ipython_nbs/efficiency/maximum-pairwise-product.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sebastian Raschka \n",
      "last updated: 2016-05-31 \n",
      "\n",
      "CPython 3.5.1\n",
      "IPython 4.2.0\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -a 'Sebastian Raschka' -u -d -v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Finding the Maximum Pairwise Product"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our task is to simply fine the largest product between 2 different numbers in an array. For example, given the array\n",
    "\n",
    "a = [7, 1, 2, 8, 1, 3],\n",
    "\n",
    "the maximum product between a pair of numbers would be 7*8 = 56.\n",
    "For simplicity, we will only consider arrays consisting of positive numbers; however, the same concepts applies to negative valued arrays. Also, to keep the code simple, we assume that the array consists of at least 2 numbers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let us create 2 arrays, a small and a large one that we will use for testing later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import random\n",
    "\n",
    "random.seed(1)\n",
    "\n",
    "a = [7, 1, 2, 8, 1, 3]\n",
    "rnd_lst = random.sample(range(0, 10000000), 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The probably simplest implementation may be to compute the product of each pair in this list while keeping track of the largest product as we traverse through the list.\n",
    "Here, we need to use two-nested for-loops. The outer for-loop traverses through the list indexes {*i ,..., n*}, and the inner loop traverses through the list indeces {*i+1, ..., n*}. Thus, we have an algorithm with quadratic complexity, $O(n^2)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "56\n",
      "99739554693120\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "\n",
    "def max_pairprod_1(ary):\n",
    "    n = len(ary)\n",
    "    max_prod = -sys.float_info.max\n",
    "    \n",
    "    for i in range(0, n):\n",
    "        for j in range(i + 1, n):\n",
    "            prod = ary[i] * ary[j]\n",
    "            if prod > max_prod:\n",
    "                max_prod = prod\n",
    "                \n",
    "    return max_prod\n",
    "\n",
    "print(max_pairprod_1(ary=a))\n",
    "print(max_pairprod_1(ary=rnd_lst))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's think about improving this solution in terms of computational efficiency. One solution would be to sort the list so that we just need to return the first (or last) 2 numbers and compute their product. This would be a substantial improvement over our previous solution, since efficient sorting algorithms have a time complexity of $O(n\\;log(n))$. However, we can do better ...\n",
    "\n",
    "If our array consists of positive numbers only, we just need to traverse through the array once and keep track of the 2 largest numbers in the array. (If the array contains negative values as well, we also want to track the 2 most negative numbers, since their product will be positive number as well.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "56\n",
      "99739554693120\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "\n",
    "def max_pairprod_2(ary):\n",
    "    pos_1 = -sys.float_info.max\n",
    "    pos_2 = -sys.float_info.max\n",
    "    \n",
    "    for i in range(0, len(ary)):\n",
    "        if ary[i] > pos_1:\n",
    "            tmp = pos_1\n",
    "            pos_1 = ary[i]\n",
    "            if tmp > pos_2:\n",
    "                pos_2 = tmp\n",
    "        elif ary[i] > pos_2:\n",
    "            pos_2 = ary[i]\n",
    "\n",
    "    return pos_1 * pos_2\n",
    "\n",
    "print(max_pairprod_2(ary=a))\n",
    "print(max_pairprod_2(ary=rnd_lst))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although our second implementation contains more if-else statements, which may come with some additional overhead, we now find the maximum pairwise product in linear time, $O(n)$, which is a big improvement over our previous $O(n^2)$ algorithm. Let's do a quick benchmark using the `%timeit` magic:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 loops, best of 3: 98.2 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit -n 1000 -r 3 max_pairprod_1(ary=rnd_lst)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 loops, best of 3: 199 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit -n 1000 -r 3 max_pairprod_2(ary=rnd_lst) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, to get a better sence of the **order of the function**, big O, let us repeat the benchmark for different array sizes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import timeit\n",
    "\n",
    "funcs = ['max_pairprod_1', 'max_pairprod_2']\n",
    "orders_n = [10**n for n in range(1, 5)]\n",
    "times_n = {f:[] for f in funcs}\n",
    "\n",
    "for n in orders_n:\n",
    "    rnd_lst = random.sample(range(0, 10**6), n)\n",
    "    for f in funcs:\n",
    "        times_n[f].append(min(timeit.Timer('%s(rnd_lst)' % f, \n",
    "                'from __main__ import %s, rnd_lst' % f)\n",
    "                    .repeat(repeat=3, number=5)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def plot_timing():\n",
    "\n",
    "    labels = [('max_pairprod_1', 'max_pairprod_1'), \n",
    "              ('max_pairprod_2', 'max_pairprod_2')]\n",
    "\n",
    "    plt.rcParams.update({'font.size': 12})\n",
    "\n",
    "    fig = plt.figure(figsize=(10, 8))\n",
    "    for lb in labels:\n",
    "        plt.plot(orders_n, times_n[lb[0]], \n",
    "             alpha=0.5, label=lb[1], marker='o', lw=3)\n",
    "    plt.xlabel('sample size n')\n",
    "    plt.ylabel('time per computation in milliseconds [ms]')\n",
    "    plt.legend(loc=2)\n",
    "    plt.ylim([-1, 60])\n",
    "    plt.grid()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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J3ZQ/91Lu3K0u5C8/37njw4IFnmKuXj245Ra4/XZ3FnOB5FNBZ4yZaYy5uvj5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\njh1+OMyeDUOHRheXiIhI0qmHTnLOOXjtNX8Lr/b2cHzyZH/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c700748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_timing()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}