08-py-timing-arraylists.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "fd9555e3",
   "metadata": {},
   "source": [
    "# Timing and Plotting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21ddd51b",
   "metadata": {},
   "source": [
    "## 1. Timing"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9d6d2c6",
   "metadata": {},
   "source": [
    "The [`time`](https://docs.python.org/3/library/time.html#module-time) module contains functions for obtaining and interpreting the current system time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "459c985a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Seconds since epoch = 1657274841.554562\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "my_time = time.time()\n",
    "print(\"Seconds since epoch =\", my_time)\n",
    "#time.time() // (365 * 24 * 60 * 60) # years since epoch"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71a5d7ee",
   "metadata": {},
   "source": [
    "Several functions in the time module such as <code>gmtime()</code>, <code>asctime()</code> etc. either take <code>time.struct_time</code> object as an argument or return it."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3b76ee6",
   "metadata": {},
   "source": [
    "The <code>time()</code> function returns the number of seconds passed since epoch. For Unix system, <code>January 1, 1970, 00:00:00</code> at UTC is epoch (the point where time begins). Monday is 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "5ab42f5f",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "time.struct_time(tm_year=2022, tm_mon=7, tm_mday=7, tm_hour=13, tm_min=4, tm_sec=58, tm_wday=3, tm_yday=188, tm_isdst=0)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "time.localtime(time.time())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc875b84",
   "metadata": {},
   "source": [
    "The <code>time.ctime()</code> function takes seconds passed since epoch as an argument and returns a string representing local time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "d1d467e1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Local time: Fri Jul  8 13:07:47 2022\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "\n",
    "# seconds passed since epoch\n",
    "my_time = time.time()\n",
    "local_time = time.ctime(my_time)\n",
    "print(\"Local time:\", local_time)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96c9c692",
   "metadata": {},
   "source": [
    "The <code>sleep()</code> function suspends (delays) execution of the current thread for the given number of seconds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "d2cf070d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Print this!\n",
      "Then print this after 2 seconds\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "\n",
    "print(\"Print this!\")\n",
    "\n",
    "time.sleep(2)\n",
    "\n",
    "print(\"Then print this after 2 seconds\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36492487",
   "metadata": {},
   "source": [
    "### Building a timing utility"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eafbec13",
   "metadata": {},
   "source": [
    "Generally, we can build a utility function for timing the execution of a passed-in function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "be47b938",
   "metadata": {},
   "outputs": [],
   "source": [
    "def timeit(fn):\n",
    "    starttime = time.time()\n",
    "    \n",
    "    fn()\n",
    "    \n",
    "    endtime = time.time()\n",
    "    \n",
    "    return endtime - starttime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "7a8cc9e2",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum Sub Array Sum = 23\n",
      "Time used to execute the code: 0.00036978721618652344 seconds\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "\n",
    "starttime = time.time()\n",
    "\n",
    "#####\n",
    "    \n",
    "def fn1():\n",
    "    lst = [14, 8, -23, 4, 6, 10, -18, 5, 5, 11]\n",
    "    maxSum = lst[0]\n",
    "    sumz = 0\n",
    "    for i in range(0, len(lst)):\n",
    "        sumz += lst[i]\n",
    "        if sumz < 0:\n",
    "            sumz = 0\n",
    "        elif (maxSum < sumz):\n",
    "            maxSum = sumz\n",
    "    return maxSum\n",
    "\n",
    "print(\"Maximum Sub Array Sum =\", fn1())\n",
    "\n",
    "####\n",
    "\n",
    "endtime = time.time()\n",
    "    \n",
    "used_time = endtime - starttime\n",
    "\n",
    "print('Time used to execute the code:',used_time, 'seconds' )\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "466ac8a2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum Sub Array Sum = 23\n",
      "Time used to execute the code: 0.0005450248718261719 seconds\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "starttime = time.time()\n",
    "\n",
    "#####\n",
    "    \n",
    "def fn2():\n",
    "    lst = [14, 8, -23, 4, 6, 10, -18, 5, 5, 11]\n",
    "    maxSum = lst[0]\n",
    "    for i in range(0, len(lst)):\n",
