106 lines
4.0 KiB
Factor
106 lines
4.0 KiB
Factor
! Copyright (c) 2007 Aaron Schaefer.
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel namespaces project-euler.common sequences
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splitting grouping ;
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IN: project-euler.011
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! http://projecteuler.net/index.php?section=problems&id=11
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! DESCRIPTION
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! -----------
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! In the 20x20 grid below, four numbers along a diagonal line have been marked
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! in red.
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! 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
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! 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
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! 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
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! 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
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! 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
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! 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
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! 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
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! 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
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! 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
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! 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
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! 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
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! 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
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! 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
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! 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
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! 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
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! 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
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! 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
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! 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
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! 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
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! 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
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! The product of these numbers is 26 * 63 * 78 * 14 = 1788696.
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! What is the greatest product of four numbers in any direction (up, down,
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! left, right, or diagonally) in the 20x20 grid?
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! SOLUTION
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! --------
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<PRIVATE
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: horizontal ( -- matrix )
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{
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08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
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49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
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81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
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52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
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22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
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24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
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32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
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67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
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24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
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21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
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78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
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16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
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86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
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19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
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04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
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88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
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04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
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20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
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20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
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01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
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} 20 group ;
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: vertical ( -- matrix )
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horizontal flip ;
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: pad-front ( matrix -- matrix )
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[
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length [ 0 <repetition> ] map
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] keep [ append ] 2map ;
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: pad-back ( matrix -- matrix )
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<reversed> [
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length [ 0 <repetition> ] map
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] keep [ <reversed> append ] 2map ;
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: diagonal/ ( -- matrix )
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horizontal reverse pad-front pad-back flip ;
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: diagonal\ ( -- matrix )
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horizontal pad-front pad-back flip ;
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: max-product ( matrix width -- n )
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[ collect-consecutive ] curry map concat
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[ product ] map supremum ; inline
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PRIVATE>
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: euler011 ( -- answer )
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[
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{ [ horizontal ] [ vertical ] [ diagonal/ ] [ diagonal\ ] }
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[ call 4 max-product , ] each
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] { } make supremum ;
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! [ euler011 ] 100 ave-time
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! 4 ms run / 0 ms GC ave time - 100 trials
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MAIN: euler011
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