Project Euler Problem 11

Problem011.clj

;;; In the 20x20 grid below, four numbers along a diagonal line have been marked in red.
;;; 
;;; 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 adjacent numbers
;;; in any direction (up, down, left, right, or diagonally)  in the 20x20 grid?

(def grid-20x20
  '(( 8  2 22 97 38 15  0 40  0 75  4  5  7 78 52 12 50 77 91  8)
    (49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48  4 56 62  0)
    (81 49 31 73 55 79 14 29 93 71 40 67 53 88 30  3 49 13 36 65)
    (52 70 95 23  4 60 11 42 69 24 68 56  1 32 56 71 37  2 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  3 45  2 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  2 62 12 20 95 63 94 39 63  8 40 91 66 49 94 21)
    (24 55 58  5 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72)
    (21 36 23  9 75  0 76 44 20 45 35 14  0 61 33 97 34 31 33 95)
    (78 17 53 28 22 75 31 67 15 94  3 80  4 62 16 14  9 53 56 92)
    (16 39  5 42 96 35 31 47 55 58 88 24  0 17 54 24 36 29 85 57)
    (86 56  0 48 35 71 89  7  5 44 44 37 44 60 21 58 51 54 17 58)
    (19 80 81 68  5 94 47 69 28 73 92 13 86 52 17 77  4 89 55 40)
    ( 4 52  8 83 97 35 99 16  7 97 57 32 16 26 26 79 33 27 98 66)
    (88 36 68 87 57 62 20 72  3 46 33 67 46 55 12 32 63 93 53 69)
    ( 4 42 16 73 38 25 39 11 24 94 72 18  8 46 29 32 40 62 76 36)
    (20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74  4 36 16)
    (20 73 35 29 78 31 90  1 74 31 49 71 48 86 81 16 23 57  5 54)
    ( 1 70 54 71 83 51 54 69 16 92 33 48 61 43 52  1 89 19 67 48)))

(defn get-value [x y]
  (if (or (< x 0) (>= x 20) (< y 0) (>= y 20)) 1
      (nth (nth grid-20x20 y) x)))

;;; horizontal
(defn get-four-values-h [x y] (map #(get-value (+ x %) y) (range 0 4)))
;;; vertical
(defn get-four-values-v [x y] (map #(get-value x (+ y %)) (range 0 4)))
;;; diagonally
(defn get-four-values-d1 [x y] (map #(get-value (+ x %) (+ y %)) (range 0 4)))
(defn get-four-values-d2 [x y] (map #(get-value (+ x %) (+ y (- %))) (range 0 4)))

;;; (get-four-values-h 0 0)
;;; => (8 2 22 97)
;;; (get-four-values-h 16 19)
;;; => (89 19 67 48)
;;; (get-four-values-v 0 0)
;;; => (8 49 81 52)
;;; (get-four-values-v 19 16)
;;; => (36 16 54 48)
;;; (get-four-values-d 0 0)
;;; => (8 49 31 23)

;;; horizontal
(defn products-of-horizontal []
  (for [x (range 0 19) y (range 0 19)]
    (apply * (get-four-values-h x y))))
;;; vertical
(defn products-of-vertical []
  (for [x (range 0 19) y (range 0 19)]
    (apply * (get-four-values-v x y))))
;;; diagonally
(defn products-of-diagonally-1 []
  (for [x (range 0 19) y (range 0 19)]
    (apply * (get-four-values-d1 x y))))
(defn products-of-diagonally-2 []
  (for [x (range 0 19) y (range 0 19)]
    (apply * (get-four-values-d2 x y))))

(max
 (apply max (products-of-horizontal))
 (apply max (products-of-vertical))
 (apply max (products-of-diagonally-1))
 (apply max (products-of-diagonally-2)))
;;;=> result