05 User input and while loops.ipynb

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    "<h5 class='prehead'>SM286D &middot; Introduction to Applied Mathematics with Python &middot; Spring 2020 &middot; Uhan</h5>\n",
    "\n",
    "<h5 class='lesson'>Lesson 5.</h5>\n",
    "\n",
    "<h1 class='lesson_title'>User input and while loops</h1>"
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   "metadata": {},
   "source": [
    "## This lesson..."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- User input\n",
    "- `while` loops"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## User input"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Often you will want to get information from a user and incorporate that information into your program.\n",
    "\n",
    "- In Python, we can use the `input()` function to do this.\n",
    "\n",
    "- __Pro tip.__ The `input()` function <span style=\"rred\">always</span> results in the user input being converted to a <span style=\"rred\">string</span>.\n",
    "\n",
    "- Consider the following example:"
   ]
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     "text": [
      "What is your age? 27\n",
      "<class 'str'>\n"
     ]
    }
   ],
   "source": [
    "# Ask for the user's age\n",
    "age = input(\"What is your age? \")\n",
    "\n",
    "# What type of data does input() return?\n",
    "print(type(age))"
   ]
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    "- You can convert a string to an integer or a float using `int()` and `float()` respectively:"
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     "text": [
      "27\n",
      "<class 'int'>\n"
     ]
    }
   ],
   "source": [
    "# Convert age to an integer\n",
    "age_int = int(age)\n",
    "\n",
    "# Print to check the new variable\n",
    "print(age_int)\n",
    "\n",
    "# What type does the new variable have?\n",
    "print(type(age_int))"
   ]
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      "27.0\n",
      "<class 'float'>\n"
     ]
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   "source": [
    "# Covert age to a float\n",
    "age_float = float(age)\n",
    "\n",
    "# Print to check the new variable\n",
    "print(age_float)\n",
    "\n",
    "# What type does the new variable have?\n",
    "print(type(age_float))"
   ]
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   "source": [
    "__Problem.__ (PCC 5-10: Checking Usernames, modified) Do the following to create a program that simulates how websites ensure that everyone has a unique username. \n",
    "\n",
    "- Make a list of five or more usernames called `current_users`.\n",
    "- Ask the user to input their desired username.\n",
    "- Check to see if the user's desired username is taken:\n",
    "    - If taken, print a message saying that username is taken.\n",
    "    - If not taken, print a message saying that username is available.\n",
    "- Assume usernames are case-sensitive (so `Nelson` and `nelson` are not the same)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "Please enter a username: ProfessorAwesome\n",
      "I'm sorry, that username is taken.\n"
     ]
    }
   ],
   "source": [
    "# List of current users\n",
    "current_users = ['ProfessorAwesome', 'Bingham', 'RustyChipmunk', 'ShineSpike', 'IAmSam15']\n",
    "\n",
    "# Ask user to input desired username\n",
    "username = input(\"Please enter a username: \")\n",
    "\n",
    "# Check if user's desired username is taken\n",
    "if username in current_users:\n",
    "    print(\"I'm sorry, that username is taken.\")\n",
    "else:\n",
    "    print(\"Congratulations, that username is available!\")"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## While loops"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- A `while` loop runs a block of code *while* some statement is true.\n",
    "\n",
    "- A `while` loop stops <span style=\"rred\">only</span> when the statement evaluates to `False`, or when the `break` statement is used\n",
    "\n",
    "- Consider the following examples:"
   ]
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    "from IPython.display import IFrame\n",
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    "from IPython.display import IFrame\n",
    "IFrame(\"http://pythontutor.com/iframe-embed.html#code=x%20%3D%200%0Awhile%20True%3A%0A%20%20%20%20print%28x%29%0A%20%20%20%20x%20%2B%3D%201%0A%20%20%20%20%0A%20%20%20%20if%20x%20%3E%205%3A%0A%20%20%20%20%20%20%20%20break%0A%20%20%20%20&codeDivHeight=400&codeDivWidth=350&cumulative=false&curInstr=0&heapPrimitives=false&origin=opt-frontend.js&py=3&rawInputLstJSON=%5B%5D&textReferences=false\", width=800, height=400)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Infinite loops and manually stopping a program"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- `for` loops always run for a fixed number of iterations.\n",