    "        sumz = 0\n",
    "        for j in range(i, len(lst)):\n",
    "            sumz += lst[j]\n",
    "            if sumz > maxSum:\n",
    "                maxSum = sumz\n",
    "    return maxSum\n",
    "\n",
    "print(\"Maximum Sub Array Sum =\", fn2())\n",
    "\n",
    "####\n",
    "\n",
    "endtime = time.time()\n",
    "    \n",
    "used_time = endtime - starttime\n",
    "\n",
    "print('Time used to execute the code:',used_time, 'seconds' )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4583bdbd",
   "metadata": {},
   "source": [
    "### The `timeit` module\n",
    "\n",
    "The [`timeit`](https://docs.python.org/3/library/timeit.html) module is a built-in library for measuring the execution of code passed in as a string."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "abca1a29",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sum = 49995000\n"
     ]
    }
   ],
   "source": [
    "total = 0\n",
    "for number in range(1, 10000):\n",
    "    total += number\n",
    "print(\"Sum =\", total)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "d8e815e1",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "49995000"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(range(10_000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "a84cf8ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "49995000"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(range(1, 10000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "b6203819",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1572331859933911"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import timeit\n",
    "timeit.timeit('sum(range(10_000))', number=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e93265d",
   "metadata": {},
   "source": [
    "It also supports passing in \"setup\" code that is not timed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "c46ad4bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.15215791700029513"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "timeit.timeit('sum(r)', \n",
    "              setup='r = range(10_000)', \n",
    "              number=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09f92423",
   "metadata": {},
   "source": [
    "We can easily use this to gather timings for multiple input values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "b42a1463",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.015224082999338862,\n",
       " 0.029374090998317115,\n",
       " 0.04232334699918283,\n",
       " 0.05501350700069452,\n",
       " 0.0679143740053405,\n",
       " 0.08323154200479621,\n",
       " 0.10028718900139211,\n",
       " 0.11414188300113892,\n",
       " 0.14012010699661914,\n",
       " 0.14760735400341218]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[timeit.timeit('sum(r)',\n",
    "               setup=f'r = range({n})',\n",
    "               number=1000)\n",
    " for n in range(1000, 11_000, 1000)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50ea6d0d",
   "metadata": {},
   "source": [
    "Sometimes we might want to make use of functions defined in our notebook in the timed/setup code passed to `timeit`. We need to use the `globals` argument for this:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff43e4ef",
   "metadata": {},
   "source": [
    "### Fibonacci sequence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "0248d3ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181\n",
    "\n",
    "def fib(n):\n",
    "    if n == 0:\n",
    "        return 0\n",
    "    elif n == 1:\n",
    "        return 1\n",
    "    else:\n",
    "        return fib(n-1) + fib(n-2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "498dd6fb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181]"
     ]
    }
   ],
   "source": [
    "# for 20 terms of the Fibonacci sequence\n",
    "print([fib(n) for n in range(20)], end=\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "de3d0b48",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.00011875000200234354,\n",
       " 0.0002775149987428449,\n",
       " 0.0006013579986756667,\n",
       " 0.0010402400002931245,\n",
       " 0.002107328000420239,\n",
       " 0.0033637919987086207,\n",
       " 0.005822557999636047,\n",
       " 0.008553992003726307,\n",
       " 0.011955415000556968,\n",
       " 0.01947221500449814,\n",
       " 0.02961901000526268,\n",
       " 0.04811121999955503,\n",
       " 0.0794843750045402,\n",
       " 0.12637863399868365]"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# \"globals()\" returns a dictionary of everything defined in this module; timeit needs it to access `fib`\n",
    "\n",
    "[timeit.timeit(f'fib({n})',\n",
    "               number=1000,\n",
    "               globals=globals()) \n",
    " for n in range(1, 15)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab6aff05",
   "metadata": {},
   "source": [
    "### Magic timing commands\n",
