euler-011-largest-product-in-a-grid-20130725.ipynb

{
 "metadata": {
  "name": "euler-011-largest-product-in-a-grid-20130725"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from euler import product"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = array([\n",
      "    [ 8,  2, 22, 97, 38, 15,  0, 40,  0, 75,  4,  5,  7, 78, 52, 12, 50, 77, 91,  8],\n",
      "    [49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48,  4, 56, 62,  0],\n",
      "    [81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30,  3, 49, 13, 36, 65],\n",
      "    [52, 70, 95, 23,  4, 60, 11, 42, 69, 24, 68, 56,  1, 32, 56, 71, 37,  2, 36, 91],\n",
      "    [22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80],\n",
      "    [24, 47, 32, 60, 99,  3, 45,  2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50],\n",
      "    [32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70],\n",
      "    [67, 26, 20, 68,  2, 62, 12, 20, 95, 63, 94, 39, 63,  8, 40, 91, 66, 49, 94, 21],\n",
      "    [24, 55, 58,  5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72],\n",
      "    [21, 36, 23,  9, 75,  0, 76, 44, 20, 45, 35, 14,  0, 61, 33, 97, 34, 31, 33, 95],\n",
      "    [78, 17, 53, 28, 22, 75, 31, 67, 15, 94,  3, 80,  4, 62, 16, 14,  9, 53, 56, 92],\n",
      "    [16, 39,  5, 42, 96, 35, 31, 47, 55, 58, 88, 24,  0, 17, 54, 24, 36, 29, 85, 57],\n",
      "    [86, 56,  0, 48, 35, 71, 89,  7,  5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58],\n",
      "    [19, 80, 81, 68,  5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77,  4, 89, 55, 40],\n",
      "    [ 4, 52,  8, 83, 97, 35, 99, 16,  7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66],\n",
      "    [88, 36, 68, 87, 57, 62, 20, 72,  3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69],\n",
      "    [ 4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18,  8, 46, 29, 32, 40, 62, 76, 36],\n",
      "    [20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74,  4, 36, 16],\n",
      "    [20, 73, 35, 29, 78, 31, 90,  1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57,  5, 54],\n",
      "    [ 1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52,  1, 89, 19, 67, 48],\n",
      "])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 4"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[2, 3]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "73"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[(2, 3)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "73"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[2, 3:3+n]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "array([73, 55, 79, 14])"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[2:2+n, 3]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "array([73, 23, 71, 60])"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit product(range(1, 100))\n",
      "product(range(1, 100))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "10000 loops, best of 3: 28.1 us per loop\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000L"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import operator\n",
      "\n",
      "def product(x):\n",
      "    return reduce(operator.mul, x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit product(range(1, 100))\n",
      "product(range(1, 100))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "10000 loops, best of 3: 27.8 us per loop\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000L"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "product(a[2:2+n, 3])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "7152540"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "(20, 20)"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "[i + 2 * n for i in a.shape]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "[28, 28]"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "aa = zeros([i + 2 * n for i in a.shape], dtype=int)\n",
      "aa[n:n+a.shape[0], n:n+a.shape[1]] = a\n",
      "print aa[4, 4]\n",
      "print aa[(4, 4)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "8\n",
        "8\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def make_directions():\n",
      "    directions = set([])\n",
      "    for dir in [(x, y) for x in (1, 0, -1) for y in (1, 0, -1)]:\n",
      "        if dir == (0, 0):\n",
      "            continue\n",
      "        if (-dir[0], -dir[1]) not in directions:\n",
      "            directions.add(dir)\n",
      "    return directions"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "make_directions()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "set([(0, 1), (1, 0), (1, -1), (1, 1)])"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def foo(n):\n",
      "    max_product = 0\n",
      "    if True:\n",
      "        for p in ((x, y) for x in xrange(n, n+a.shape[0]) for y in xrange(n, n+a.shape[1])):\n",
      "           max_product  = max(\n",
      "                max_product, \n",
      "                product(aa[p[0], p[1]:p[1]+n]), \n",
      "                product(aa[p[0]:p[0]+n, p[1]]))\n",
      "    return max_product"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit foo(n)\n",
      "foo(n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100 loops, best of 3: 7.31 ms per loop\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "51267216"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def foo(n):\n",
      "    max_product = 0\n",
      "    for dir in make_directions():\n",
      "        dir = array(dir)\n",
      "        for p in ((x, y) for x in xrange(n, n+a.shape[0]) for y in xrange(n, n+a.shape[1])):\n",
      "            q = product([aa[tuple(p + i * dir)] for i in range(n)])\n",
      "            # print p, q\n",
      "            if q > max_product:\n",
      "                max_product = q\n",
      "    return max_product"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit foo(n)\n",
      "foo(n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 loops, best of 3: 209 ms per loop\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "70600674"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def foo(n):\n",
      "    max_product = 0\n",
      "    for dir in make_directions():\n",
      "        dir = array(dir)\n",
      "        for p in ((x, y) for x in xrange(n, n+a.shape[0]) for y in xrange(n, n+a.shape[1])):\n",
      "            max_product = max(max_product,\n",
      "                product([aa[tuple(p + i * dir)] for i in range(n)]))\n",
      "    return max_product"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit foo(n)\n",
      "foo(n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 loops, best of 3: 209 ms per loop\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "70600674"
       ]
      }
     ],
     "prompt_number": 23
    }
   ],
   "metadata": {}
  }
 ]
}