    "\n",
    "- On the other hand, it is possible for a `while` loop to run forever!\n",
    "\n",
    "- The code cell below contains an example of an infinite loop.\n",
    "\n",
    "- To stop the code in the cell below, you will need to click on the <kbd>&#9724;</kbd> button (interrupt the kernel) or the <kbd>&#8635;</kbd> button (restart the kernel) in the toolbar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "x = 0\n",
    "while True:\n",
    "    print(x)\n",
    "    x += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Problem. (PCC 5-10: Checking Usernames, modified again)__ Do the following to create a program that simulates how websites ensure that everyone has a unique username. \n",
    "\n",
    "- Make a list of five or more usernames called `current_users`.\n",
    "- Ask the user to input their desired username.\n",
    "- Check to see if the user's desired username is taken.\n",
    "    - If taken, print a message saying that username is taken <span style=\"rred\">and ask the user again for their desired username</span>.\n",
    "    - If not taken, print a message saying that username is available.\n",
    "- Assume usernames are case-sensitive (so `Nelson` and `nelson` are not the same)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Please enter a username: ProfessorAwesome\n",
      "I'm sorry, that username is taken.\n",
      "Please enter a username: ProfessorBoring\n",
      "Congratulations, that username is available!\n"
     ]
    }
   ],
   "source": [
    "# List of current users\n",
    "current_users = ['ProfessorAwesome', 'Bingham', 'RustyChipmunk', 'ShineSpike', 'IAmSam15']\n",
    "\n",
    "# Ask user to input desired username\n",
    "while True:\n",
    "    username = input(\"Please enter a username: \")\n",
    "    \n",
    "    # Check if user's desired username is taken\n",
    "    # If it isn't, stop the while loop\n",
    "    if username in current_users:\n",
    "        print(\"I'm sorry, that username is taken.\")\n",
    "    else:\n",
    "        print(\"Congratulations, that username is available!\")\n",
    "        break"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Flags"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- A __flag__ is a variable that acts as a symbol to either stop a program or exit a loop.  \n",
    "\n",
    "- Usually a flag variable is either `True` or `False`.  \n",
    "\n",
    "- Let's use a flag and a while loop to simulate the precarious position Robin Williams found himself in during the movie *Jumanji*. In the movie, the following rule had to be observed:\n",
    "\n",
    "    > In the jungle, you must wait, until the dice read five or eight."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n",
      "4\n",
      "5\n"
     ]
    }
   ],
   "source": [
    "# Below we import the randint function from the random library\n",
    "# so that we can \"roll\" the dice in the code below\n",
    "from random import randint\n",
    "\n",
    "# Create a flag representing whether we're in the jungle\n",
    "# Initialize flag to True\n",
    "in_jungle = True\n",
    "\n",
    "while in_jungle:\n",
    "    # Simulate the roll of 2 dice\n",
    "    die1 = randint(1, 6)\n",
    "    die2 = randint(1, 6)\n",
    "    \n",
    "    # Get the total\n",
    "    dice_roll = die1 + die2\n",
    "    print(dice_roll)\n",
    "    \n",
    "    # If the total is 5 or 8, update the flag to False\n",
    "    if dice_roll == 5 or dice_roll == 8:\n",
    "        in_jungle = False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classwork &mdash; on your own!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Problem 1. (PCC 7-1: Rental Car)__ Write a program that asks the user what kind of rental car they\n",
    "would like. Print a message about that car, such as\n",
    "\n",
    "```\n",
    "Let me see if I can find you a Subaru.\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "What kind of car would you like? DeLorean\n",
      "Let me see if I can find you a DeLorean.\n"
     ]
    }
   ],
   "source": [
    "# Ask user for car type\n",
    "car = input(\"What kind of car would you like? \")\n",
    "\n",
    "# Print message with user input\n",
    "print(f\"Let me see if I can find you a {car}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Problem 2. (PCC 7-3: Multiples of Ten)__ Ask the user for a number, and then report whether the\n",
    "number is a multiple of 10 or not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Please enter a number: 792\n",
      "That is not a multiple of ten!\n"
     ]
    }
   ],
   "source": [
    "# Ask user for number\n",
    "number = input(\"Please enter a number: \")\n",
    "\n",
    "# Check if the number is a multiple of 10\n",