    "\n",
    "There are also \"magic\" notebook commands that can be used to time code -- they are `%time`, `%timeit`, and `%%timeit`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "39d3f8ae",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 137 µs, sys: 0 ns, total: 137 µs\n",
      "Wall time: 139 µs\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "49995000"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time sum(range(10_000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "d8aa5fcd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "145 µs ± 4.13 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit -n 1000 sum(range(10_000))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76d8a502",
   "metadata": {},
   "source": [
    "## 2. Plottings\n",
    "\n",
    "The [matplotlib library](https://matplotlib.org) supports the creation of all sorts of visualizations. We will use it for drawing simple 2-dimensional plots.\n",
    "\n",
    "The primary plotting function we will use is `matplotlib.pyplot.plot` ([full documentation here](https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot)), which, when passed two \"array-like\" objects of equal length, will interpret and plot their contents as x and y axis coordinates. We will generally use tuples, lists, and ranges as array-like objects. Note that generators are *not* considered array-like by matplotlib.\n",
    "\n",
    "Some examples (note that we use a semicolon after the call to `plot` to hide its return value):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "b4783189",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "cf1f70bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([1, 2, 3, 4, 5], [50, 20, 30, 10, 40]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffb82a72",
   "metadata": {},
   "source": [
    "We can also provide an optional format string to `plot`, which controls marker, line-style, and color for the plot.\n",
    "\n",
    "Here's a shortened list of options copied from the [full documentation of `plot`](https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot):\n",
    "\n",
    "**Markers**\n",
    "\n",
    "  - `.` : point marker\n",
    "  - `o` : circle marker\n",
    "  - `s` : square marker\n",
    "  - `d` : diamond marker\n",
    "\n",
    "**Line-styles**\n",
    " \n",
    "  - `-` : solid line style\n",
    "  - `--` : dashed line style\n",
    "  - `:` : dotted line style\n",
    "\n",
    "**Colors**\n",
    "\n",
    "  - `k` : black\n",
    "  - `r` : red\n",
    "  - `g` : blue\n",
    "  - `b` : green\n",
    "  - `y` : yellow\n",
    "  - `c` : cyan\n",
    "  \n",
    "Here are the above plots with some color and styling (if we omit a line style no connecting line is drawn between data points):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "d787967f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([1, 2, 3, 4, 5], [50, 20, 30, 10, 40], 'o--r');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "7b886ec5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = range(11)\n",
    "ys = [x*2 for x in xs]\n",
    "plt.plot(xs, ys, 'dg');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5ec80f9",
   "metadata": {},
   "source": [
    "## 3. Array Lists"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e412958e",
   "metadata": {},
   "source": [
    "### NumPy Package\n",
    "\n",
    "Instead of regular `range` objects, which only allow for integral start/stop/step values, we typically prefer to use the [numpy library](https://numpy.org)'s `arange` and `linspace` functions with matplotlib. `arange` is like `range`, except we can use floating point values for start/stop/step. `linspace` lets us specify start and stop values (both inclusive), and the number of values to return in that interval.\n",
    "\n",
    "Examples of `arange` and `linspace` calls (note that both functions return numpy arrays, which are iterable and can be passed to `plot`):\n",
    "\n",
    "We also use NumPy which is a general-purpose array-processing package. It provides a high-performance multidimensional array object, and tools for working with these arrays. It is the fundamental package for scientific computing with Python. It is open-source software. It contains various features including these important ones:\n",
    "\n",
    "- A powerful N-dimensional array object\n",
    "- Sophisticated (broadcasting) functions\n",
    "- Tools for integrating C/C++ and Fortran code\n",
    "- Useful linear algebra, Fourier transform, and random number capabilities\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "fa6ad0a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.5, 0.6, 0.7, 0.8, 0.9, 1. , 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7,\n",
       "       1.8, 1.9, 2. , 2.1, 2.2, 2.3, 2.4])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "np.arange(0.5, 2.5, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "777bb6af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10.  , 10.25, 10.5 , 10.75, 11.  , 11.25, 11.5 , 11.75, 12.  ,\n",
