency\n",
    "of all four of these approaches and report your findings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "6a0e1a76-b2e9-4cc5-bf39-306c358dc082",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "import sys\n",
    "\n",
    "def time_mem_analysis(func):\n",
    "\n",
    "    def wrapper(*args,**kwargs):\n",
    "        start = time.perf_counter()\n",
    "        rs = func(*args,**kwargs)\n",
    "        end = time.perf_counter()\n",
    "        size_in_mb = sys.getsizeof(rs)/(1024**2)\n",
    "        return {'data':rs, 'secs':end-start, 'mem in mb':size_in_mb}\n",
    "\n",
    "    return wrapper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2a68bceb-634b-4efe-843d-3dfcd48f6549",
   "metadata": {},
   "outputs": [],
   "source": [
    "@time_mem_analysis\n",
    "def concat_1(strings):\n",
    "    output = \"\"\n",
    "    for string in strings:\n",
    "        output = output + string +\" \"\n",
    "    return output\n",
    "\n",
    "@time_mem_analysis\n",
    "def concat_2(strings):\n",
    "    return \" \".join(strings,)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6b7ea35a-3604-4b0c-b20b-f14371597fa5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'data': 'hello fanny reguieg from RayRay ', 'secs': 3.7000000006059963e-06, 'mem in mb': 7.724761962890625e-05}\n"
     ]
    }
   ],
   "source": [
    "hfr = [\"hello\", \"fanny\", \"reguieg\", \"from\", \"RayRay\"]\n",
    "print(concat_1(hfr))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e8fd3899-1f3f-4ecc-9042-0eb11612294c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'data': 'hello fanny reguieg from RayRay',\n",
       " 'secs': 2.0000000020559128e-06,\n",
       " 'mem in mb': 7.62939453125e-05}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "concat_2(hfr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f7303fdb-6b5a-42a5-87e9-8e44126a780e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'data': 'hello fanny reguieg from RayRay',\n",
       " 'secs': 2.9000000019152594e-06,\n",
       " 'mem in mb': 7.62939453125e-05}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "concat_2(string for string in hfr)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30c1cc1d-e06a-4b1a-9dc6-393f3d6fb0d1",
   "metadata": {},
   "source": [
    "### C-5.22 \n",
    "Develop an experiment to compare the relative efficiency of the extend\n",
    "method of Python’s list class versus using repeated calls to append to\n",
    "accomplish the equivalent task"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a6ec112a-ec11-47dd-a03d-4be7b9fd190c",
   "metadata": {},
   "outputs": [],
   "source": [
    "l1 = [i for i in range(1000000)]\n",
    "l2 = [i*2 for i in range(1000000)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f36ebd7e-a35c-482a-aed8-770289e62cab",
   "metadata": {},
   "outputs": [],
   "source": [
    "@time_mem_analysis\n",
    "def append_iter(target,iterable):\n",
    "    for i in iterable:\n",
    "        target.append(i)\n",
    "    return target\n",
    "\n",
    "@time_mem_analysis\n",
    "def extend_iter(target,iterable):\n",
    "    target.extend(iterable)\n",
    "    return target\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "26474f27-7bd8-4385-a61c-d4f376110d18",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.05140159999999838 ,  16.334800720214844\n"
     ]
    }
   ],
   "source": [
    "rs = append_iter(l1,l2)\n",
    "print(rs['secs'],', ',rs['mem in mb'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f916a27d-7bb0-40ad-aa63-4ff289c19e16",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.006606499999996629 ,  15.258842468261719\n"
     ]
    }
   ],
   "source": [
    "l1 = [i for i in range(1000000)]\n",
    "l2 = [i*2 for i in range(1000000)]\n",
    "rs =extend_iter(l1,l2)\n",
    "print(rs['secs'],', ',rs['mem in mb'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40cdc717-1ea8-4410-adb0-24b27619f60c",
   "metadata": {},
   "source": [
    "### C-5.23 \n",
    "Based on the discussion of page 207, develop an experiment to compare\n",
    "the efficiency of Python’s list comprehension syntax versus the construction of a list by means of repeated calls to append."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "66ba9c64-af21-42ef-a11f-cc96c82bd812",
   "metadata": {},
   "outputs": [],
   "source": [
    "@time_mem_analysis\n",
    "def append_to_list(iterable,start,end):\n",
    "    for i in range(start,end):\n",
    "        iterable.append(i)\n",
    "    return iterable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "404aa920-0bbe-42a6-8099-7eb1223c59d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "@time_mem_analysis\n",
    "def create_list_comp(start,end):\n",
    "    return [i for i in range(start,end)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "bcb9966d-7b65-4f17-a68a-eeae21b1352d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5.000000001587068e-06, 0.00017547607421875]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(append_to_list([],0,10).values())[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "aef5e1c3-e468-4dc3-a94a-3d7a6f8626fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4.300000000512227e-06, 0.00017547607421875]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(create_list_comp(0,10).values())[1:]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52f6f41d-1e0a-485a-8531-81a31713506e",
   "metadata": {},
   "source": [
    "### C-5.24 \n",
    "Perform experiments to evaluate the efficiency of the remove method of\n",
    "Python’s list class, as we did for insert on page 205. Use known values so\n",
    "that all removals occur either at the beginning, middle, or end of the list.\n",
    "Report your results akin to Table 5.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "68cdf79e-2301-4bc9-be58-4b8bba6590e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "arrays_size = [1,10,100,1000,10000, 100000, 1000000]\n",
    "index_loc_names = ['k==0','k==n//2', 'k=n']\n",
    "\n",
    "@time_mem_analysis\n",
    "def pop_index(index,iterable):\n",
    "    if index < len(iterable):\n",
    "        return iterable.pop(index)\n",
    "\n",
    "def analyze_pop(arrays_size):\n",
    "    data = []\n",
    "    for size in arrays_size:\n",
    "        array_size_data = []\n",
    "        indices_loc = [0,len(arrays_size)//2,len(arrays_size)-1]\n",
    "        for index in indices_loc:\n",
    "            temp = [i for i in range(size)]\n",
    "            array_size_data.append(pop_index(index,temp)['secs'])\n",
    "        data.append(array_size_data)\n",
    "    return data\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "25a11bb6-f377-4445-a7ad-d934f5352cf8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2.2999999984563146e-06, 4.999999987376214e-07, 2.0000000233721948e-07], [3.999999975690116e-07, 3.999999975690116e-07, 3.0000000350582923e-07], [3.999999975690116e-07, 2.9999999640040187e-07, 2.9999999640040187e-07], [9.000000034120603e-07, 7.999999951380232e-07, 7.999999951380232e-07], [4.599999996912629e-06, 4.0000000041118255e-06, 3.7000000006059963e-06], [5.2900000000022374e-05, 5.230000000011614e-05, 4.909999999824777e-05], [0.00115780000000143, 0.0005632000000019843, 0.0005666999999931477]]\n",
      "<class 'float'>\n"
     ]
    }
   ],
   "source": [
    "data = analyze_pop(arrays_size)\n",
    "print(data)\n",
    "print(type(data[0][0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a9f26741-f46a-4613-955e-92b7eac3cfdc",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(data, columns=index_loc_names, index=arrays_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "612f0117-387c-47ec-abfb-b2bbd206ce5d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>k==0</th>\n",
       "      <th>k==n//2</th>\n",
       "      <th>k=n</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.300000e-06</td>\n",
       "      <td>5.000000e-07</td>\n",
       "      <td>2.000000e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>4.000000e-07</td>\n",
       "      <td>4.000000e-07</td>\n",
       "      <td>3.000000e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>4.000000e-07</td>\n",
       "      <td>3.000000e-07</td>\n",
       "      <td>3.000000e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1000</th>\n",
       "      <td>9.000000e-07</td>\n",
       "      <td>8.000000e-07</td>\n",
       "      <td>8.000000e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10000</th>\n",
       "      <td>4.600000e-06</td>\n",
       "      <td>4.000000e-06</td>\n",
       "      <td>3.700000e-06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100000</th>\n",
       "      <td>5.290000e-05</td>\n",
       "      <td>5.230000e-05</td>\n",
       "      <td>4.910000e-05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1000000</th>\n",
       "      <td>1.157800e-03</td>\n",
       "      <td>5.632000e-04</td>\n",
       "      <td>5.667000e-04</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 k==0       k==n//2           k=n\n",
       "1        2.300000e-06  5.000000e-07  2.000000e-07\n",
       "10       4.000000e-07  4.000000e-07  3.000000e-07\n",
       "100      4.000000e-07  3.000000e-07  3.000000e-07\n",
       "1000     9.000000e-07  8.000000e-07  8.000000e-07\n",
       "10000    4.600000e-06  4.000000e-06  3.700000e-06\n",
       "100000   5.290000e-05  5.230000e-05  4.910000e-05\n",
       "1000000  1.157800e-03  5.632000e-04  5.667000e-04"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "2999bb46-a4b4-4f87-9c1d-a0b53520829a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "for column in df.columns:\n",
    "    plt.plot(df.index, df[column], marker='o', label=column)\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Array Size')\n",
    "plt.ylabel('Time (secs)')\n",
    "plt.title('Time to Pop an Index in an Array')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "faa97d7d-43ca-4560-979e-238983d3266c",
   "metadata": {},
   "source": [
    "### C-5.25\n",
    "The syntax data.remove(value) for Python list data removes only the first\n",
    "occurrence of element value from the list. Give an implementation of a\n",
    "function, with signature remove all(data, value), that removes all occurrences of value from the given list, such that the worst-case running time\n",
    "of the function is O(n) on a list with n elements. Not that it is not efficient\n",
    "enough in general to rely on repeated calls to remove."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "988d0f62-7157-4832-9c82-0b6afe34622b",
   "metadata": {},
   "outputs": [],
   "source": [
    "@time_mem_analysis\n",
    "def remove_all(iterable,value):\n",
    "    count = 0\n",
    "    for i in range(len(iterable)):\n",
    "        if iterable[count] == value:\n",
    "            iterable.pop(count)\n",
    "            count-=1\n",
    "        count+=1 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "2bab4cfe-4baf-4b0f-bfd1-3e3a18364949",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'data': None, 'secs': 35.5994458, 'mem in mb': 1.52587890625e-05}"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iterable = [1,2,3,4,4,5,7,8,4,10]*100000\n",
    "remove_all(iterable,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "29196aa3-ad2c-4968-97e0-ea331f4ea867",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       " ...]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iterable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 350,
   "id": "9a030ab2-e92d-4a96-9159-7459969214de",
   "metadata": {},
   "outputs": [],
   "source": [
    "l = [1,2,3]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 351,
   "id": "995d2bed-0cab-4314-925a-7b90e881324b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2]"
      ]
     },
     "execution_count": 351,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l[:(len(l)//2)+1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 352,
   "id": "4e861444-b958-46da-8db4-f6f5ebaa424d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3]"
      ]
     },
     "execution_count": 352,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l[((len(l)//2))*-1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 327,
   "id": "4580d20b-5157-40f3-bbe6-e3fd8f70da12",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 327,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l.pop(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 328,
   "id": "c17f8d9b-73e0-48c5-a0ba-5c86383db46d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2]"
      ]
     },
     "execution_count": 328,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "29900980-422d-4b9c-856d-f17e67ea0626",
   "metadata": {},
   "outputs": [],
   "source": [
    "@time_mem_analysis\n",
    "def remove_all_mid(iterable,value):\n",
    "    l_count = 0\n",
    "    r_count = -1\n",
    "    for i in range(((len(iterable)//2))):\n",
    "        if iterable[l_count] == value:\n",
    "            iterable.pop(l_count)\n",
    "            l_count-=1\n",
    "        else:\n",
    "            l_count+=1\n",
    "\n",
    "        if iterable[r_count] == value:\n",
    "            iterable.pop(r_count)\n",
    "            r_count+=1\n",
    "        else:\n",
    "            r_count-=1\n",
    "    mid = len(iterable)//2\n",
    "    if iterable[mid] == value and len(iterable)%2 != 0:\n",
    "        iterable.pop(mid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "0ac0e9d5-2181-47d0-8009-997a843cc330",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'data': None, 'secs': 25.352128100000016, 'mem in mb': 1.52587890625e-05}"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iterable2 = [1,2,3,4,4,5,7,8,4,10]*100000\n",
    "remove_all_mid(iterable2,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 355,
   "id": "753c0ce8-9f11-4720-a08b-f6285f126b7e",
   "metadata": {},
   "outputs": [
    {
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       " 10]"
      ]
     },
     "execution_count": 355,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iterable2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5267f46c-df4e-4702-b62f-ec99ffe25b43",
   "metadata": {},
   "source": [
    "### C-5.26 \n",
    "Let B be an \n",
    "- array of size n ≥ 6 \n",
    "containing integers from 1 to n−5, inclusive, with exactly five repeated.\n",
    "Describe a good algorithm for finding the five integers in B that are repeated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "a34f2af1-6d90-44de-b03f-ca4e080a9ea3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_5n(iterable):\n",
    "    counter_map = dict()\n",
    "    for i in iterable:\n",