    "if (int(number) % 10) == 0:\n",
    "    print(\"That is a multiple of ten!\")\n",
    "else: \n",
    "    print(\"That is not a multiple of ten!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Problem 3.__  Write code that asks for 2 numbers from the user and sets the variable `total` equal to their sum. Print the value of `total`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter the first number:  42\n",
      "Enter the second number: 36\n",
      "The sum of your two numbers is 78.0.\n"
     ]
    }
   ],
   "source": [
    "# Ask the user for two numbers\n",
    "first_num = input(\"Enter the first number:  \")\n",
    "second_num = input(\"Enter the second number: \")\n",
    "\n",
    "# Convert the user input from strings to floats\n",
    "first_num = float(first_num)\n",
    "second_num = float(second_num)\n",
    " \n",
    "# Add the numbers\n",
    "total = first_num + second_num\n",
    " \n",
    "# Print the total value\n",
    "print(f\"The sum of your two numbers is {total}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Problem 4 (PCC 7-5: Movie Tickets).__ A movie theater charges different ticket prices depending on a person’s age. If a person is under the age of 3, the ticket is free; if they are between 3 and 12, the ticket is \\\\$10; and if they are over age 12, the ticket is \\\\$15. Write a loop in which you repeatedly ask users their age, and then tell them the cost of their movie ticket."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "What is your age? 78\n",
      "Your ticket costs $15\n",
      "What is your age? 32\n",
      "Your ticket costs $15\n",
      "What is your age? oops\n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "invalid literal for int() with base 10: 'oops'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-13-5de926418892>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mwhile\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# loops forever but you get an error if you enter text\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0mage\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"What is your age? \"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0;32mif\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mage\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m         \u001b[0mmessage\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"Your ticket is free!\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mage\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0;36m12\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: invalid literal for int() with base 10: 'oops'"
     ]
    }
   ],
   "source": [
    "while True: # loops forever but you get an error if you enter text\n",
    "    age = input(\"What is your age? \")\n",
    "    if int(age) < 3: \n",
    "        message = \"Your ticket is free!\"\n",
    "    elif int(age) <= 12: \n",
    "        message = \"Your ticket costs $10.\"\n",
    "    else: \n",
    "        message = \"Your ticket costs $15\"\n",
    "    print(message)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Problem 5.__ Take a quick break."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Problem 6. (PCC 7-6: Three Exits)__ Read pages 118-123 of PCC on `while` loops and make sure you understand the different ways of stopping a `while` loop.\n",
    "\n",
    "Write different versions of Problem 4 that do each of the following:\n",
    "\n",
    " - Use a conditional test in the while statement to stop the loop when the user enters `q`.\n",
    " - Use a flag to stop the loop when the user enters `q`.\n",
    " - Use a break statement to stop the loop when the user enters `q`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "What is your age? (enter q to quit) 1\n",
      "Your ticket is free!\n",
      "What is your age? (enter q to quit) 10\n",
      "Your ticket costs $10.\n",
      "What is your age? (enter q to quit) q\n",
      "See you soon!\n"
     ]
    }
   ],
   "source": [
    "# Conditional exit\n",
    "age = 0\n",
    "while age != 'q': \n",
    "    age = input(\"What is your age? (enter q to quit) \")\n",
    "    if age == 'q':\n",
    "        message = \"See you soon!\"\n",
    "    elif int(age) < 3: \n",
    "        message = \"Your ticket is free!\"\n",
    "    elif int(age) <= 12: \n",
    "        message = \"Your ticket costs $10.\"\n",
    "    else: \n",
    "        message = \"Your ticket costs $15\"\n",
    "    print(message)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "What is your age? (enter q to quit) 1\n",
      "Your ticket is free!\n",
      "What is your age? (enter q to quit) 10\n",
      "Your ticket costs $10.\n",
      "What is your age? (enter q to quit) q\n",
      "See you soon!\n"
     ]
    }
   ],
   "source": [