       "       12.25, 12.5 , 12.75, 13.  , 13.25, 13.5 , 13.75, 14.  , 14.25,\n",
       "       14.5 , 14.75, 15.  , 15.25, 15.5 , 15.75, 16.  , 16.25, 16.5 ,\n",
       "       16.75, 17.  , 17.25, 17.5 , 17.75, 18.  , 18.25, 18.5 , 18.75,\n",
       "       19.  , 19.25, 19.5 , 19.75, 20.  ])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# from 10 to 20 inclusive get 41 values\n",
    "\n",
    "np.linspace(10, 20, 41)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "80039146",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([     1,   2041,   4082,   6123,   8164,  10204,  12245,  14286,\n",
       "        16327,  18368,  20408,  22449,  24490,  26531,  28572,  30612,\n",
       "        32653,  34694,  36735,  38776,  40816,  42857,  44898,  46939,\n",
       "        48980,  51020,  53061,  55102,  57143,  59184,  61224,  63265,\n",
       "        65306,  67347,  69388,  71428,  73469,  75510,  77551,  79592,\n",
       "        81632,  83673,  85714,  87755,  89796,  91836,  93877,  95918,\n",
       "        97959, 100000])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(1, 100000, 50, dtype=int) # we can specify the data type to coerce values into integers"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c74f8fa",
   "metadata": {},
   "source": [
    "`plot` can be called multiple times in the same cell to draw multiple lines in the same chart. Below we use this facility together with `linspace` and a handful of list comprehensions to plot some common runtime complexity bounding functions (more on that soon) over a small interval: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "60bb54a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "count = 100\n",
    "xs = np.linspace(0.1, 4, count)\n",
    "ys_const        = [1] * count\n",
    "ys_log          = [math.log(x) for x in xs]\n",
    "ys_linear       = [x for x in xs]\n",
    "ys_linearithmic = [x * math.log(x) for x in xs]\n",
    "ys_quadratic    = [x**2 for x in xs]\n",
    "ys_exponential  = [2**x for x in xs]\n",
    "\n",
    "plt.plot(xs, ys_const, 'c')\n",
    "plt.plot(xs, ys_log, 'r')\n",
    "plt.plot(xs, ys_linear, 'b')\n",
    "plt.plot(xs, ys_linearithmic, 'g')\n",
    "plt.plot(xs, ys_quadratic, 'y');\n",
    "plt.plot(xs, ys_exponential, 'm');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46870f84",
   "metadata": {},
   "source": [
    "### Plotting timings"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9445ad4",
   "metadata": {},
   "source": [
    "Plotting timing data collected from functions may help give us a sense of how their runtimes scale with increasing input sizes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "aaf3bb9b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# runtimes for sum for increasing sizes of input\n",
    "\n",
    "import timeit\n",
    "\n",
    "ns = np.linspace(10, 10_000, 50, dtype=int)\n",
    "ts = [timeit.timeit(f'sum(range({n}))', number=100)\n",
    "      for n in ns]\n",
    "\n",
    "plt.plot(ns, ts, 'or');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea81ec10",
   "metadata": {},
   "source": [
    "Clearly, the runtime of `sum` is directly proportional to the number of values it operates on. \n",
    "\n",
    "If we assume a linear relationship, we can compute the average slope between adjacent data points to come up with an line of approximate fit that may help us predict the runtime of `sum`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "f2113d83",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.338174756126575e-06"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total = 0\n",
    "\n",
    "for i in range(len(ns)-1):\n",
    "    total += (ts[i+1] - ts[i]) / (ns[i+1] - ns[i]) # recall: slope = rise / run\n",
    "    \n",
    "avg_slope = total / (len(ns)-1)\n",
    "\n",
    "avg_slope"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2081b58d",
   "metadata": {},
   "source": [
    "We can also use the statistics module to help us compute the mean:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "4c6bbb0e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3381747561265745e-06"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statistics\n",
    "avg_slope = statistics.mean((ts[i+1] - ts[i]) / (ns[i+1] - ns[i]) for i in range(len(ns)-1))\n",
    "avg_slope"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b711ddc",
   "metadata": {},
   "source": [
    "## Exercise 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aa1cb7cb",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
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   "language": "python",
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   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.4"
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 },
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