    "        if counter_map.get(i):\n",
    "            counter_map[i] = counter_map[i]+1\n",
    "        else:\n",
    "            counter_map[i] = 1\n",
    "\n",
    "    for k,v in counter_map.items():\n",
    "        if v == 5:\n",
    "            return k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "26e4f907-b3e0-4915-aa98-0642ad83de15",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [1,1,1,1,1,3]\n",
    "find_5n(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "9042ef0c-c11d-491f-a926-8ce992b689c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [1,2,3,4,5,5,5,5,2,5]\n",
    "find_5n(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4351abe-7bd5-41e4-9965-43a2dc8c537b",
   "metadata": {},
   "source": [
    "### C-5.31\n",
    "Describe a way to use recursion to add all the numbers in an n × n data\n",
    "set, represented as a list of lists."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "964df46a-694b-41f4-900b-b1e2c7da8eea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "63"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def add_items(iterables):\n",
    "    total = 0\n",
    "    for iterable in iterables:\n",
    "        for i in iterable:\n",
    "            total+=i\n",
    "    return total\n",
    "\n",
    "add_items([ [i for i in range(3)], [i for i in range(10)], [i for i in range(6)] ])\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "ece8f398-ce1a-44c1-9605-147d78c75891",
   "metadata": {},
   "source": [
    "# CH 6: Stacks, Queues, and Deques\n",
    "\n",
    "    Stack(FILO):\n",
    "        - A stack is a collection of objects that are inserted and removed according to the last-in, first-out (LIFO) principle.\n",
    "        - Loading/Inserting from the top of the stack\n",
    "        - Ops\n",
    "            - Push - pushing down or loading down item on top of a stack\n",
    "            - Pop - pops item from the top of the stack\n",
    "        - Amortization:\n",
    "            Operation    | Running Time:\n",
    "            s.push(e)    | o(1)\n",
    "            s.pop()      | o(1)\n",
    "            s.top()      | o(1)\n",
    "            s.is_empty() | o(1)\n",
    "            len(s)       | o(1)\n",
    "            \n",
    "    Adapter Design Pattern:\n",
    "        - Applies to any context where we effectively want to modify an existing class so that its method match those of a related, but different\n",
    "          class or interface\n",
    "\n",
    "    Queue(FIFO):\n",
    "        - A queue, is a collection of objects that are inserted and removed according to the first-in, first-out(FIFO) principle\n",
    "            Operations:\n",
    "                - enqueue(e) - adds an element(e) to the back of the queue\n",
    "                - dequeue() - removes and return the first element from queue, an error occurs if queue is empty\n",
    "                - first() - returns a reference to the element at the front of the queue, without removing it, error occurs if queue is empty \n",
    "                - is_empty() - returns true if queue is empty, else false\n",
    "                - len(Q) - return number of elements in queue\n",
    "\n",
    "    Double-Ended Queues:\n",
    "        - Queue like data structure that supports insertition and delection at both the front and the back of the queue\n",
    "        - Deque or deck for double - ended queues\n",
    "        - Functions:\n",
    "            - add_first(e) - add element to the front of deque\n",
    "            - add_last(e) - add element to the last of deque\n",
    "            - delete_first() - remove and return element of the front of deque\n",
    "            - delete_last() - remove and return element of the end of deque\n",
    "            - first() - return but do not remove the first element, errors if deque is empty\n",
    "            - last() - return but do not remove the last element, errors if deque s empty\n",
    "            - len() - return size of the deque via __len__()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 319,
   "id": "55f2896b-a309-432e-be21-6d025e07cb34",
   "metadata": {},
   "outputs": [],
   "source": [
    "class ArrayStack:\n",
    "    \n",
    "    def check_is_empty(self):\n",
    "        if self.is_empty():\n",
    "                raise Exception('Stack is Empty')\n",
    "    \n",
    "    def __init__(self,):\n",
    "        self._data = []\n",
    "\n",
    "    def __len__(self,):\n",
    "        return len(self._data)\n",
    "\n",
    "    def is_empty(self,):\n",
    "        return len(self._data) == 0\n",
    "\n",
    "    def push(self,element):\n",
    "        self._data.append(element)\n",
    "\n",
    "    def top(self,):\n",
    "        self.check_is_empty()\n",
    "        return self._data[-1]\n",
    "\n",
    "    def pop(self,):\n",
    "        self.check_is_empty()\n",
    "        return self._data.pop()\n",
    "\n",
    "    def __str__(self):\n",
    "        return f'Stack: {self._data}'\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 320,
   "id": "efe45260-f14c-4218-8c16-a9bf7f306083",
   "metadata": {},
   "outputs": [],
   "source": [
    "stack = ArrayStack()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 321,
   "id": "717c1588-4a43-4a99-8535-6f843671f427",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(10):\n",
    "    stack.push(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 322,
   "id": "00073770-9663-42e4-96a2-d321d959e4ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 322,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(stack)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 323,
   "id": "6a58db5c-3b86-4e00-b63b-4b123bce6793",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Stack: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]'"
      ]
     },
     "execution_count": 323,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(stack)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 324,
   "id": "ad5ed901-3113-4331-99b2-48d75457bb72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 324,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stack.is_empty()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 325,
   "id": "b9f4af5a-5334-4a20-a6e5-9f6d1584fbca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 325,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stack.top()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 326,
   "id": "00576bd6-e380-402e-9f80-9e8e730a3363",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 326,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stack.pop()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 327,
   "id": "e2fc81a5-e905-48d0-8119-4295c0d47ed3",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "Exception",
     "evalue": "Stack is Empty",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mException\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[327], line 2\u001b[0m\n\u001b[0;32m      1\u001b[0m stack2 \u001b[38;5;241m=\u001b[39m ArrayStack()\n\u001b[1;32m----> 2\u001b[0m \u001b[43mstack2\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcheck_is_empty\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
      "Cell \u001b[1;32mIn[319], line 5\u001b[0m, in \u001b[0;36mArrayStack.check_is_empty\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mcheck_is_empty\u001b[39m(\u001b[38;5;28mself\u001b[39m):\n\u001b[0;32m      4\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mis_empty():\n\u001b[1;32m----> 5\u001b[0m             \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mException\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mStack is Empty\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
      "\u001b[1;31mException\u001b[0m: Stack is Empty"
     ]
    }
   ],
   "source": [
    "stack2 = ArrayStack()\n",
    "stack2.check_is_empty()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 328,
   "id": "27fc6ef5-7a5f-4713-8844-8ba9952479be",
   "metadata": {},
   "outputs": [],
   "source": [
    "### Reverse Data using Stack\n",
    "# o(n) solution to reverse a list\n",
    "\n",
    "def reversal(data):\n",
    "    stack = ArrayStack()\n",
    "    for i in data:\n",
    "        stack.push(i)\n",
    "    return stack"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 329,
   "id": "eb1afdac-825b-43a7-b43a-efdd4c2d3914",
   "metadata": {},
   "outputs": [],
   "source": [
    "iterable = list(range(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 330,
   "id": "d8d4c1fc-0fb1-4965-bfcc-7e17f648c05b",
   "metadata": {},
   "outputs": [],
   "source": [
    "stack = reversal(iterable)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 331,
   "id": "765b4e08-8436-4d2c-9ded-c07010d89d10",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 331,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stack.pop()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b25c7a29-fd0d-477f-b4f8-fd2368960807",
   "metadata": {},
   "source": [
    "### Matching Parentheses and HTML Tag\n",
    "    - This is a common easy coding challenge, where you have to find matching left and right parenthese () or hard bracket []\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 332,
   "id": "04c48b42-4483-4602-b1b2-9e0f4764f884",
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_matched(expr):\n",
    "\n",
    "    lefty = '([{<'\n",
    "    righty = ')]}>'\n",
    "    s = ArrayStack()\n",
    "    for characters in expr:\n",
    "        if characters in lefty:\n",
    "            s.push(characters)\n",
    "        elif characters in righty:\n",
    "            if s.is_empty():\n",
    "                return False\n",
    "            if righty.index(characters) != lefty.index(s.pop()):\n",
    "                return False\n",
    "    return s.is_empty()              "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 333,
   "id": "d99dcc16-1096-4356-9f81-1466d171d882",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 333,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr = \"( )(( )){([( )])}\"\n",
    "is_matched(expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 334,
   "id": "7edb79d7-206f-4b13-8159-922f6fc0aac6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 334,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr2 = ')(( )){([( )])}'\n",
    "is_matched(expr2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 335,
   "id": "7d9067b3-30b8-4666-b9a1-9f95100bed71",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 335,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr3 = '[(5+x)-(y+z)]'\n",
    "is_matched(expr3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 336,
   "id": "611f58b8-9280-4fb5-9170-be701b617171",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 336,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "html_data = \"\"\"\n",
    "<body>\n",
    "    <center>\n",
    "        <h1> The Little Boat </h1>\n",
    "    </center>\n",
    "    <p> \n",
    "        The storm tossed the little\n",
    "        boat like a cheap sneaker in an\n",
    "        old washing machine. The three\n",
    "        drunken fishermen were used to\n",
    "        such treatment, of course, but\n",
    "        not the tree salesman, who even as\n",
    "        a stowaway now felt that he\n",
    "        had overpaid for the voyage.\n",
    "    </p>\n",
    "    <ol>\n",
    "        <li>\n",
    "            Will the salesman die?\n",
    "        </li>\n",
    "        <li> \n",
    "            What color is the boat?\n",
    "        </li>\n",
    "        <li>\n",
    "            And what about Naomi? \n",
    "        </li>\n",
    "    </ol>\n",
    "</body>\n",
    "\"\"\"\n",
    "is_matched(html_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 337,
   "id": "9267ff13-9e19-4ce6-afcb-ad95dbbac612",
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_matched_html(raw):\n",
    "    S = ArrayStack()\n",
    "    j = raw.find('<')\n",
    "    while j != -1:\n",
    "        k = raw.find('>',j+1)\n",
    "        if k == -1:\n",
    "            return False\n",
    "        tag = raw[j+1:k]\n",
    "        if not tag.startswith('/'):\n",
    "            S.push(tag)\n",
    "        else:\n",
    "            if S.is_empty():\n",
    "                return False\n",
    "            if tag[1:] != S.pop():\n",
    "                return False\n",
    "        j = raw.find('<', k+1)\n",
    "    return S.is_empty()\n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 338,
   "id": "0f074a83-e9a0-4b56-b7f1-6adf6efc0d81",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 338,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_matched_html(html_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4edc1aeb-7017-4e41-9081-c410b586b749",
   "metadata": {},
   "outputs": [],
   "source": [
    "### Implement my version of stack \n",
    "\n",
    "class Stack:\n",
    "\n",
    "    def __init__(self):\n",
    "        self._data = []\n",
    "\n",
    "    def __len__(self):\n",
    "        return len(self._data)\n",
    "\n",
    "    def __str__(self):\n",
    "        return f'{self._data}'\n",
    "\n",
    "    def is_empty(self):\n",
    "        return self.__len__() == 0\n",
    "    \n",
    "    def top(self):\n",
    "        if len(self._data) > 0:\n",
    "            return self._data[len(self._data)-1]\n",
    "\n",
    "    def pop(self):\n",
    "        return self._data.pop()\n",
    "\n",
    "    def push(self, element):\n",
    "        self._data.append(element)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "id": "7e58359c-0007-4d08-ad0a-26ebe4d6892a",
   "metadata": {},
   "outputs": [],
   "source": [
    "stack1 = Stack()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "id": "3c7169ad-89e9-4e8b-9372-9c14dfe2c8d4",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(3):\n",
    "    stack1.push(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "id": "a5fa55bd-19d4-413d-b6c5-586091d206d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[0, 1, 2]'"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(stack1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "id": "ef83f760-d129-4102-9e69-1ddd9e2c54df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stack1.pop()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "id": "f96e3725-d163-49e1-b2f1-2717a14305c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[0, 1]'"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(stack1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "eebb8ad7-df1e-45b5-a0ec-32ec462f3960",
   "metadata": {},
   "outputs": [],
   "source": [
    "### Queue Implementation\n",
