11.ss

#lang scheme

(require srfi/25
         "coordinates.ss")

(define *grid*
  (array (shape 0 20 0 20)
         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
         ))

;; returns a list of 4 lists; each has coordinates
(define (below-and-right x y)
  (define (something x-factor y-factor)
    (filter
     (lambda (coords)
       (match coords
         [(list x y)
          (and
           (<= (array-start *grid* 0) x (sub1 (array-end *grid* 0)))
           (<= (array-start *grid* 1) y (sub1 (array-end *grid* 1))))]))
     (map (lambda (i)
           (list (+ (* x-factor i)
                    x)
                 (+ (* y-factor i)
                    y)))
         (build-list 4 values))))
  (define east      (something 1 0))
  (define southeast (something 1 1))
  (define south     (something 0 1))
  (define southwest (something -1 1))
  (filter (lambda (seq)
            (= 4 (length seq)))
          (list east southeast south southwest)))

(define *quadruplets*
  (for/fold ([accum '()])
    ([(a b) (in-array-coordinates *grid*)])
    (let ([bar (below-and-right a b)])
      (if (null? bar)
          accum
          (append
           accum
           (map
            (lambda (line-of-four)
              (map
               (lambda (x-and-y) (apply array-ref *grid* x-and-y))
               line-of-four))
            bar))))))

(for/fold ([max-product 0]
           [winner #f])
  ([quad (in-list *quadruplets*)])
  (let ((prod (apply * quad)))
    (if (< max-product prod)
        (values prod quad)
        (values max-product winner))))