Algorithms Toolbox - Week 2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import timeit\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### BigO Notation\n",
    "\n",
    "When working with algorithms, it's typical to measure their \"time\" as, not a function of how long it takes an algorithm to run according to a wall clock, but rather as a function of the size of the input of the algorithm. This is called the **rate of growth** of of the running time.\n",
    "\n",
    "When utilizing BigO notation we can distill the \"most important\" parts and cast out the less important parts. We can see this by looking at the `ex_run_time` function we've defined below. This imaginary algorithm runtime, $6n^{2}+100n+300$, takes as many machine instruction to execute. Again, this is an example.\n",
    "\n",
    "In the example below, we've defined two functions that calculate this imaginary runtime according to a user defined input size. We're going to use this illustration to show that the upper bound on this execution time for this algorithm is defined by the $n^2$ portion of the imaginary runtime of $6n_2 + 100n + 300$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def ex_run_time(coef, n):\n",
    "    rt = []\n",
    "    for i in range(n):\n",
    "         rt.append((i, (coef*(i**2))))\n",
    "    return rt\n",
    "\n",
    "def decomp_run_time(coef_a, coef_b, n):\n",
    "    rt = []\n",
    "    for i in range(n):\n",
    "        rt.append((i, ((coef_a*i) + coef_b)))\n",
    "    return rt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ex_rt = ex_run_time(6, 100)\n",
    "decomp_rt = decomp_run_time(100, 300, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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MsNA6xkngU8AntRcjIiI5y+9Hf6fNrDbEJsQC0LdaX4Y9MczmqsRVakNITaAv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\nIiIiIiIiIiIiIiIiMg38HxDFI9LZBBk7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f500c9ae490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "line1_plt = plt.plot(ex_rt, label='Line 1', linewidth=2)\n",
    "line2_plt = plt.plot(decomp_rt, 'b', label='Line 2', linewidth=2)\n",
    "plt.legend(['100n + 300','6n^2'], loc=2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the graph above, we can see that the runtime of the $6n^2$ portion of the runtime dominates the total runtime of the algorithm, overall. Using this assumption, when working with BigO notation, we can drop the $100n+300$ portion of the runtime complexity, as we're working against the squared element of the overall runtime. Looking at the graph, we also see that the runtime complexity for the $n^2$ term of our algorithm intersects the line for the other terms, as well. But the safe assumption here is that this algorithm's complexity will be overall dominated by the squared term, in any reasonable size input.\n",
    "\n",
    "We can even scale the coefficients of the imaginary complexity to prove that this intersection won't shift much and we'll still be bounded by the squared term."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "scaled_ex_rt = ex_run_time(0.6, 2500)\n",
    "scaled_decomp_rt = decomp_run_time(1000, 3000, 2500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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yyUhWa26CMCMmocA3mFGQCpgExSEJMyrSzN6Oxjw6co35G9gCNLW3m2Ieea13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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f500decd8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_scaled_line1_plt = plt.plot(scaled_ex_rt, label='Line 1', linewidth=2)\n",
    "_scaled_line2_plt = plt.plot(scaled_decomp_rt, 'b', label='Line 2', linewidth=2)\n",
    "plt.legend(['1000n + 3000','0.6n^2'], loc=2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Checking out the graph above, we see that the size of the input was able to be scaled pretty considerably. But we can also see that around the input size of 1650, we still end up losing our to the squared term in the runtime of out algorithm. Using this logic, for general purposes, for any reasonable input we can use define the runtime complexity of this algorithm as $n^2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Generator methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def generate_seq(start, stop, size):\n",
    "    '''\n",