    "\n",
    "class Empty(Exception):\n",
    "    ...\n",
    "\n",
    "class ArrayQueue:\n",
    "    DEFAULT_CAPACITY = 10\n",
    "\n",
    "    def error_if_empty(self):\n",
    "        if self.is_empty():\n",
    "            raise Empty('Queue is empty')\n",
    "    \n",
    "    def __init__(self):\n",
    "        self._data = [None] * self.DEFAULT_CAPACITY\n",
    "        self._size = 0\n",
    "        self._front = 0 \n",
    "\n",
    "    def __len__(self):\n",
    "        return len(self._data)\n",
    "\n",
    "    def is_empty(self):\n",
    "        if len(self) > 0:\n",
    "            return False\n",
    "        return True\n",
    "\n",
    "    def first(self):\n",
    "        self.error_if_empty()\n",
    "        return self._data[0]\n",
    "\n",
    "    def dequeue(self):\n",
    "        self.error_if_empty()\n",
    "        print('Front',self._front)\n",
    "        answer = self._data[self._front]\n",
    "        self._data[self._front] = None\n",
    "        self._front = (self._front + 1) % len(self._data)\n",
    "        self._size -= 1\n",
    "        return answer\n",
    "\n",
    "    def enqueue(self,element):\n",
    "        if self._size == len(self._data):\n",
    "            self._resize(2*len(self._data))\n",
    "        avail = (self._front + self._size) % len(self._data)\n",
    "        self._data[avail] = element\n",
    "        self._size += 1\n",
    "\n",
    "\n",
    "    def _resize(self, cap):\n",
    "        old = self._data\n",
    "        self._data = [None] * cap\n",
    "        walk = self._front\n",
    "        for k in range(self._size):\n",
    "            self._data[k] = old[walk]\n",
    "            walk = (1 + walk) % len(old)\n",
    "        self._front = 0 \n",
    "\n",
    "    def __str__(self,):\n",
    "        return f'Queue: {self._data}'\n",
    "        \n",
    "    \n",
    "                         \n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "id": "12d4e0de-55a5-44df-9079-ca9a461a0e92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[None, None, None, None, None, None, None, None, None, None]"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "queue = ArrayQueue()\n",
    "queue._data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "id": "949b9f3f-ff16-4d2d-b38c-992bb4180060",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 178,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(queue)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "id": "bc634e94-13ef-497e-a718-ea2e7e8665c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "queue.is_empty()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "id": "73588300-fb56-48ee-8d80-defbc8de0cfc",
   "metadata": {},
   "outputs": [
    {
     "ename": "Empty",
     "evalue": "Queue is empty",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mEmpty\u001b[0m                                     Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[180], line 3\u001b[0m\n\u001b[0;32m      1\u001b[0m q2 \u001b[38;5;241m=\u001b[39m ArrayQueue()\n\u001b[0;32m      2\u001b[0m q2\u001b[38;5;241m.\u001b[39m_data \u001b[38;5;241m=\u001b[39m []\n\u001b[1;32m----> 3\u001b[0m \u001b[43mq2\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mfirst\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
      "Cell \u001b[1;32mIn[176], line 27\u001b[0m, in \u001b[0;36mArrayQueue.first\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m     26\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mfirst\u001b[39m(\u001b[38;5;28mself\u001b[39m):\n\u001b[1;32m---> 27\u001b[0m     \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43merror_if_empty\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m     28\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_data[\u001b[38;5;241m0\u001b[39m]\n",
      "Cell \u001b[1;32mIn[176], line 11\u001b[0m, in \u001b[0;36mArrayQueue.error_if_empty\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m      9\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21merror_if_empty\u001b[39m(\u001b[38;5;28mself\u001b[39m):\n\u001b[0;32m     10\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mis_empty():\n\u001b[1;32m---> 11\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m Empty(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mQueue is empty\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
      "\u001b[1;31mEmpty\u001b[0m: Queue is empty"
     ]
    }
   ],
   "source": [
    "q2 = ArrayQueue()\n",
    "q2._data = []\n",
    "q2.first()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e9593e85-8756-4ddf-a8f7-24e475189a8e",
   "metadata": {},
   "outputs": [],
   "source": [
    "queue.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "id": "1f4cde25-4add-4492-ba90-d4e70feffe52",
   "metadata": {},
   "outputs": [],
   "source": [
    "queue.first()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "id": "01e8f556-165d-49ec-90ce-ca604d32fad0",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(10):\n",
    "    queue.enqueue(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "id": "382ecdf2-3aed-4762-9a01-13249618f67f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "queue._data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "id": "38923b03-eb6e-4a51-8ca6-339ea1e7505d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "queue.first()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "id": "92878ceb-362a-4121-b6a9-2b36e0a894ca",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Front 0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "queue.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "id": "9217d917-f894-48b9-ad1b-6ba270d5814e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Front 1\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 186,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "queue.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "id": "c212d3a7-057a-4add-a480-4689cd506ee9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Queue: [None, None, 2, 3, 4, 5, 6, 7, 8, 9]'"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(queue)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "id": "5ff0252e-f67d-41d5-a949-0d832473c9a3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Front 2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 188,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "queue.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b4785f2a-81e8-4ebc-846c-dec60493dc0d",
   "metadata": {},
   "outputs": [],
   "source": [
    "### Refactor Queue\n",
    "### No need for dynamic array cause data utilizes list which is a dynamic array as it is\n",
    "### There are queue\n",
    "\n",
    "class Queue:\n",
    "\n",
    "    def __init__(self,size=10):\n",
    "        self._data = []\n",
    "        self.__front = 0\n",
    "        self._size = size\n",
    "\n",
    "    def __len__(self,):\n",
    "        return len(self._data)\n",
    "\n",
    "    def is_empty(self):\n",
    "        return len(self._data) < 0\n",
    "\n",
    "    def is_full(self):\n",
    "        return len(self._data) == self._size\n",
    "\n",
    "    def first(self):\n",
    "        return self._data[self.__front]\n",
    "    \n",
    "    def dequeue(self,):\n",
    "        if self.__len__() > 0:\n",
    "            return self._data.pop(0)\n",
    "        \n",
    "    def enqueue(self,element):\n",
    "        if  self.is_full():\n",
    "            raise Exception('Queue is full')    \n",
    "        self._data.append(element)\n",
    "        \n",
    "    def __str__(self):\n",
    "        return f\"{self._data}\"\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "id": "b995aeb2-ca89-4912-8767-af41d3b59b8f",
   "metadata": {},
   "outputs": [],
   "source": [
    "queue2 = Queue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "id": "8d97260d-d91c-49ff-aafd-d1490fef5d4b",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(10,0,-1):\n",
    "    queue2.enqueue(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "id": "b0e4fb63-33c2-4424-81e2-5f61152e6028",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[10, 9, 8, 7, 6, 5, 4, 3, 2, 1]'"
      ]
     },
     "execution_count": 238,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(queue2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "id": "ca0fc8dc-393d-48dd-847c-42010bce756b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 239,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(queue2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "id": "52f389af-077b-4106-8cc7-3d10c6c5dd9f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 240,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "queue2.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "id": "f6ab756e-4730-48a4-ac9c-88932fe71da8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[9, 8, 7, 6, 5, 4, 3, 2, 1]'"
      ]
     },
     "execution_count": 241,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(queue2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "id": "1f4f06ab-5bc3-4290-9dc5-5be3af998eb5",
   "metadata": {},
   "outputs": [],
   "source": [
    "queue2.enqueue(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "id": "2a32548e-ecda-420d-b352-db5298364071",
   "metadata": {},
   "outputs": [
    {
     "ename": "Exception",
     "evalue": "Queue is full",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mException\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[243], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[43mqueue2\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menqueue\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m100\u001b[39;49m\u001b[43m)\u001b[49m\n",
      "Cell \u001b[1;32mIn[235], line 30\u001b[0m, in \u001b[0;36mQueue.enqueue\u001b[1;34m(self, element)\u001b[0m\n\u001b[0;32m     28\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menqueue\u001b[39m(\u001b[38;5;28mself\u001b[39m,element):\n\u001b[0;32m     29\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m  \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mis_full():\n\u001b[1;32m---> 30\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mException\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mQueue is full\u001b[39m\u001b[38;5;124m'\u001b[39m)    \n\u001b[0;32m     31\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_data\u001b[38;5;241m.\u001b[39mappend(element)\n",
      "\u001b[1;31mException\u001b[0m: Queue is full"
     ]
    }
   ],
   "source": [
    "queue2.enqueue(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "id": "715924c0-82ed-44d3-ad81-b9c3cfe80206",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[9, 8, 7, 6, 5, 4, 3, 2, 1, -1]'"
      ]
     },
     "execution_count": 244,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(queue2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "id": "6223570d-1c81-44e7-b63a-37aa27157192",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 245,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "queue2.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "id": "ff8076dc-c93a-4ae8-8ff2-23a492a2caae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[8, 7, 6, 5, 4, 3, 2, 1, -1]'"
      ]
     },
     "execution_count": 246,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(queue2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f6a41a3d-07ef-44a8-bdfe-5f0352ad4ef6",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Dequeue:\n",
    "\n",
    "    def __init__(self):\n",
    "        self._data = []\n",
    "\n",
    "    def error_if_empty(self):\n",
    "        if not self.__len__() > 0:\n",
    "            raise Exception('Deque is empty')\n",
    "            \n",
    "    def __len__(self):\n",
    "        return len(self._data)\n",
    "\n",
    "    def __str__(self):\n",
    "        return f\"{self._data}\"\n",
    "\n",
    "    def first(self):\n",
    "        self.error_if_empty()\n",
    "        return self._data[0]\n",
    "        \n",
    "    def last(self):\n",
    "        self.error_if_empty()\n",
    "        return self._data[-1]\n",
    "    \n",
    "    def add_first(self,element):\n",
    "        self._data.insert(0,element)\n",
    "\n",
    "    def add_last(self,element):\n",
    "        self._data.append(element)\n",
    "\n",
    "    def delete_first(self):\n",
    "        return self._data.pop(0)\n",
    "\n",
    "    def delete_last(self):\n",
    "        return self._data.pop()\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "id": "b3928c01-4887-4d54-a2a1-dd385fb2df0b",
   "metadata": {},
   "outputs": [],
   "source": [
    "deque = Dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "id": "cc80baff-56ec-4f16-8aaa-3be6fab2a70a",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(10):\n",
    "    deque.add_last(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "id": "c59937f9-cbae-4ece-8c63-3d5dc430643a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]'"
      ]
     },
     "execution_count": 250,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(deque)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "id": "9361151e-7f05-4788-90f5-caedf7093d6e",
   "metadata": {},
   "outputs": [],
   "source": [
    "deque.add_first(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "id": "f46626b4-221e-467d-a2a9-efb3b87f859a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]'"
      ]
     },
     "execution_count": 252,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(deque)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "id": "86204030-989a-4f52-b686-29fe97844c05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 253,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "deque.delete_last()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "id": "528bd9d6-8a06-4869-baf8-1daa68fe4bcb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1"
      ]
     },
     "execution_count": 254,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "deque.delete_first()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "id": "58fa6204-a2a8-4a2d-8b3f-6385ba4c0c85",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[0, 1, 2, 3, 4, 5, 6, 7, 8]'"
      ]
     },
     "execution_count": 255,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(deque)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "105b4519-f976-461e-8813-af097b95dc69",
   "metadata": {},
   "source": [
    "### R-6.1\n",
    "What values are returned during the following series of stack operations, if\n",
    "executed upon an initially empty stack? push(5), push(3), pop(), push(2),\n",
    "push(8), pop(), pop(), push(9), push(1), pop(), push(7), push(6), pop(),\n",
