{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ca803775",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Division Operators\n",
    "#### CS 65: Introduction to Computer Science I"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "889205e3",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Floating-point division operator\n",
    "\n",
    "The `/` operator will always give you a _float_ as a result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e1b0808b",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16.0"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "320 / 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "444b97cc",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16.791666666666668"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "403.0 / 24.0"
   ]
  },
  {
   "attachments": {
    "longdivisionexample.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "6758a163",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Integer division operators\n",
    "\n",
    "Sometimes, instead of getting the full floating-point expansion, you might want the quotient and remainder separately. \n",
    "\n",
    "<center>\n",
    "<div>\n",
    "<img src=\"attachment:longdivisionexample.png\" width=\"200\"/>\n",
    "</div>\n",
    "</center>\n",
    "\n",
    "\n",
    "\n",
    "The `//` is the _floor_ division operator - it gives you the quotient and _ignores_ and fractional/remainder part.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ba5c7b58",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "320 // 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bf2c89c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "403 // 24"
   ]
  },
  {
   "attachments": {
    "longdivisionexample.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "8b3120bc",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Modulo operator\n",
    "\n",
    "The `%` operator is the __modulo__ operator - another word for remainder - it will ignore the quotient and just give you the remainder.\n",
    "\n",
    "<center>\n",
    "<div>\n",
    "<img src=\"attachment:longdivisionexample.png\" width=\"200\"/>\n",
    "</div>\n",
    "</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "90ca74b7",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "403 // 24"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "06e46976",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "403 % 24"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0fde33e",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Group Exercises\n",
    "\n",
    "Try each of the following in your interactive shell. What pattern do you notice?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f6d4c71b",
   "metadata": {},
   "outputs": [],
   "source": [
    "0 // 2\n",
    "1 // 2\n",
    "3 // 2\n",
    "4 // 2\n",
    "5 // 2\n",
    "6 // 2\n",
    "20 // 5\n",
    "21 // 5\n",
    "22 // 5\n",
    "23 // 5\n",
    "24 // 5\n",
    "25 // 5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e9807b0",
   "metadata": {},
   "source": [
    "Try each of the following in your interactive shell. What pattern do you notice?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "00a3ce35",
   "metadata": {},
   "outputs": [],
   "source": [
    "0 % 2\n",
    "1 % 2\n",
    "3 % 2\n",
    "4 % 2\n",
    "5 % 2\n",
    "6 % 2\n",
    "20 % 5\n",
    "21 % 5\n",
    "22 % 5\n",
    "23 % 5\n",
    "24 % 5\n",
    "25 % 5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d46f278",
   "metadata": {},
   "source": [
    "Write down in your notes:\n",
    "* What is the difference between `//` and `/`?\n",
    "* What is the difference between `//` and `%`?\n",
    "\n",
    "Try each of the following in your interactive shell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "47b997cd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.0\n"
     ]
    },
    {
     "ename": "ZeroDivisionError",
     "evalue": "division by zero",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mZeroDivisionError\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-9-5c56365b62c3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m23\u001b[0m \u001b[0;34m//\u001b[0m \u001b[0;36m5.50\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0;36m23\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mZeroDivisionError\u001b[0m: division by zero"
     ]
    }
   ],
   "source": [
    "print(23 // 5.50)\n",
    "23 / 0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d841a73",
   "metadata": {},
   "source": [
    "Write down in your notes:\n",
    "* What happens when you use a float with the floor division operator?\n",
    "* What happens in Python if you try to divide by 0?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2247adf6",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## When is this useful?\n",
    "\n",
    "Example: Let's say I'm programming a super computer with 64 processors to perform 1500 variations of a simulation for a physics experiment, and each of the simulations takes about the same amount of time to run. How many simulations should be given to each processor?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c772ebb0",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Each processor should get 23 simulations\n",
      "and 28 processors will each get one extra\n"
     ]
    }
   ],
   "source": [
    "num_processors = 64\n",
    "num_simulations = 1500\n",
    "simulations_per_processor = num_simulations // num_processors\n",
    "leftover_simulations = num_simulations % num_processors\n",
    "print(\"Each processor should get\",simulations_per_processor,\"simulations\")\n",
    "print(\"and\",leftover_simulations,\"processors will each get one extra\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0a71c3d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Modulo is also good if you need to check if a number is even or odd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0ce296dc",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "253 % 2 #odd numbers have a remainder of 1 when divided by 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "92ce5911",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "254 % 2 #even numbers have a remainder of 0 when divided by 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcbd282c",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Or, if you want to check if a number is divisible by 4 - say you're checking to see if the year is a presidential election year, Olympic year, leap year, etc., you can see if the result is 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a428acee",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2024 % 4"
   ]
  }
 ],
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