1. Miki Tebeka
  2. euler

Source

euler / clojure / 11.clj

; In the 20×20 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 20×20 grid?

(def grid [
  [ 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 item [row col]
  (nth (nth grid row) col))

(defn horizontal []
  (for [row (range 20)
        col (range 16)]
    [[row col] [row (+ col 1)] [row (+ col 2)] [row (+ col 3)]]))

(defn vertical []
  (for [col (range 20)
        row (range 16)]
    [[row col] [(+ row 1) col] [(+ row 2) col] [(+ row 3) col]]))

(defn diagonal1 []
  (for [row (range 16)
        col (range 16)]
    [[row col] [(+ row 1) (+ col 1)] 
     [(+ row 2) (+ col 2)] [(+ row 3) (+ col 3)]]))

(defn diagonal2 []
  (for [row (range 16)
        col (range 3 20)]
    [[row col] [(+ row 1) (- col 1)] 
     [(+ row 2) (- col 2)] [(+ row 3) (- col 3)]]))

(defn product [v]
  (apply * (map (fn [xy] (apply item xy)) v)))

(let [vectors (concat (horizontal) (vertical) (diagonal1) (diagonal2))]
  (prn (apply max (map product vectors))))