    "pop(), push(4), pop(), pop()."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "id": "13bf3aa2-d73e-4086-b4f0-05efa7f51c15",
   "metadata": {},
   "outputs": [],
   "source": [
    "stack_6_1 = Stack()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "id": "3cf707ce-33e1-4610-9a3b-79ff7f4c498d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 257,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stack_6_1.push(5)\n",
    "stack_6_1.push(3)\n",
    "stack_6_1.pop()\n",
    "stack_6_1.push(2)\n",
    "stack_6_1.push(8)\n",
    "stack_6_1.pop()\n",
    "stack_6_1.pop()\n",
    "stack_6_1.push(9)\n",
    "stack_6_1.push(1)\n",
    "stack_6_1.pop()\n",
    "stack_6_1.push(7)\n",
    "stack_6_1.push(6)\n",
    "stack_6_1.pop()\n",
    "stack_6_1.pop()\n",
    "stack_6_1.push(4)\n",
    "stack_6_1.pop()\n",
    "stack_6_1.pop()\n",
    "# 5 only in the stack"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "id": "5e793868-ffaf-4564-a79a-8168ce75eee4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[5]'"
      ]
     },
     "execution_count": 258,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(stack_6_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "id": "6740a216-7ba7-495f-8351-d12adc39235a",
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (3127328487.py, line 2)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  Cell \u001b[1;32mIn[259], line 2\u001b[1;36m\u001b[0m\n\u001b[1;33m    Suppose an initially empty stack S has executed a total of 25 push operations, 12 top operations, and 10 pop operations, 3 of which raised Empty\u001b[0m\n\u001b[1;37m            ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "### R-6.2\n",
    "Suppose an initially empty stack S has executed a total of 25 push operations, 12 top operations, and 10 pop operations, 3 of which raised Empty\n",
    "errors that were caught and ignored. What is the current size of S?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 260,
   "id": "3bf1e546-58c1-4038-ad18-930d2b9cc44b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24\n",
      "23\n",
      "22\n",
      "21\n",
      "20\n",
      "19\n",
      "18\n",
      "18\n"
     ]
    }
   ],
   "source": [
    "stack_6_2 = Stack()\n",
    "for i in range(25):\n",
    "    stack_6_2.push(i)\n",
    "\n",
    "for i in range(12):\n",
    "    stack_6_2.top()\n",
    "\n",
    "for i in range(1,11):\n",
    "    if i%3 != 0:\n",
    "        print(stack_6_2.pop())\n",
    "\n",
    "print(len(stack_6_2))\n",
    "assert len(stack_6_2._data) == 18\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fbf685af-8b7a-4194-8c8c-c6ba11945825",
   "metadata": {},
   "source": [
    "### R-6.3 \n",
    "Implement a function with signature transfer(S, T) that transfers all elements from stack S onto stack T, so that the element that starts at the top\n",
    "of S is the first to be inserted onto T, and the element at the bottom of S\n",
    "ends up at the top of T."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 261,
   "id": "326802b1-aee4-4a60-9b2b-3ce0dca5195d",
   "metadata": {},
   "outputs": [],
   "source": [
    "stack63_1 = Stack()\n",
    "stack63_2 = Stack()\n",
    "\n",
    "for i in range(10):\n",
    "    stack63_1.push(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "id": "35c5edad-bf5b-43af-a438-f2f19f7a7ad7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]'"
      ]
     },
     "execution_count": 262,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(stack63_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "id": "a7e2555d-9285-4a7c-a60e-831e7380cf71",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[9, 8, 7, 6, 5, 4, 3, 2, 1, 0]\n"
     ]
    }
   ],
   "source": [
    "for _ in range(len(stack63_1)):\n",
    "    stack63_2.push(stack63_1.pop())\n",
    "print(str(stack63_2)) # return reverse of the stack63_1 so top should be 0 now"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "75373a13-79cf-42fb-835c-3bb7d0860d2d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def transfer(S,T):\n",
    "    for _ in range(len(S)):\n",
    "        T.push(S.pop())\n",
    "    return T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "02475570-b55a-4f75-824f-01d999e56834",
   "metadata": {},
   "outputs": [],
   "source": [
    "stack63_3 = Stack()\n",
    "stack63_4 = Stack()\n",
    "\n",
    "for i in range(10):\n",
    "    stack63_3.push(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "aa2790a1-c42e-4828-92ec-c28f404d8df6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[9, 8, 7, 6, 5, 4, 3, 2, 1, 0]'"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(transfer(stack63_3,stack63_4))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd1e9177-4bf4-4e2f-b70e-eb33ebfd2cf3",
   "metadata": {},
   "source": [
    "### R-6.4 \n",
    "Give a recursive method for removing all the elements from a stack"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 264,
   "id": "2dc801fd-5e1d-4872-a275-272a29daba42",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[]'"
      ]
     },
     "execution_count": 264,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stack64 = Stack()\n",
    "for i in range(10):\n",
    "    stack64.push(i)\n",
    "def pop_recursive(stack:Stack):\n",
    "    if len(stack):\n",
    "        stack.pop()\n",
    "        return pop_recursive(stack)\n",
    "pop_recursive(stack64)\n",
    "str(stack64)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05626b3e-9e81-4d40-822d-2032ed362a72",
   "metadata": {},
   "source": [
    "### R-6.5\n",
    "Implement a function that reverses a list of elements by pushing them onto\n",
    "a stack in one order, and writing them back to the list in reversed order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 265,
   "id": "3a058f41-2464-4307-b13f-1200bf4682e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9, 8, 7, 6, 5, 4, 3, 2, 1, 0]"
      ]
     },
     "execution_count": 265,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def reverse_list(iterable):\n",
    "    stack = Stack()\n",
    "    for _ in range(len(iterable)):\n",
    "        stack.push(iterable.pop(0))\n",
    "\n",
    "    for i in range(len(stack)):\n",
    "        iterable.append(stack.pop())\n",
    "\n",
    "\n",
    "iterable_65 = list(range(10))\n",
    "reverse_list(iterable_65)\n",
    "iterable_65"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "294965a3-935f-478d-a780-21cc3ccab9ab",
   "metadata": {},
   "source": [
    "### R-6.6 \n",
    "Give a precise and complete definition of the concept of matching for\n",
    "grouping symbols in an arithmetic expression. Your definition may be\n",
    "recursive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "id": "a513a400-676e-45c8-9214-a8a075e75165",
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_matched(expr):\n",
    "\n",
    "    lefty = '([{<'\n",
    "    righty = ')]}>'\n",
    "    s = Stack()\n",
    "    for characters in expr:\n",
    "        if characters in lefty:\n",
    "            s.push(characters)\n",
    "        elif characters in righty:\n",
    "            if s.is_empty():\n",
    "                return False\n",
    "            if righty.index(characters) != lefty.index(s.pop()):\n",
    "                return False\n",
    "    return s.is_empty()           "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 267,
   "id": "1ddcd300-e88b-43e8-9737-f061dcb471da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 267,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr = \"(a + b) = y\"\n",
    "\n",
    "is_matched(expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 268,
   "id": "e2c56b88-3815-461c-89c6-244860d388f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 268,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr = \"(a + b = y\"\n",
    "\n",
    "is_matched(expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "id": "252447ac-7a0f-4323-ac0e-0bf3dbc74fef",
   "metadata": {},
   "outputs": [],
   "source": [
    "expr = \"((a + b)-2)+1 = y\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "id": "683d4b1c-4f2a-4a1a-bd3c-726e8fb25894",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 270,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_matched(expr)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e302dd3-73cc-40ad-b886-48d591ad92e7",
   "metadata": {},
   "source": [
    "### R-6.7 \n",
    "What values are returned during the following sequence of queue operations, if executed on an initially empty queue? enqueue(5), enqueue(3),\n",
    "dequeue(), enqueue(2), enqueue(8), dequeue(), dequeue(), enqueue(9),\n",
    "enqueue(1), dequeue(), enqueue(7), enqueue(6), dequeue(), dequeue(),\n",
    "enqueue(4), dequeue(), dequeue()."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "id": "8a52ca8b-28bf-471d-90c0-8d0c38d9c9ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "queue_67 = Queue()\n",
    "queue_67.enqueue(5)\n",
    "queue_67.enqueue(3)\n",
    "queue_67.dequeue()\n",
    "queue_67.enqueue(2)\n",
    "queue_67.enqueue(8)\n",
    "queue_67.dequeue()\n",
    "queue_67.dequeue()\n",
    "queue_67.enqueue(9)\n",
    "queue_67.enqueue(1)\n",
    "queue_67.dequeue()\n",
    "queue_67.enqueue(7)\n",
    "queue_67.enqueue(6)\n",
    "queue_67.dequeue()\n",
    "queue_67.dequeue()\n",
    "queue_67.enqueue(4)\n",
    "queue_67.dequeue()\n",
    "queue_67.dequeue()\n",
    "\n",
    "assert queue_67.first() == 4"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98998e8b-18aa-4ec3-9883-6149a485323a",
   "metadata": {},
   "source": [
    "### R-6.8\n",
    "Suppose an initially empty queue Q has executed a total of 32 enqueue\n",
    "operations, 10 first operations, and 15 dequeue operations, 5 of which\n",
    "raised Empty errors that were caught and ignored. What is the current\n",
    "size of Q?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "id": "501a41d6-74f9-4903-8877-90c258bcee7b",
   "metadata": {},
   "outputs": [],
   "source": [
    "queue_68 = Queue(50)\n",
    "for i in range(32):\n",
    "    queue_68.enqueue(i)\n",
    "for i in range(10):\n",
    "    queue_68.first()\n",
    "for i in range(10):\n",
    "    queue_68.dequeue()\n",
    "\n",
    "assert len(queue_68) == 22"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84be4535-335b-445a-afec-95ca9a27f237",
   "metadata": {},
   "source": [
    "### R-6.11 \n",
    "Give a simple adapter that implements our queue ADT while using a\n",
    "collections.deque instance for storage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "id": "97206c16-7e56-46a9-899a-19e4fcbc25eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import deque"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "id": "092ad80d-08f8-4c51-9a4f-3f69d2f50f29",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['__add__',\n",
       " '__bool__',\n",
       " '__class__',\n",
       " '__class_getitem__',\n",
       " '__contains__',\n",
       " '__copy__',\n",
       " '__delattr__',\n",
       " '__delitem__',\n",
       " '__dir__',\n",
       " '__doc__',\n",
       " '__eq__',\n",
       " '__format__',\n",
       " '__ge__',\n",
       " '__getattribute__',\n",
       " '__getitem__',\n",
       " '__gt__',\n",
       " '__hash__',\n",
       " '__iadd__',\n",
       " '__imul__',\n",
       " '__init__',\n",
       " '__init_subclass__',\n",
       " '__iter__',\n",
       " '__le__',\n",
       " '__len__',\n",
       " '__lt__',\n",
       " '__mul__',\n",
       " '__ne__',\n",
       " '__new__',\n",
       " '__reduce__',\n",
       " '__reduce_ex__',\n",
       " '__repr__',\n",
       " '__reversed__',\n",
       " '__rmul__',\n",
       " '__setattr__',\n",
       " '__setitem__',\n",
       " '__sizeof__',\n",
       " '__str__',\n",
       " '__subclasshook__',\n",
       " 'append',\n",
       " 'appendleft',\n",
       " 'clear',\n",
       " 'copy',\n",
       " 'count',\n",
       " 'extend',\n",
       " 'extendleft',\n",
       " 'index',\n",
       " 'insert',\n",
       " 'maxlen',\n",
       " 'pop',\n",
       " 'popleft',\n",
       " 'remove',\n",
       " 'reverse',\n",
       " 'rotate']"
      ]
     },
     "execution_count": 281,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(deque)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "id": "34749439-d110-4c88-ab8b-dcc7713bb3b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "dq = deque([1,2,3]*3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 290,
   "id": "906d7e7c-9af4-4a32-8417-f7b95b51de58",
   "metadata": {},
   "outputs": [],
   "source": [
    "dq.append(1)\n",
    "dq.append(2)\n",
    "dq.appendleft(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 291,
   "id": "db910c64-bec6-470c-a019-d28de447425c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'deque([3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2])'"
      ]
     },
     "execution_count": 291,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(dq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 344,
   "id": "d8f08be5-ca57-40ac-9f97-9ce3e95893a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "This implementation of enque and deque focus on ensuring the front and size is relavant to index why most of these operations are o(1)\n",
    "\"\"\"\n",
    "class Empty(Exception):\n",
    "    ...\n",
    "\n",
    "class ArrayQueue:\n",
    "    DEFAULT_CAPACITY = 10\n",
    "\n",
    "    def error_if_empty(self):\n",
    "        if self.is_empty():\n",
    "            raise Empty('Queue is empty')\n",
    "    \n",
    "    def __init__(self):\n",
    "        self._data = deque([None] * self.DEFAULT_CAPACITY)\n",
    "        self._size = 0\n",
    "        self._front = 0 \n",
    "\n",
    "    def __len__(self):\n",
    "        return len(self._data)\n",
    "\n",
    "    def is_empty(self):\n",
    "        if len(self) > 0:\n",
    "            return False\n",
    "        return True\n",
    "\n",
    "    def first(self):\n",
    "        self.error_if_empty()\n",
    "        return self._data[self._front]\n",
    "\n",
    "    def dequeue(self):\n",
    "        self.error_if_empty()\n",
    "        answer = self._data[self._front]\n",
    "        self._data[self._front] = None\n",
    "        self._front = (self._front + 1) % len(self._data)\n",
    "        self._size -= 1\n",
    "        return answer\n",
    "\n",
    "    def enqueue(self,element):\n",
    "        if self._size == len(self._data):\n",
    "            self._resize(2*len(self._data))\n",
    "        avail = (self._front + self._size) % len(self._data)\n",
    "        self._data[avail] = element\n",
    "        self._size += 1\n",
    "\n",
    "\n",
    "    def _resize(self, cap):\n",
