euler-011 Largest product in a grid.ipynb

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   "cells": [
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     "cell_type": "markdown",
     "source": [
      "In the 20\u00d720 grid below, four numbers along a diagonal line have been marked in red.\n",
      "\n",
      "08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08\n",
      "49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00\n",
      "81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65\n",
      "52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 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 03 45 02 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 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21\n",
      "24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72\n",
      "21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95\n",
      "78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92\n",
      "16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57\n",
      "86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58\n",
      "19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40\n",
      "04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66\n",
      "88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69\n",
      "04 42 16 73 38 25 39 11 24 94 72 18 08 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 04 36 16\n",
      "20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54\n",
      "01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48\n",
      "\n",
      "The product of these numbers is 26 \u00d7 63 \u00d7 78 \u00d7 14 = 1788696.\n",
      "\n",
      "What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20\u00d720 grid?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = [[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",
      "\n",
      "nil"
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def right(row, col)\n",
      "  [[row, col], [row, col + 1], [row, col + 2], [row, col + 3]]\n",
      "end\n",
      "\n",
      "def down(row, col)\n",
      "  [[row, col], [row + 1, col], [row + 2 , col], [row + 3, col]]\n",
      "end\n",
      "\n",
      "def digonal(row, col)\n",
      "  [[row, col], [row + 1, col + 1], [row + 2 , col + 2 ], [row + 3, col +3]]\n",
      "end\n",
      "\n",
      "def rdigonal(row, col)\n",
      "  result = [[row, col], [row + 1, col - 1], [row + 2 , col - 2 ], [row + 3, col -3]]\n",
      "  result.map do |index|\n",
      "    index[1] = index[1] >= 0 ? index[1] : nil\n",
      "  end\n",
      "  return result\n",
      "end\n",
      "\n",
      "right(1, 1)"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "[[1, 1], [1, 2], [1, 3], [1, 4]]"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def product(data, row, col)\n",
      "  return yield(row, col).map{|index|data[index[0]][index[1]]}.inject(1, &:*)\n",
      "  return 0\n",
      "rescue\n",
      "  return 0\n",
      "end\n",
      "\n",
      "puts product(data, 0, 0){ |row, col| right(row, col) }\n",
      "puts product(data, 0, 0){ |row, col| down(row, col) }\n",
      "puts product(data, 0, 0){ |row, col| digonal(row, col) }"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "34144\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1651104\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "279496\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "max = 0\n",
      "\n",
      "data.each_with_index do |_x, x|\n",
      "  _x.each_with_index do |_y, y|\n",
      "    products = [product(data, x, y){ |row, col| right(row, col) },\n",
      "    product(data, x, y){ |row, col| down(row, col) },\n",
      "    product(data, x, y){ |row, col| digonal(row, col) },\n",
      "    product(data, x, y){ |row, col| rdigonal(row, col) }]\n",
      "    max = products.max if products.max > max\n",
      "  end\n",
      "end\n",
      "\n",
      "max"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "70600674"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "outputs": []
    }
   ]
  }
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