notebooks/Lecture 6.1.ipynb

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    "# Lecture 6.1. \n",
    "\n",
    "# Loops, using `while`\n",
    "\n",
    "# Friday, September 29"
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    "## 6.1.1. Loops and `while`\n",
    "\n",
    "* Loops allow **conditional repetition** of a set of statements. \n",
    "\n",
    "\n",
    "* In simple terms, loops **repeatedly execute** a **block of indented statements** as long as a corresponding **boolean condition** evaluates to `True`.\n",
    "\n",
    "\n",
    "* **`while` loops** are the most basic looping construct in the most programming languages, including Python.  "
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   "source": [
    "Recall, for `if...else` statements:"
   ]
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    "if boolean_condition_A: \n",
    "    #Indented Block B\n",
    "else:\n",
    "    #Indented Block C"
   ]
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   "source": [
    "<img align=\"center\" width=\"450\" src=\"https://upload.wikimedia.org/wikipedia/commons/c/c5/If-Then-Else-diagram.svg\">"
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    "<table>\n",
    "    <tr>\n",
    "        <td style=\"border: 1px solid black;\"><img align=\"center\" width=\"500\" src=\"https://upload.wikimedia.org/wikipedia/commons/c/c5/If-Then-Else-diagram.svg\"></td>\n",
    "        <td></td>\n",
    "        <td style=\"border: 1px solid black;\"><img align=\"center\" width=\"500\" src=\"https://upload.wikimedia.org/wikipedia/commons/4/43/While-loop-diagram.svg\"></td>\n",
    "     </tr>\n",
    "</table>\n"
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    "* It is called a **loop** because **flow of execution keeps looping back to the start** of the while statement **until the condition becomes `False`**. \n",
    "\n",
    "\n",
    "* When the condition becomes `False`, flow of execution moves to the statement that follows the indented `while` block. \n",
    "\n",
    "\n",
    "* The net effect is that the loop’s body is executed repeatedly while the condition at the top is `True`.\n",
    "\n",
    "\n",
    "* Each execution of the loop's body is called an **iteration** and the variable(s) in the condition are called **iterator(s)**.\n"
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    "* The `while` statement consists of: \n",
    "  * a header line with a **boolean condition**\n",
    "  * a body of one or more indented statements\n",
    "<hr />\n",
    "\n",
    "statement 0 \n",
    "\n",
    " `while` (boolean condition): \n",
    "> statement 1 \\\n",
    "> statement 2 \\\n",
    "    .\\\n",
    "    .\\\n",
    "    .\\\n",
    "    statement n\n",
    "    \n",
    "statement n+1"
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     "text": [
      "0\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "Outside loop\n"
     ]
    }
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   "source": [
    "i = 0\n",
    "\n",
    "while i < 5:\n",
    "    \n",
    "    print(i)\n",
    "    \n",
    "    i = i + 1\n",
    "    \n",
    "print(\"Outside loop\")"
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   "source": [
    "$\\sum_{i=1}^{n} k = kn$"
   ]
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      "n 4\n",
      "summ 5\n",
      "n 3\n",
      "summ 10\n",
      "n 2\n",
      "summ 15\n",
      "n 1\n",
      "summ 20\n",
      "All test cases passed successfully\n"
     ]
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   "source": [
    "def summation_k(k, n):\n",
    "    \"\"\"The sum of constant k, n-times. \n",
    "    \n",
    "    Arguments:\n",
    "    k: The constant to be added repeated time\n",
    "    n: The number of times to add k\n",
    "    \n",
    "    Returns:\n",
    "    sum: Sum of k repeated n times\n",
    "    \"\"\"\n",
    "\n",
    "    summ = 0\n",
    "    while n > 0:\n",
    "        print(\"n\", n)\n",
    "        summ = summ + k #n = summ#k*i\n",
    "        print(\"summ\", summ )\n",
    "        n = n - 1\n",
    "    return summ\n",
    "\n",
    "assert summation_k(5, 4) == 5*4,  \"Test case 1 failed\"\n",
    "# assert summation_k(99, 9)== 99*9, \"Test case 2 failed\"\n",
    "# assert summation_k(0, 0) == 0*0,  \"Test case 3 failed\"\n",
    "# assert summation_k(0, 99)== 0*99, \"Test case 4 failed\"\n",
    "\n",
    "print(\"All test cases passed successfully\")"
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   "source": [
    "$\\sum_{i=1}^{n} i = \\frac{n(n+1)}{2}$"
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      "All test cases passed successfully\n"
     ]
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   "source": [
    "def summation_i(n):\n",
    "    \"\"\"Given a positive integer n, returns the sum of\n",
    "    all positive integers less than or equal to n\n",
    "    \n",
    "    Arguments:\n",
    "    n: A positive integer n\n",
    "    \n",
    "    Returns:\n",
    "    sum: Sum of all positive less than or equal to n\n",
    "    \"\"\"\n",
    "    out = 0\n",
    "    i = 1\n",
    "    while i <= n:\n",
    "        out = out + i\n",
    "        i = i + 1\n",
    "    return out\n",
    "\n",
    "assert summation_i(4) == (4*(4+1))/2,  \"Test case 1 failed\"\n",
    "assert summation_i(0) == (0*(0+1))/2,  \"Test case 2 failed\"\n",
    "assert summation_i(999) == (999*(999+1))/2,  \"Test case 3 failed\"\n",
    "\n",
    "print(\"All test cases passed successfully\")"
   ]
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    "def shift_right(num, n):\n",
    "    return num // (10**n)\n",
    "\n",
    "def count_digits(num): \n",
    "    \"\"\"Given a positive integer num,\n",
    "    returns the count of digits in num\n",
    "    \n",
    "    Arguments:\n",
    "    num: A positive integer num\n",
    "    \n",
    "    Returns:\n",
    "    ndigits: Number of digits in num\n",
    "    \"\"\"\n",
    "    count = 0\n",
    "    while num > 0:\n",
    "        num = shift_right(num, 1)\n",
    "        count = count+ 1\n",
    "        \n",
    "    return count"
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   "source": [
    "count_digits(1234)"
   ]
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   "source": [
    "# 6.1.2. Infinite Loops"
   ]
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   "source": [
    "i = 0\n",
    "\n",
    "while i >= 0:\n",
    "    \n",
    "    print(i)\n",
    "    i = i + 1\n",
    "\n",
    "print(\"Outside loop\")"
   ]
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   "source": [
    "# 6.1.3. `break`"
   ]
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   "source": [
    "* For **immediately exiting** the loop i.e. Python jumps out of the loop's body (past the entire loop statement) when it encounters a `break statement`\n",
    "\n",
    "\n",
    "* Generally **used within an `if` statement** within the loop's body\n",
    "\n",
    "\n",
    "* Inside the loop's body, the **code that follows the `break` statement is never executed**"
   ]
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   "source": [
    "<img width=\"500\" src=\"https://www.askpython.com/wp-content/uploads/2019/07/break-statement-flow-diagram.png\">"
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