    "        old = self._data\n",
    "        self._data = [None] * cap\n",
    "        walk = self._front\n",
    "        for k in range(self._size):\n",
    "            self._data[k] = old[walk]\n",
    "            walk = (1 + walk) % len(old)\n",
    "        self._front = 0 \n",
    "\n",
    "    def __str__(self,):\n",
    "        return f'Queue: {self._data}'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 345,
   "id": "2ff3023f-e151-4976-91ce-6fbed65c0f2d",
   "metadata": {},
   "outputs": [],
   "source": [
    "aq = ArrayQueue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 346,
   "id": "e57dbc16-8f6e-46e9-98dc-a9ddb3e719f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "deque([None, None, None, None, None, None, None, None, None, None])"
      ]
     },
     "execution_count": 346,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aq._data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 347,
   "id": "26f2ca72-3fe6-48d5-b9c5-4609d75d3de1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 347,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(aq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 348,
   "id": "db2dc6b1-dae7-4668-864b-cbdab33f2be8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 348,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aq.is_empty()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 349,
   "id": "7875ca56-78d3-41b5-9dd6-d06dfebbaadb",
   "metadata": {},
   "outputs": [],
   "source": [
    "aq.enqueue(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 350,
   "id": "f0201fe1-f9e5-4aa3-9865-6605288120a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "aq.enqueue(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 351,
   "id": "f87892ba-de8c-4f53-a362-272919923758",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Queue: deque([1, 2, None, None, None, None, None, None, None, None])'"
      ]
     },
     "execution_count": 351,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(aq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 352,
   "id": "b3e2204e-40c8-4185-bfea-39ffcebfdfef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 352,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aq.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 353,
   "id": "c068525c-b61e-4568-bd84-fa2959d194d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Queue: deque([None, 2, None, None, None, None, None, None, None, None])'"
      ]
     },
     "execution_count": 353,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(aq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 354,
   "id": "e108a0cb-3748-4134-9235-aba8f2973b68",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 354,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aq.first()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 355,
   "id": "679f2450-913a-45ec-945e-f82063cb9e2f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 355,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aq.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 356,
   "id": "d4502d71-7b1c-4331-a73a-7cb8d0945bb6",
   "metadata": {},
   "outputs": [],
   "source": [
    "aq.first()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 357,
   "id": "58a4ed65-437b-4fba-af38-217efe839f98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 357,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aq._front"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 358,
   "id": "0703c003-84d8-44c1-99b7-f1993960d2d4",
   "metadata": {},
   "outputs": [],
   "source": [
    "aq.enqueue(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 359,
   "id": "3e9ff011-7816-4179-97b7-aa4ce4018535",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 359,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aq.first()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 360,
   "id": "2b767693-a877-43ae-8222-8bab283e7762",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 360,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aq._front"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 361,
   "id": "aaee1f65-37d4-42c2-8d59-7136e5086706",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 361,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aq.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 362,
   "id": "01407c68-4dd9-48d4-bd76-ba4be949ca0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "aq.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 363,
   "id": "d067d6cc-65dc-48e2-ac77-e81768a791c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "aq.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 364,
   "id": "2298037c-fcb9-4983-ac6f-fb897355f2c0",
   "metadata": {},
   "outputs": [],
   "source": [
    "aq.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 365,
   "id": "8a9ffd16-3e9d-4118-ab2b-529b699e4b01",
   "metadata": {},
   "outputs": [],
   "source": [
    "aq.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 366,
   "id": "e084dafb-d4f0-4bda-8f15-463384aaf789",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 366,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aq._front"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 367,
   "id": "5de717f1-f5d2-4431-8202-27b319e978a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "aq.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 368,
   "id": "aeb059d1-ef69-4c17-a63b-26694a2104cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "aq.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 369,
   "id": "377c195c-f3f0-42c9-8fb7-839e36fa2cab",
   "metadata": {},
   "outputs": [],
   "source": [
    "aq.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 370,
   "id": "53593651-be62-4973-9a8f-c5828f81d877",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 370,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aq._front"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7a50af0-6dc0-464c-8fae-339f307cd1a9",
   "metadata": {},
   "source": [
    "### R-6.12\n",
    "What values are returned during the following sequence of deque ADT operations, on initially empty deque? add first(4), add last(8), add last(9),\n",
    "add first(5), back( ), delete first( ), delete last( ), add last(7), first( ),\n",
    "last( ), add last(6), delete first( ), delete first( )."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 376,
   "id": "0c1a0844-ed5a-43f6-b818-aad0fddde0f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[7, 6]'"
      ]
     },
     "execution_count": 376,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dq = Dequeue()\n",
    "dq.add_first(4)\n",
    "dq.add_last(8)\n",
    "dq.add_last(9)\n",
    "dq.add_first(5)\n",
    "dq.delete_first()\n",
    "dq.delete_last()\n",
    "dq.add_last(7)\n",
    "dq.first()\n",
    "dq.last()\n",
    "dq.add_last(6)\n",
    "dq.delete_first()\n",
    "dq.delete_first()\n",
    "\n",
    "str(dq)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0cacb4db-973d-4736-a665-650e4951199a",
   "metadata": {},
   "source": [
    "### R-6.13\n",
    "Suppose you have a deque D containing the numbers (1,2,3,4,5,6,7,8),\n",
    "in this order. Suppose further that you have an initially empty queue Q.\n",
    "Give a code fragment that uses only D and Q (and no other variables) and\n",
    "results in D storing the elements in the order (1,2,3,5,4,6,7,8)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 407,
   "id": "2482b3e4-8d2f-4203-adc9-f5dca7837fa5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[1, 2, 3, 4, 5, 6, 7, 8]'"
      ]
     },
     "execution_count": 407,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = Dequeue()\n",
    "for i in range(1,9):\n",
    "    d.add_last(i)\n",
    "str(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 408,
   "id": "f079b7e4-8d54-467b-94db-4e8d27797ce3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[8, 7, 6, 5, 4, 3, 2, 1]'"
      ]
     },
     "execution_count": 408,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = Queue()\n",
    "for i in range(len(d)):\n",
    "    q.enqueue(d.delete_last())\n",
    "str(q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 409,
   "id": "0b84ef33-35a8-42eb-a8c9-9325304245cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(len(q)):\n",
    "    temp = q.dequeue()\n",
    "    if temp == 5:\n",
    "        d.add_last(temp)\n",
    "        continue\n",
    "    elif temp == 4:\n",
    "        d.add_first(temp)\n",
    "        d.add_first(d.delete_last())\n",
    "        continue\n",
    "    d.add_first(temp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 410,
   "id": "d11eb203-c0e7-485b-8faa-d4e0915a866d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[1, 2, 3, 5, 4, 6, 7, 8]'"
      ]
     },
     "execution_count": 410,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(d)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9273e8d6-baf2-4c98-bb73-c180fa2f03cc",
   "metadata": {},
   "source": [
    "### R-6.14 \n",
    "Repeat the previous problem using the deque D and an initially empty\n",
    "stack S."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 452,
   "id": "03262190-38df-4556-8f34-aa78560e1ab0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[1, 2, 3, 4, 5, 6, 7, 8]'"
      ]
     },
     "execution_count": 452,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2 = Dequeue()\n",
    "for i in range(1,9):\n",
    "    d2.add_last(i)\n",
    "str(d2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 453,
   "id": "d181bcf9-a485-4f45-8cd4-bfeabf4da8b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[1, 2, 3, 4, 5, 6, 7, 8]'"
      ]
     },
     "execution_count": 453,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = Stack()\n",
    "for i in range(len(d2)):\n",
    "    s.push(d2.delete_first())\n",
    "str(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 454,
   "id": "7c3542cb-7553-4b57-8e76-5121e536a9f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(len(s)):\n",
    "    temp = s.pop()\n",
    "    if temp == 5:\n",
    "        d2.add_last(temp)\n",
    "        continue\n",
    "    elif temp == 4:\n",
    "        d2.add_first(temp)\n",
    "        d2.add_first(d2.delete_last())\n",
    "        continue\n",
    "    d2.add_first(temp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 455,
   "id": "d8aa26cb-002a-4cfb-87ac-1c41941ccb50",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[1, 2, 3, 5, 4, 6, 7, 8]'"
      ]
     },
     "execution_count": 455,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(d2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5fe7afd3-5d25-4f04-8670-a301c4db0b50",
   "metadata": {},
   "source": [
    "### C-6.15 \n",
    "Suppose Alice has picked three distinct integers and placed them into a\n",
    "stack S in random order. Write a short, straight-line piece of pseudo-code\n",
    "(with no loops or recursion) that uses only one comparison and only one\n",
    "variable x, yet that results in variable x storing the largest of Alice’s three\n",
    "integers with probability 2/3. Argue why your method is correct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 459,
   "id": "53cac727-705b-4a54-953f-e43dcd8f965a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[3, 2, 1]'"
      ]
     },
     "execution_count": 459,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stack_615 = Stack()\n",
    "for i in range(3,0,-1):\n",
    "    stack_615.push(i)\n",
    "str(stack_615)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 460,
   "id": "4e915885-de80-4fe4-a265-b364c1622aed",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    }
   ],
   "source": [
    "x = stack_615.pop()\n",
    "if x < stack_615.top():\n",
    "    x = stack_615.pop()\n",
    "else:\n",
    "    stack_615.pop()\n",
    "\n",
    "if x < stack_615.top():\n",
    "    x = stack_615.pop()\n",
    "\n",
    "print(x)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb43475e-101f-4e58-a823-32db2c473f06",
   "metadata": {},
   "source": [
    "### C-6.16 \n",
    "Modify the ArrayStack implementation so that the stack’s capacity is limited to maxlen elements, where maxlen is an optional parameter to the\n",
    "constructor (that defaults to None). If push is called when the stack is at\n",
    "full capacity, throw a Full exception (defined similarly to Empty)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 475,
   "id": "e34a433a-06a5-4800-b745-ee7fb0f9e9cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "class FullException(Exception):\n",
    "    ...\n",
    "\n",
    "class ArrayStack:\n",
    "    \n",
    "    def check_is_empty(self):\n",
    "        if self.is_empty():\n",
    "                raise Exception('Stack is Empty')\n",
    "    \n",
    "    def __init__(self,maxlen=None):\n",
    "        self._data = []\n",
    "        self._maxlen = maxlen\n",
    "\n",
    "    def __len__(self,):\n",
    "        return len(self._data)\n",
    "\n",
    "    def is_empty(self,):\n",
    "        return len(self._data) == 0\n",
    "\n",
    "    def push(self,element):\n",
    "        if self._maxlen:\n",
    "            if self.__len__() < self._maxlen:\n",
    "                self._data.append(element)\n",
    "            else:\n",
    "                raise FullException(f'Stack too full limit is {self._maxlen}')\n",
    "        else:\n",
    "            self._data.append(element)\n",
    "\n",
    "    def top(self,):\n",
    "        self.check_is_empty()\n",
    "        return self._data[-1]\n",
    "\n",
    "    def pop(self,):\n",
    "        self.check_is_empty()\n",
    "        return self._data.pop()\n",
    "\n",
    "    def __str__(self):\n",
    "        return f'Stack: {self._data}'\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 476,
   "id": "3499e195-af18-46eb-a5af-69f01ee65e9c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Stack: [1]'"
      ]
     },
     "execution_count": 476,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "astack_616 = ArrayStack()\n",
    "astack_616.push(1)\n",
    "str(astack_616)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 477,
   "id": "d3484fdc-2cb4-4937-977f-0d4ee491c859",
   "metadata": {},
   "outputs": [
    {
     "ename": "FullException",
     "evalue": "Stack too full limit is 2",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mFullException\u001b[0m                             Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[477], line 4\u001b[0m\n\u001b[0;32m      2\u001b[0m astack_616_2\u001b[38;5;241m.\u001b[39mpush(\u001b[38;5;241m1\u001b[39m)\n\u001b[0;32m      3\u001b[0m astack_616_2\u001b[38;5;241m.\u001b[39mpush(\u001b[38;5;241m2\u001b[39m)\n\u001b[1;32m----> 4\u001b[0m \u001b[43mastack_616_2\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mpush\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m3\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[0;32m      5\u001b[0m \u001b[38;5;28mstr\u001b[39m(astack_616_2)\n",
