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p11.scm
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;; Project Euler
;;
;; http://projecteuler.net/index.php?section=problems&id=11
;;
;; Problem 11
;; 22 February 2002
;;
;; In the 20×20 grid below, four numbers along a diagonal line have been marked
;; in red (can't see it here).
;;
;; 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
;; 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
;; 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
;; 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
;; 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
;; 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
;; 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
;; 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
;; 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
;; 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
;; 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
;; 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
;; 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
;; 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
;; 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
;; 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
;; 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
;; 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
;; 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
;; 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
;;
;; The product of these numbers is 26 × 63 × 78 × 14 = 1788696.
;;
;; What is the greatest product of four numbers in any direction (up, down,
;; left, right, or diagonally) in the 20×20 grid?
;;
;; Answer: 70600674
;; Dimensions of the data.
(define Nrows 20)
(define Ncols 20)
;; Global data (vector).
(define data '#(
08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
))
;; Cells accessor
(define (N x y) (vector-ref data (+ x (* Ncols y))))
;; Get product of four cells starting from cell (x,y) and moving to direction
;; specified by dx and dy.
(define (by-four x y dx dy)
(if (or (not (<= 0 (+ x (* dx 4)) (1- Ncols)))
(not (<= 0 (+ y (* dy 4)) (1- Nrows))))
0
(fold (lambda (i res)
(* res (N (+ x (* dx i))
(+ y (* dy i)))))
1
'(0 1 2 3))))
;; Problem 11.
(define (p11)
(fold (lambda (x res)
(max res
(fold (lambda (y res)
(max res
(apply max
(map (lambda (dx dy) (by-four x y dx dy))
'(1 0 1 1) ;; list of dx
'(0 1 1 -1))))) ;; list of dy
0
(iota Nrows))))
0
(iota Ncols)))
;; end of file
;; vim: ts=4 sw=4 et