    "    Generate a sequence of integers useful in testing the functions below\n",
    "    '''\n",
    "    \n",
    "    return np.random.random_integers(low=start, high=stop, size=size)\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Programming Assignments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def calc_fib(n):\n",
    "    '''\n",
    "    Task : Given n, find the last digit of the nth Fibonacci number F_n\n",
    "    \n",
    "    Input : Single integer n\n",
    "    \n",
    "    Constraints : 0 \\ge n \\ge 10**7\n",
    "    \n",
    "    Output : Last digit of F_n\n",
    "    \n",
    "    '''\n",
    "    int_a = 0\n",
    "    int_b = 1\n",
    "    \n",
    "    if n <= 1:\n",
    "        return n\n",
    "    \n",
    "    elif n >= 0 and n <= 45:\n",
    "        fib_int = calc_fib(n-1) + calc_fib(n-2)\n",
    "        return fib_int\n",
    "    \n",
    "    else:\n",
    "        print(\"%s is out of range. Please try an integer between 0 and 45.\" % n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 10 ms, sys: 0 ns, total: 10 ms\n",
      "Wall time: 1.52 ms\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/dist-packages/ipykernel/__main__.py:6: DeprecationWarning: This function is deprecated. Please call randint(1, 2000 + 1) instead\n"
     ]
    }
   ],
   "source": [
    "%%time \n",
    "for i in generate_seq(1,2000,1):\n",
    "    calc_fib(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def get_fibonacci_last_digit(n):\n",
    "    '''\n",
    "    Task : Given n, find the last digit of the nth Fibonacci number F_n\n",
    "    \n",
    "    Input : Single integer n\n",
    "    \n",
    "    Constraints : 0 \\ge n \\ge 10**7\n",
    "    \n",
    "    Output : Last digit of F_n\n",
    "    \n",
    "    '''\n",
    "    fib_array = np.zeros(shape=n, dtype=int)\n",
    "    fib_array[0] = int(0)\n",
    "    fib_array[1] = int(1)\n",
    "    \n",
    "    if n >= 0 and n <= 10**7:\n",
    "        counter = 2\n",
    "        for i in fib_array[2:n]:\n",
    "            fib_array[counter] = ((fib_array[counter-1] % 10) + (fib_array[counter-2] % 10))\n",
    "            counter += 1\n",
    "        return (fib_array[counter-1] % 10) + (fib_array[counter-2] % 10)\n",
    "    else:\n",
    "        print(\"%s is out of range. Please try an integer between 0 and 10,000,000.\" % n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
      "Wall time: 18.8 µs\n",
      "2\n",
      "9\n",
      "5\n"
     ]
    }
   ],
   "source": [
    "%time\n",
    "print(get_fibonacci_last_digit(3))\n",
    "print(get_fibonacci_last_digit(331))\n",
    "print(get_fibonacci_last_digit(327305))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Greatest common divisor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def euclidean_gcd(a,b):\n",
    "    if b == 0:\n",
    "        return a\n",
    "    a_prime = a % b\n",
    "    return(euclidean_gcd(b,a_prime))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "17657\n",
      "CPU times: user 10 ms, sys: 0 ns, total: 10 ms\n",
      "Wall time: 981 µs\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "print(euclidean_gcd(18,35))\n",
    "print(euclidean_gcd(28851538, 1183019))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Least common multiple"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def lcm(a, b):\n",
    "    if a >= 1 and a <= (2*(10**9)) and b >= 1 and b <= (2*(10**9)):\n",
    "        return (a*b) // euclidean_gcd(a,b)\n",
    "    else:\n",
    "        print(\"something is wrong\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
      "Wall time: 15 µs\n",
      "24\n",
      "1933053046\n"
     ]
    }
   ],
   "source": [
    "%time\n",
    "print(lcm(6,8))\n",
    "print(lcm(28851538, 1183019))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_fibonacci_huge_naive(n, m):\n",
    "    if n <= 1:\n",
    "        return n\n",
    "\n",
    "    previous = 0\n",
    "    current  = 1\n",
    "\n",
    "    for _ in range(n - 1):\n",
    "        previous, current = current, previous + current\n",
    "\n",
    "    return current % m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%time\n",
    "get_fibonacci_huge_naive(2816213588,30524)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
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