      "Cell \u001b[1;32mIn[475], line 25\u001b[0m, in \u001b[0;36mArrayStack.push\u001b[1;34m(self, element)\u001b[0m\n\u001b[0;32m     23\u001b[0m         \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_data\u001b[38;5;241m.\u001b[39mappend(element)\n\u001b[0;32m     24\u001b[0m     \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m---> 25\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m FullException(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mStack too full limit is \u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_maxlen\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m'\u001b[39m)\n\u001b[0;32m     26\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m     27\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_data\u001b[38;5;241m.\u001b[39mappend(element)\n",
      "\u001b[1;31mFullException\u001b[0m: Stack too full limit is 2"
     ]
    }
   ],
   "source": [
    "astack_616_2 = ArrayStack(2)\n",
    "astack_616_2.push(1)\n",
    "astack_616_2.push(2)\n",
    "astack_616_2.push(3)\n",
    "str(astack_616_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acdfc625-2e97-4e02-8ce4-5ce75c109256",
   "metadata": {},
   "source": [
    "### C-6.17\n",
    "In the previous exercise, we assume that the underlying list is initially\n",
    "empty. Redo that exercise, this time preallocating an underlying list with\n",
    "length equal to the stack’s maximum capacity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1940211b-b850-4d44-b38f-ddec4b07c730",
   "metadata": {},
   "outputs": [],
   "source": [
    "class FullException(Exception):\n",
    "    ...\n",
    "\n",
    "class ArrayStack:\n",
    "    \n",
    "    def check_is_empty(self):\n",
    "        if self.is_empty():\n",
    "                raise Exception('Stack is Empty')\n",
    "    \n",
    "    def __init__(self,maxlen=10):\n",
    "        self._maxlen = maxlen\n",
    "        self._data = []\n",
    "    \n",
    "    def __len__(self,):\n",
    "        return len(self._data)\n",
    "\n",
    "    def is_empty(self,):\n",
    "        return len(self._data) == 0\n",
    "\n",
    "    def push(self,element):\n",
    "        if self._maxlen:\n",
    "            if self.__len__() < self._maxlen:\n",
    "                self._data.append(element)\n",
    "            else:\n",
    "                raise FullException(f'Stack too full limit is {self._maxlen}')\n",
    "        else:\n",
    "            self._data.append(element)\n",
    "\n",
    "    def top(self,):\n",
    "        self.check_is_empty()\n",
    "        return self._data[-1]\n",
    "\n",
    "    def pop(self,):\n",
    "        self.check_is_empty()\n",
    "        return self._data.pop()\n",
    "\n",
    "    def __str__(self):\n",
    "        return f'Stack: {self._data}'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "db9a09be-b9d2-4493-b596-aa6d0bc026ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "stack_617 = ArrayStack()\n",
    "for i in range(10):\n",
    "    stack_617.push(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9a2bad02-fd61-4218-8fff-83e8255f55f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Stack: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]'"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(stack_617)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2c36bfd8-1bbd-403d-b02c-0908c3b6d017",
   "metadata": {},
   "outputs": [
    {
     "ename": "FullException",
     "evalue": "Stack too full limit is 10",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mFullException\u001b[0m                             Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[8], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[43mstack_617\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mpush\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m11\u001b[39;49m\u001b[43m)\u001b[49m\n",
      "Cell \u001b[1;32mIn[4], line 25\u001b[0m, in \u001b[0;36mArrayStack.push\u001b[1;34m(self, element)\u001b[0m\n\u001b[0;32m     23\u001b[0m         \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_data\u001b[38;5;241m.\u001b[39mappend(element)\n\u001b[0;32m     24\u001b[0m     \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m---> 25\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m FullException(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mStack too full limit is \u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_maxlen\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m'\u001b[39m)\n\u001b[0;32m     26\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m     27\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_data\u001b[38;5;241m.\u001b[39mappend(element)\n",
      "\u001b[1;31mFullException\u001b[0m: Stack too full limit is 10"
     ]
    }
   ],
   "source": [
    "stack_617.push(11)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "699ccc2e-7328-4920-a3ed-6d4abdca79dc",
   "metadata": {},
   "source": [
    "C-6.18 Show how to use the transfer function, described in Exercise R-6.3, and\n",
    "two temporary stacks, to replace the contents of a given stack S with those\n",
    "same elements, but in reversed order."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "501cdf66-da77-4e9c-bdf4-04d462eb50c7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[9, 8, 7, 6, 5, 4, 3, 2, 1, 0]'"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stack_618_1 = Stack()\n",
    "stack_618_2 = Stack()\n",
    "\n",
    "for i in range(10):\n",
    "    stack_618_1.push(i)\n",
    "\n",
    "str(transfer(stack_618_1,stack_618_2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6fb63f6-f262-48c6-86c9-5bbc4f52c982",
   "metadata": {},
   "source": [
    "C-6.20 Describe a nonrecursive algorithm for enumerating all permutations of the\n",
    "numbers {1,2,...,n} using an explicit stack."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "d27eacb9-030f-4e79-b57b-ca05a29bab2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def enumerate_num(n):\n",
    "    stack = Stack()\n",
    "    for i in range(n+1):\n",
    "        stack.push(i)\n",
    "    return stack"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "d1c4422d-5c6f-4691-80be-4385fd2f7739",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]'"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(enumerate_num(10))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adcea4e8-e409-4540-95bd-5e3f008b99d5",
   "metadata": {},
   "source": [
    "### C-6.21\n",
    "Show how to use a stack S and a queue Q to generate all possible subsets\n",
    "of an n-element set T nonrecursively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "5a9f6eeb-a431-4cb7-ab1d-3da99bca3ac5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(10, 1),\n",
       " (9, 2),\n",
       " (8, 3),\n",
       " (7, 4),\n",
       " (6, 5),\n",
       " (5, 6),\n",
       " (4, 7),\n",
       " (3, 8),\n",
       " (2, 9),\n",
       " (1, 10)]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def sub_q_s(n):\n",
    "    stack = Stack()\n",
    "    queue = Queue()\n",
    "    for i in range(1,n+1):\n",
    "        stack.push(i)\n",
    "        queue.enqueue(i)\n",
    "\n",
    "    subset = []\n",
    "    for _ in range(len(stack)):\n",
    "        subset.append((stack.pop(),queue.dequeue()))\n",
    "\n",
    "    return subset\n",
    "\n",
    "sub_q_s(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e34b817b-822f-4d43-8a50-da5d6317a607",
   "metadata": {},
   "source": [
    "### C-6.23 \n",
    "Suppose you have three nonempty stacks R, S, and T. Describe a sequence\n",
    "of operations that results in S storing all elements originally in T below all\n",
    "of S’s original elements, with both sets of those elements in their original\n",
    "order. The final configuration for R should be the same as its original\n",
    "configuration. For example, if R = [1,2,3], S = [4,5], and T = [6,7,8,9],\n",
    "the final configuration should have R = [1,2,3] and S = [6,7,8,9,4,5]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "851ca876-e4df-4523-9a03-f27600a01fcf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3]\n",
      "[6, 7, 8, 9, 4, 5]\n",
      "[]\n"
     ]
    }
   ],
   "source": [
    "def transfer_2nd_to_3rd_stack(s1,s2,s3):\n",
    "    length = len(s2)+len(s3)\n",
    "    for _ in range(len(s2)):\n",
    "        s1.push(s2.pop())\n",
    "    for _ in range(len(s3)):\n",
    "        s1.push(s3.pop())\n",
    "    for _ in range(length):\n",
    "        s2.push(s1.pop())\n",
    "    return s1,s2,s3\n",
    "\n",
    "r = Stack()\n",
    "s = Stack()\n",
    "t = Stack()\n",
    "\n",
    "for i in range(1,4):\n",
    "    r.push(i)\n",
    "\n",
    "for i in range(4,6):\n",
    "    s.push(i)\n",
    "\n",
    "for i in range(6,10):\n",
    "    t.push(i)\n",
    "\n",
    "transfer_2nd_to_3rd_stack(r,s,t)\n",
    "print(str(r))\n",
    "print(str(s))\n",
    "print(str(t))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57be4b97-9a6c-4752-9e25-bd56e3ba7185",
   "metadata": {},
   "source": [
    "### C-6.24 \n",
    "Describe how to implement the stack ADT using a single queue as an\n",
    "instance variable, and only constant additional local memory within the\n",
    "method bodies. What is the running time of the push(), pop(), and top()\n",
    "methods for your design?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8b26a8f0-ef71-4ca3-b457-d6445a1d013f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "import sys\n",
    "\n",
    "def time_mem_analysis(func):\n",
    "\n",
    "    def wrapper(*args,**kwargs):\n",
    "        start = time.perf_counter()\n",
    "        rs = func(*args,**kwargs)\n",
    "        end = time.perf_counter()\n",
    "        size_in_mb = sys.getsizeof(rs)/(1024**2)\n",
    "        return {'data':rs, 'secs':end-start, 'mem in mb':size_in_mb}\n",
    "\n",
    "    return wrapper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "60ebfb9e-2ab8-42a7-b51f-ed7fb2bcdf82",
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import deque\n",
    "\n",
    "class StackADT:\n",
    "    def __init__(self):\n",
    "        self.queue = deque()\n",
    "\n",
    "    def push(self, x):\n",
    "        # Get the current size of the queue\n",
    "        size = len(self.queue)\n",
    "        # Enqueue the new element\n",
    "        self.queue.append(x)\n",
    "        # Rotate the queue to move the new element to the front\n",
    "        for _ in range(size):\n",
    "            self.queue.append(self.queue.popleft())\n",
    "\n",
    "    def pop(self):\n",
    "        # Dequeue the front element\n",
    "        if self.is_empty():\n",
    "            raise IndexError(\"pop from an empty stack\")\n",
    "        return self.queue.popleft()\n",
    "\n",
    "    def top(self):\n",
    "        # Get the front element\n",
    "        if self.is_empty():\n",
    "            raise IndexError(\"top from an empty stack\")\n",
    "        return self.queue[0]\n",
    "\n",
    "    def is_empty(self):\n",
    "        return len(self.queue) == 0\n",
    "\n",
    "    def size(self):\n",
    "        return len(self.queue)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d7c3b8ab-b8d7-41b0-a280-8a090492e7cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "stacks = [StackADT() for i in range(0,4)]\n",
    "num_of_times = [10**i for i in range(0,4)]\n",
    "\n",
    "stacks_num_of_time = zip(stacks,num_of_times)\n",
    "\n",
    "@time_mem_analysis\n",
    "def push_x_times(x,stack_adt):\n",
    "    for i in range(x):\n",
    "        stack_adt.push(i)\n",
    "\n",
    "x_push = [push_x_times(num_of_time,stack) for stack,num_of_time in stacks_num_of_time]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e38425b8-9e7d-474e-afdb-858c72712135",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'data': None, 'secs': 6.100000064179767e-06, 'mem in mb': 1.52587890625e-05}\n",
      "{'data': None, 'secs': 8.499999921696144e-06, 'mem in mb': 1.52587890625e-05}\n",
      "{'data': None, 'secs': 0.0004129999999804568, 'mem in mb': 1.52587890625e-05}\n",
      "{'data': None, 'secs': 0.050465699999904245, 'mem in mb': 1.52587890625e-05}\n"
     ]
    }
   ],
   "source": [
    "for i in x_push:\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fb81cb7-15bf-493f-bb20-56d4d992c0e6",
   "metadata": {},
   "source": [
    "### C-6.25 \n",
    "\n",
    "Describe how to implement the queue ADT using two stacks as instance\n",
    "variables, such that all queue operations execute in amortized O(1) time.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "b236d3a5-8309-49b6-8737-3ee824177107",
   "metadata": {},
   "outputs": [],
   "source": [
    "class QueueUsingStacks:\n",
    "    def __init__(self):\n",
    "        self.stack1 = []  # Stack to handle enqueue operations\n",
    "        self.stack2 = []  # Stack to handle dequeue operations\n",
    "\n",
    "    def enqueue(self, item):\n",
    "        # Push the item onto stack1\n",
    "        self.stack1.append(item)\n",
    "\n",
    "    def dequeue(self):\n",
    "        if not self.stack2:\n",
    "            # Transfer elements from stack1 to stack2 if stack2 is empty\n",
    "            while self.stack1:\n",
    "                self.stack2.append(self.stack1.pop())\n",
    "        \n",
    "        if not self.stack2:\n",
    "            # If stack2 is still empty, that means the queue is empty\n",
    "            raise IndexError(\"dequeue from an empty queue\")\n",
    "        \n",
    "        # Pop the item from stack2\n",
    "        return self.stack2.pop()\n",
    "\n",
    "    def is_empty(self):\n",
    "        # The queue is empty if both stacks are empty\n",
    "        return not self.stack1 and not self.stack2\n",
    "\n",
    "    def size(self):\n",
    "        # The size of the queue is the total number of elements in both stacks\n",
    "        return len(self.stack1) + len(self.stack2)\n",
    "\n",
    "    def front(self):\n",
    "        # Get the front element without dequeuing it\n",
    "        if not self.stack2:\n",
    "            # Transfer elements from stack1 to stack2 if stack2 is empty\n",
    "            while self.stack1:\n",
    "                self.stack2.append(self.stack1.pop())\n",
    "        \n",
    "        if not self.stack2:\n",
    "            # If stack2 is still empty, that means the queue is empty\n",