    "# Flag exit\n",
    "active = True\n",
    "while active: \n",
    "    age = input(\"What is your age? (enter q to quit) \")\n",
    "    if age == 'q':\n",
    "        active = False\n",
    "        message = \"See you soon!\"\n",
    "    elif int(age) < 3: \n",
    "        message = \"Your ticket is free!\"\n",
    "    elif int(age) <= 12: \n",
    "        message = \"Your ticket costs $10.\"\n",
    "    else: \n",
    "        message = \"Your ticket costs $15\"\n",
    "    print(message)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "What is your age? (enter q to quit) 1\n",
      "Your ticket is free!\n",
      "What is your age? (enter q to quit) 10\n",
      "Your ticket costs $10.\n",
      "What is your age? (enter q to quit) q\n",
      "See you soon!\n"
     ]
    }
   ],
   "source": [
    "# Break exit\n",
    "while True: \n",
    "    age = input(\"What is your age? (enter q to quit) \")\n",
    "    if age == 'q':\n",
    "        print(\"See you soon!\")\n",
    "        break\n",
    "    if int(age) < 3: \n",
    "        message = \"Your ticket is free!\"\n",
    "    elif int(age) <= 12: \n",
    "        message = \"Your ticket costs $10.\"\n",
    "    else: \n",
    "        message = \"Your ticket costs $15\"\n",
    "    print(message)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Problem 7.__ Use a while loop to approximate $\\sum_{k=1}^{\\infty} \\frac{1}{k^3}$ by summing all terms whose value is greater than  $10^{-6}.$ Print your approximation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The sum of 1/k^3 for all k >= 1 is approximately 1.2020064006596782.\n"
     ]
    }
   ],
   "source": [
    "# Initialize total value\n",
    "# Don't call the variable sum, which is a function name\n",
    "total = 0\n",
    "\n",
    "# Keep going while 1 / k^3 is greater than 10^-6\n",
    "k = 1\n",
    "while 1 / k**3 > 1e-6: \n",
    "    total += 1 / k**3\n",
    "    k += 1\n",
    "\n",
    "# Print the approximation\n",
    "print(f\"The sum of 1/k^3 for all k >= 1 is approximately {total}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Problem 8.__ Add up the squares from $1^2$ to $1000^2$ by\n",
    "\n",
    "1. creating a list of the squares $1^2$, $2^2$, ..., $1000^2$ __with a list comprehension__, and then \n",
    "2. compute their sum using the `sum` function. \n",
    "\n",
    "Print your answer. (This doesn't use material from this lesson; this is just a warm up for the next problem.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The sum of the first 1000 squares is 333833500.\n"
     ]
    }
   ],
   "source": [
    "# Create list of squares using a list comprehension\n",
    "values = [i**2 for i in range(1, 1001)]\n",
    "\n",
    "# Add the squares, print the total\n",
    "print(f\"The sum of the first 1000 squares is {sum(values)}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Problem 9.__  Use a `while` loop to add the squares from $1^2$ to $1000^2$. Print your answer. Hopefully you get the same answer as you did in Problem !"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The sum of the first 1000 squares is 333833500.\n"
     ]
    }
   ],
   "source": [
    "# Variable to hold total value\n",
    "# Don't call the variable sum, which is a function name\n",
    "total = 0 \n",
    "\n",
    "# Start with 1^2, and keep on going until we reach 1000^2\n",
    "i = 1\n",
    "while i <= 1000: \n",
    "    total += i**2\n",
    "    i += 1\n",
    "    \n",
    "# Print the total\n",
    "print(f\"The sum of the first 1000 squares is {total}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Problem 10.__  What does the following code do? Run this code. Then run it with other positive integers instead of 17. What do you think happens in general? You've just made a conjecture. Compare it with the Collatz conjecture (search on the internet for this term). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "17\n",
      "52\n",
      "26\n",
      "13\n",
      "40\n",
      "20\n",
      "10\n",
      "5\n",
      "16\n",
      "8\n",
      "4\n",
      "2\n",
      "1\n"
     ]
    }
   ],
   "source": [
    "number = 17\n",
    "print(number)\n",
    "\n",
    "while number != 1: \n",
    "    if (number % 2)==0:\n",
    "        number = int(number / 2)\n",
    "    else:\n",
    "        number = 3 * number + 1\n",
    "    print(number)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Write your notes here. Double-click to edit._\n",
    "\n",
    "The code repeatedly divides an even number by 2 and multiplies an odd number by 3 and adds 1. It does this until the number reaches 1. I predict that this process will reach 1 no matter our choice of starting number. This is called the Collatz conjecture."
   ]
  }
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