1 ! Copyright (c) 2007 Aaron Schaefer.
2 ! See http://factorcode.org/license.txt for BSD license.
3 USING: kernel namespaces make project-euler.common sequences
7 ! http://projecteuler.net/index.php?section=problems&id=11
12 ! In the 20x20 grid below, four numbers along a diagonal line have been marked
15 ! 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
16 ! 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
17 ! 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
18 ! 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
19 ! 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
20 ! 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
21 ! 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
22 ! 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
23 ! 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
24 ! 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
25 ! 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
26 ! 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
27 ! 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
28 ! 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
29 ! 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
30 ! 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
31 ! 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
32 ! 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
33 ! 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
34 ! 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
36 ! The product of these numbers is 26 * 63 * 78 * 14 = 1788696.
38 ! What is the greatest product of four numbers in any direction (up, down,
39 ! left, right, or diagonally) in the 20x20 grid?
47 : horizontal ( -- matrix )
49 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
50 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
51 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
53 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
54 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
55 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
56 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
57 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
58 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
59 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
60 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
61 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
62 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
63 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
64 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
65 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
66 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
67 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
68 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
71 : vertical ( -- matrix )
74 : pad-front ( matrix -- matrix )
76 length [ 0 <repetition> ] map
77 ] keep [ append ] 2map ;
79 : pad-back ( matrix -- matrix )
81 length [ 0 <repetition> ] map
82 ] keep [ <reversed> append ] 2map ;
84 : diagonal/ ( -- matrix )
85 horizontal reverse pad-front pad-back flip ;
87 : diagonal\ ( -- matrix )
88 horizontal pad-front pad-back flip ;
90 : max-product ( matrix width -- n )
91 [ collect-consecutive ] curry map concat
92 [ product ] map supremum ; inline
96 : euler011 ( -- answer )
98 { [ horizontal ] [ vertical ] [ diagonal/ ] [ diagonal\ ] }
99 [ call 4 max-product , ] each
100 ] { } make supremum ;
102 ! [ euler011 ] 100 ave-time
103 ! 4 ms run / 0 ms GC ave time - 100 trials