    "            raise IndexError(\"front from an empty queue\")\n",
    "        \n",
    "        # Return the top item from stack2\n",
    "        return self.stack2[-1]\n",
    " \n",
    "\n",
    "    def __str__(self):\n",
    "        return f\"\"\"\n",
    "        enque: {self.stack1}\n",
    "        deque: {self.stack2}\n",
    "        \"\"\"\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "cbad75ad-f4dc-4d13-91cc-31b637b586b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\n        enque: []\\n        deque: []\\n        '"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qus = QueueUsingStacks()\n",
    "assert qus.size() == 0 \n",
    "qus.enqueue(1)\n",
    "assert qus.size() == 1\n",
    "qus.dequeue()\n",
    "str(qus)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "5a908e62-8907-4e70-9cb9-5095c30f481d",
   "metadata": {},
   "outputs": [],
   "source": [
    "assert qus.is_empty()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "9d0d78c7-95b3-4b82-a433-512b0c7ffc7e",
   "metadata": {},
   "outputs": [],
   "source": [
    "qus.enqueue(1)\n",
    "assert qus.is_empty() == False"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ca01919-c2a0-4867-a1b1-eef839143235",
   "metadata": {},
   "source": [
    "### C-6.27 \n",
    "Suppose you have a stack S containing n elements and a queue Q that is\n",
    "initially empty. Describe how you can use Q to scan S to see if it contains a\n",
    "certain element x, with the additional constraint that your algorithm must\n",
    "return the elements back to S in their original order. You may only use S,\n",
    "Q, and a constant number of other variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "737b6c3e-90cb-468f-8757-1b26fe237bb4",
   "metadata": {},
   "outputs": [],
   "source": [
    "class EmptyException(Exception):\n",
    "    ...\n",
    "\n",
    "class Stack:\n",
    "\n",
    "    def __init__(self,):\n",
    "        self._data = []\n",
    "\n",
    "    def __len__(self):\n",
    "        return len(self._data)\n",
    "\n",
    "    def __str__(self):\n",
    "        return f\"{self._data}\"\n",
    "    \n",
    "    def raise_empty_exception(self):\n",
    "        if not self._data:\n",
    "            raise EmptyException(f\"{self} is empty\")\n",
    "\n",
    "    def pop(self,):\n",
    "        self.raise_empty_exception()\n",
    "        return self._data.pop()\n",
    "\n",
    "    def push(self,item):\n",
    "        return self._data.append(item)\n",
    "\n",
    "    def peek(self,):\n",
    "        self.raise_empty_exception()\n",
    "        return self._data[-1]\n",
    "    \n",
    "    def is_empty(self):\n",
    "        return len(self._data) == 0\n",
    "\n",
    "\n",
    "\n",
    "class Queue:\n",
    "\n",
    "    def __init__(self,):\n",
    "        self._data = []\n",
    "\n",
    "    def __len__(self):\n",
    "        return len(self._data)\n",
    "\n",
    "    def __str__(self):\n",
    "        return f\"{self._data}\"\n",
    "    \n",
    "    def raise_empty_exception(self):\n",
    "        if not self._data:\n",
    "            raise EmptyException(f\"{self} is empty\")\n",
    "\n",
    "    def dequeue(self,):\n",
    "        self.raise_empty_exception()\n",
    "        return self._data.pop(0)\n",
    "\n",
    "    def enqueue(self,item):\n",
    "        return self._data.append(item)\n",
    "\n",
    "    def front(self,):\n",
    "        self.raise_empty_exception()\n",
    "        return self._data[0]\n",
    "    \n",
    "    def is_empty(self):\n",
    "        return len(self._data) == 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "e383d199-e4bf-4fd6-b158-4b72df1d9068",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    },
    {
     "ename": "EmptyException",
     "evalue": "[] is empty",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mEmptyException\u001b[0m                            Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[53], line 3\u001b[0m\n\u001b[0;32m      1\u001b[0m s \u001b[38;5;241m=\u001b[39m Stack()\n\u001b[0;32m      2\u001b[0m \u001b[38;5;28mprint\u001b[39m(s\u001b[38;5;241m.\u001b[39mis_empty())\n\u001b[1;32m----> 3\u001b[0m \u001b[43ms\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mpop\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
      "Cell \u001b[1;32mIn[48], line 20\u001b[0m, in \u001b[0;36mStack.pop\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m     19\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mpop\u001b[39m(\u001b[38;5;28mself\u001b[39m,):\n\u001b[1;32m---> 20\u001b[0m     \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mraise_empty_exception\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m     21\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_data\u001b[38;5;241m.\u001b[39mpop()\n",
      "Cell \u001b[1;32mIn[48], line 17\u001b[0m, in \u001b[0;36mStack.raise_empty_exception\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m     15\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mraise_empty_exception\u001b[39m(\u001b[38;5;28mself\u001b[39m):\n\u001b[0;32m     16\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_data:\n\u001b[1;32m---> 17\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m EmptyException(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[38;5;28mself\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m is empty\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "\u001b[1;31mEmptyException\u001b[0m: [] is empty"
     ]
    }
   ],
   "source": [
    "s = Stack()\n",
    "print(s.is_empty())\n",
    "s.pop()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "8c471e25-1d45-4a88-b356-a7e331f0ee1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "s.push(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "38d3bc0a-fe96-4fae-b750-1047efa58a06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.peek()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "1561849c-9d7f-4cf0-aae0-19fdf9fda5fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.pop()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "f634d0d4-10ee-41c6-96b2-61e48d1f8d64",
   "metadata": {},
   "outputs": [],
   "source": [
    "s.push(1)\n",
    "s.push(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "7f7741e4-7eb0-4d46-abdd-d1fbdc504089",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[1, 2]'"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "5575c26a-9509-45fc-965d-e5cc0e907b34",
   "metadata": {},
   "outputs": [
    {
     "ename": "EmptyException",
     "evalue": "[] is empty",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mEmptyException\u001b[0m                            Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[56], line 2\u001b[0m\n\u001b[0;32m      1\u001b[0m q \u001b[38;5;241m=\u001b[39m Queue()\n\u001b[1;32m----> 2\u001b[0m \u001b[43mq\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mfront\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
      "Cell \u001b[1;32mIn[48], line 58\u001b[0m, in \u001b[0;36mQueue.front\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m     57\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mfront\u001b[39m(\u001b[38;5;28mself\u001b[39m,):\n\u001b[1;32m---> 58\u001b[0m     \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mraise_empty_exception\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m     59\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_data[\u001b[38;5;241m0\u001b[39m]\n",
      "Cell \u001b[1;32mIn[48], line 48\u001b[0m, in \u001b[0;36mQueue.raise_empty_exception\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m     46\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mraise_empty_exception\u001b[39m(\u001b[38;5;28mself\u001b[39m):\n\u001b[0;32m     47\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_data:\n\u001b[1;32m---> 48\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m EmptyException(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[38;5;28mself\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m is empty\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "\u001b[1;31mEmptyException\u001b[0m: [] is empty"
     ]
    }
   ],
   "source": [
    "q = Queue()\n",
    "q.front()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "99f8e2cc-d4d4-4215-a73c-2d8b6fbd9940",
   "metadata": {},
   "outputs": [
    {
     "ename": "EmptyException",
     "evalue": "[] is empty",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mEmptyException\u001b[0m                            Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[57], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[43mq\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdequeue\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
      "Cell \u001b[1;32mIn[48], line 51\u001b[0m, in \u001b[0;36mQueue.dequeue\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m     50\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mdequeue\u001b[39m(\u001b[38;5;28mself\u001b[39m,):\n\u001b[1;32m---> 51\u001b[0m     \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mraise_empty_exception\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m     52\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_data\u001b[38;5;241m.\u001b[39mpop(\u001b[38;5;241m0\u001b[39m)\n",
      "Cell \u001b[1;32mIn[48], line 48\u001b[0m, in \u001b[0;36mQueue.raise_empty_exception\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m     46\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mraise_empty_exception\u001b[39m(\u001b[38;5;28mself\u001b[39m):\n\u001b[0;32m     47\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_data:\n\u001b[1;32m---> 48\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m EmptyException(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[38;5;28mself\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m is empty\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "\u001b[1;31mEmptyException\u001b[0m: [] is empty"
     ]
    }
   ],
   "source": [
    "q.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "fab1e63e-026c-4d6e-a8d7-bb042d327290",
   "metadata": {},
   "outputs": [],
   "source": [
    "q.enqueue(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "f5df521b-0534-4ee4-a3c8-76dfc988f775",
   "metadata": {},
   "outputs": [],
   "source": [
    "assert q.front() == 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "e0bc0da3-0776-4270-b49e-44011af44f20",
   "metadata": {},
   "outputs": [],
   "source": [
    "assert len(q) == 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "10f36098-f470-4813-9433-b4ef5c55a7c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "assert type(str(q)) == str"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "40a3f2ea-5853-49a1-bae7-dabefc249d38",
   "metadata": {},
   "outputs": [],
   "source": [
    "assert q.is_empty() == False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8385bdc0-0001-41c3-8a71-a5bbc7e8e745",
   "metadata": {},
   "outputs": [],
   "source": [
    "q.enqueue(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "bafb1998-b478-4207-8bc5-ae07c42b4cb9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q.front()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "5b0a5ef2-b691-409a-a4c2-43f58379f06f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "1aa9f9c6-9642-450c-b78e-a0a619d4efd3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "af0f82af-eae6-4239-845b-f24456e3d8d6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n"
     ]
    }
   ],
   "source": [
    "s1 = Stack()\n",
    "for i in range(10):\n",
    "    s1.push(i)\n",
    "\n",
    "print(str(s1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "d9c9b7e1-0a4f-4076-8df4-bd9659834100",
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_x(target,stack):\n",
    "    q = Queue()\n",
    "    is_exist = False\n",
    "    count = 0 \n",
    "    for _ in range(len(stack)):\n",
    "        if  stack.peek() == target:\n",
    "            is_exist = True\n",
    "            break\n",
    "        count+=1\n",
    "        q.enqueue(stack.pop())\n",
    "    for _ in range(count):\n",
    "        stack.push(q.dequeue())\n",
    "    for _ in range(count):\n",
    "        q.enqueue(stack.pop())\n",
    "    for _ in range(count):\n",
    "        stack.push(q.dequeue())\n",
    "    return is_exist\n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "f96fd415-c174-4009-9bdc-7c0b6469a52c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_x(1,s1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "d19ca231-03dd-47ae-b6eb-4922a38e9f0d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]'"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(s1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "900da460-00cb-4e62-8491-b3302eb0adbe",
   "metadata": {},
   "source": [
    "### C-6.28 \n",
    "Modify the ArrayQueue implementation so that the queue’s capacity is\n",
    "limited to maxlen elements, where maxlen is an optional parameter to the\n",
    "constructor (that defaults to None). If enqueue is called when the queue\n",
    "is at full capacity, throw a Full exception (defined similarly to Empty)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "id": "3f2a7b96-a775-4379-8081-946f2cf477a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "class EmptyException(Exception):\n",
    "    pass\n",
    "\n",
    "class ArrayQueue:\n",
    "    def __init__(self, maxlen=10):\n",
    "        self.capacity = maxlen\n",
    "        self.size = 0\n",
    "        self._data = [None] * maxlen\n",
    "        self.front_index = 0  # Index of the front element\n",
    "        self.rear_index = 0   # Index where the next element will be inserted\n",
    "\n",
    "    def __len__(self):\n",
    "        return self.size\n",
    "\n",
    "    def __str__(self):\n",
    "        return str([self._data[(self.front_index + i) % self.capacity] for i in range(self.size)])\n",
    "    \n",
    "    def raise_empty_exception(self):\n",
    "        if self.is_empty():\n",
    "            raise EmptyException(\"Queue is empty\")\n",
    "\n",
    "    def dequeue(self):\n",
    "        self.raise_empty_exception()\n",
    "        front_item = self._data[self.front_index]\n",
    "        self._data[self.front_index] = None  # Help garbage collection\n",
    "        self.front_index = (self.front_index + 1) % self.capacity\n",
    "        self.size -= 1\n",
    "        return front_item\n",
    "\n",
    "    def enqueue(self, item):\n",
    "        if self.size == self.capacity:\n",
    "            self._resize(2 * self.capacity)  # Double the capacity\n",
    "        self._data[self.rear_index] = item\n",
    "        self.rear_index = (self.rear_index + 1) % self.capacity\n",
    "        self.size += 1\n",
    "\n",
    "    def front(self):\n",
    "        self.raise_empty_exception()\n",
    "        return self._data[self.front_index]\n",
    "    \n",
    "    def is_empty(self):\n",
    "        return self.size == 0\n",
    "\n",
    "    def _resize(self, new_capacity):\n",
    "        old_data = self._data\n",
    "        self._data = [None] * new_capacity\n",
    "        for i in range(self.size):\n",
    "            self._data[i] = old_data[(self.front_index + i) % self.capacity]\n",
    "        self.front_index = 0\n",
    "        self.rear_index = self.size\n",
    "        self.capacity = new_capacity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "id": "f9101b44-0537-466d-8301-5a61e4485bc5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "[None, None, None, None, None, None, None, None, None, None]\n"
     ]
    }
   ],
   "source": [
    "aq = ArrayQueue()\n",
    "print(aq.size)\n",
    "print(aq._data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "id": "f6ac49e9-1eab-4119-b0ea-1698e90abaf7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "0\n",
      "0\n"
     ]
    }
   ],
   "source": [
    "print(aq.capacity)\n",
    "print(aq.front_index)\n",
    "print(aq.rear_index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "id": "45be59e3-a0d8-4b9c-b346-d1932e3c0fb5",
   "metadata": {},
   "outputs": [],
   "source": [
    "assert len(aq) == 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "id": "2c2e8eb5-48df-4a4b-a8c3-ccbf1cca17e5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pytest\n",
    "with pytest.raises(EmptyException):\n",
    "    aq.raise_empty_exception()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "id": "a6ac7deb-1342-42f5-a4d9-d48dac122c59",
   "metadata": {},
   "outputs": [],
   "source": [
    "with pytest.raises(EmptyException):\n",
    "    aq.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "id": "3f3ead96-3082-4234-b141-224a593178cd",
   "metadata": {},
   "outputs": [],
   "source": [
    "aq.enqueue(1)\n",
    "assert aq.size == 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "id": "095a591c-bcfa-49f6-bcd7-5100e3eb6cc5",
   "metadata": {},
   "outputs": [],
   "source": [
    "item = aq.dequeue()\n",
    "assert aq.size == 0\n",
    "assert item == 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "id": "1df0110a-2451-4fcc-9e42-cba8a9e17366",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(20):\n",
    "    aq.enqueue(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "id": "44cf2ebe-eed0-42ab-9eb3-efecd59bbb66",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]'"
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(aq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "id": "6531263d-2d0a-4a06-8185-371ace49aae8",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(20):\n",
    "    aq.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "id": "48b6aaa8-49ad-4d22-bc40-4103961a94b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[]'"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(aq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "id": "c9dbbf9f-27ca-4380-8a7a-5293995baa14",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aq.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "id": "1fc6492f-b81b-4e11-958d-dbb76e355b59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aq.capacity"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7015499f-7f78-4480-8a53-3b9ca53c5a2f",
   "metadata": {},
   "source": [
    "### C-6.29 \n",
    "In certain applications of the queue ADT, it is common to repeatedly\n",
    "dequeue an element, process it in some way, and then immediately enqueue the same element. Modify the ArrayQueue implementation to include a rotate( ) method that has semantics identical to the combination, Q.enqueue(Q.dequeue( )). However, your implementation should\n",
    "be more efficient than making two separate calls (for example, because\n",
    "there is no need to modify size)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "id": "fae50c89-9bc0-4051-a831-1b3f92322216",
   "metadata": {},
   "outputs": [],
   "source": [
    "class EmptyException(Exception):\n",
    "    pass\n",
    "\n",
    "class ArrayQueue:\n",
    "    def __init__(self, maxlen=10):\n",
    "        self.capacity = maxlen\n",
    "        self.size = 0\n",
    "        self._data = [None] * maxlen\n",
    "        self.front_index = 0  # Index of the front element\n",
    "        self.rear_index = 0   # Index where the next element will be inserted\n",
    "\n",
    "    def __len__(self):\n",
    "        return self.size\n",
    "\n",
    "    def __str__(self):\n",
    "        return str([self._data[(self.front_index + i) % self.capacity] for i in range(self.size)])\n",
    "    \n",
    "    def raise_empty_exception(self):\n",
    "        if self.is_empty():\n",
    "            raise EmptyException(\"Queue is empty\")\n",
    "\n",
    "    def dequeue(self):\n",
    "        self.raise_empty_exception()\n",
    "        front_item = self._data[self.front_index]\n",
    "        self._data[self.front_index] = None  # Help garbage collection\n",
    "        self.front_index = (self.front_index + 1) % self.capacity\n",
    "        self.size -= 1\n",
    "        return front_item\n",
    "\n",
    "    def enqueue(self, item):\n",
    "        if self.size == self.capacity:\n",
    "            self._resize(2 * self.capacity)  # Double the capacity\n",
    "        self._data[self.rear_index] = item\n",
    "        self.rear_index = (self.rear_index + 1) % self.capacity\n",
    "        self.size += 1\n",
    "\n",
    "    def rotate(self,f,*args,**kwargs):\n",
    "        item = self.dequeue()\n",
    "        print(item)\n",
    "        rs = f(item,*args,**kwargs)\n",
    "        print(rs)\n",
    "        self.enqueue(rs)\n",
    "    \n",
    "    def front(self):\n",
    "        self.raise_empty_exception()\n",
    "        return self._data[self.front_index]\n",
    "    \n",
    "    def is_empty(self):\n",
    "        return self.size == 0\n",
    "\n",
    "    def _resize(self, new_capacity):\n",
    "        old_data = self._data\n",
    "        self._data = [None] * new_capacity\n",
    "        for i in range(self.size):\n",
    "            self._data[i] = old_data[(self.front_index + i) % self.capacity]\n",
    "        self.front_index = 0\n",
    "        self.rear_index = self.size\n",
    "        self.capacity = new_capacity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "id": "72bf73b1-ab32-405c-b7c6-9e5eb4816f85",
   "metadata": {},
   "outputs": [],
   "source": [
    "aq = ArrayQueue()\n",
    "for i in range(1,10):\n",
    "    aq.enqueue(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "id": "86df26fb-5ad0-44f5-ab05-d642f92b4223",
   "metadata": {},
   "outputs": [],
   "source": [
    "def multiple_2(x,multiple=2):\n",
    "    return x*multiple"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "id": "68916155-761e-4c24-98c3-fe081e44768a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n"
     ]
    }
   ],
   "source": [
    "aq.rotate(multiple_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "id": "e9893332-4f1d-4161-b2f9-3d88f2b7f01a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[2, 3, 4, 5, 6, 7, 8, 9, 2]'"
      ]
     },
     "execution_count": 246,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(aq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "id": "16d9ec96-8181-41ac-a3fc-622f3a5a7508",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n",
      "20\n"
     ]
    }
   ],
   "source": [
    "aq.rotate(multiple_2,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "id": "f273f820-d464-4c02-8c01-68febc3d3254",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[3, 4, 5, 6, 7, 8, 9, 2, 20]'"
      ]
     },
     "execution_count": 248,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(aq)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "daf4ead3-4282-473a-97fe-bea5d5ce6d4a",
   "metadata": {},
   "source": [
    "### C-6.30\n",
    "Alice has two queues, Q and R, which can store integers. Bob gives Alice\n",
    "50 odd integers and 50 even integers and insists that she store all 100\n",
    "integers in Q and R. They then play a game where Bob picks Q or R\n",
    "at random and then applies the round-robin scheduler, described in the\n",
    "chapter, to the chosen queue a random number of times. If the last number\n",
    "to be processed at the end of this game was odd, Bob wins. Otherwise,\n",
    "Alice wins. How can Alice allocate integers to queues to optimize her\n",
    "chances of winning? What is her chance of winning?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 305,
   "id": "49be4b15-d145-4f47-af19-21ba8b7dae03",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100"
      ]
     },
     "execution_count": 305,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import random\n",
    "# Two Ques Q and R\n",
    "# 100 ints, 50 odds, 50 evens\n",
    "\n",
    "# player randomly selects between 2 queues\n",
    "# if last item is odd, the player win\n",
    "# else house wins with evens\n",
    "\n",
    "# obj make house win more\n",
    "\n",
    "q = ArrayQueue() # even\n",
    "r = ArrayQueue() # odds \n",
    "\n",
    "q_map = {'evens':q,'odds':r}\n",
    "for i in range(1,101):\n",
    "    if i%2 == 0:\n",
    "        q.enqueue(i)\n",
    "    else:\n",
    "        r.enqueue(i)\n",
    "\n",
    "def fair_game(q_map,chance=0.5):\n",
    "    q_name = None \n",
    "    last_item = None \n",
    "    for _ in range(100):\n",
    "        if random.random() > chance:\n",
    "            que = q_map['evens']\n",
    "            q_name = 'evens'\n",
    "        else:\n",
    "            que = q_map['odds']\n",
    "            q_name = 'odds'\n",
    "            \n",
    "        if que.is_empty():\n",
    "            if q_name =='odds':\n",
    "                que = q_map['evens']\n",
    "            else:\n",
    "                que = q_map['odds']\n",
    "    \n",
    "        last_item = que.dequeue()\n",
    "        \n",
    "    return last_item\n",
    "\n",
    "fair_game(q_map)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b080f42-f438-4ef9-b44e-e1c7743e19ae",
   "metadata": {},
   "source": [
    "### C-6.31\n",
    "Suppose Bob has four cows that he wants to take across a bridge, but only\n",
    "one yoke, which can hold up to two cows, side by side, tied to the yoke.\n",
    "The yoke is too heavy for him to carry across the bridge, but he can tie\n",
    "(and untie) cows to it in no time at all. Of his four cows, Mazie can cross\n",
    "the bridge in 2 minutes, Daisy can cross it in 4 minutes, Crazy can cross\n",
    "it in 10 minutes, and Lazy can cross it in 20 minutes. Of course, when\n",
    "two cows are tied to the yoke, they must go at the speed of the slower cow.\n",
    "Describe how Bob can get all his cows across the bridge in 34 minutes.\n",
    "\n",
    "\n",
    "B with 4 Cows\n",
    "Bridge\n",
    "Yolk can take 2 cows \n",
    "B cant carry yolk \n",
    "You can untie and tie a cow\n",
    "\n",
    "4 cows\n",
    "M = 2 mins\n",
    "D = 4 mins\n",
    "C = 10 mins\n",
    "L = 20 mins\n",
    "\n",
    "Need to cross in 34 mins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 353,
   "id": "43473071-4549-41e7-9161-5c479596e374",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Dequeue:\n",
    "\n",
    "    def __init__(self):\n",
    "        self._data = []\n",
    "\n",
    "    def error_if_empty(self):\n",
    "        if len(self._data) < 1:\n",
    "            raise Exception('Deque is empty')\n",
    "            \n",
    "    def __len__(self):\n",
    "        return len(self._data)\n",
    "\n",
    "    def __str__(self):\n",
    "        return f\"{self._data}\"\n",
    "\n",
    "    def first(self):\n",
    "        self.error_if_empty()\n",
    "        return self._data[0]\n",
    "        \n",
    "    def last(self):\n",
    "        self.error_if_empty()\n",
    "        return self._data[-1]\n",
    "    \n",
    "    def add_first(self,element):\n",
    "        self._data.insert(0,element)\n",
    "\n",
    "    def add_last(self,element):\n",
    "        self._data.append(element)\n",
    "\n",
    "    def delete_first(self):\n",
    "        return self._data.pop(0)\n",
    "\n",
    "    def delete_last(self):\n",
    "        return self._data.pop()\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 374,
   "id": "a4142759-07fc-4154-8036-7d7ca31d7aa8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Yolk:[] \n",
      " Time to Cross:34 mins\n",
      "Cows At End of Bridge: {'Crazy': <__main__.Cow object at 0x0000028F8332A670>, 'Lazy': <__main__.Cow object at 0x0000028F8332A190>, 'Daisy': <__main__.Cow object at 0x0000028F8332A9A0>, 'Mazie': <__main__.Cow object at 0x0000028F8332A9D0>}\n",
      "Cows:{}\n"
     ]
    }
   ],
   "source": [
    "class Cow:\n",
    "\n",
    "    def __init__(self,name,time_to_cross):\n",
    "        self.name = name\n",
    "        self.mins = time_to_cross\n",
    "\n",
    "\n",
    "\n",
    "cows = {\n",
    "    'Daisy': Cow('Daisy',4),\n",
    "    'Mazie': Cow('Mazie',2),\n",
    "    'Crazy': Cow('Crazy',10),\n",
    "    'Lazy': Cow('Lazy',20),\n",
    "}\n",
    "cows_end_of_bridge = dict()\n",
    "yolk = Dequeue()\n",
    "time_to_cross = 0\n",
    "\n",
    "yolk.add_last(cows.pop('Daisy'))\n",
    "yolk.add_last(cows.pop('Mazie'))\n",
    "time_to_cross += yolk.first().mins\n",
    "cows_end_of_bridge['Daisy'] = yolk.delete_first()\n",
    "time_to_cross += yolk.first().mins\n",
    "cows['Mazie'] = yolk.delete_first()\n",
    "yolk.add_last(cows.pop('Crazy'))\n",
    "yolk.add_last(cows.pop('Lazy'))\n",
    "time_to_cross += yolk.last().mins\n",
    "cows_end_of_bridge['Crazy'] = yolk.delete_first()\n",
    "cows_end_of_bridge['Lazy'] = yolk.delete_first()\n",
    "yolk.add_last(cows_end_of_bridge.pop('Daisy'))\n",
    "time_to_cross += yolk.last().mins\n",
    "yolk.add_last(cows.pop('Mazie'))\n",
    "time_to_cross += yolk.first().mins\n",
    "cows_end_of_bridge['Daisy'] = yolk.delete_first()\n",
    "cows_end_of_bridge['Mazie'] = yolk.delete_first()\n",
    "print(f'Yolk:{str(yolk)} \\n Time to Cross:{time_to_cross} mins\\nCows At End of Bridge: {cows_end_of_bridge}\\nCows:{cows}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "280f270c-7da6-4a6c-9d71-31d19848b2dd",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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