Project Euler - Problem 11

euler11

(ns euler)

(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 verticals [] (apply map vector grid))
(defn flip [grid] (map reverse grid))

(defn grid-with-indexes [grid] (apply concat (map-indexed (fn [x coll] (map-indexed (fn [y ele] [x y ele]) coll)) grid)))
(defn right-diagonal? [[x y ele]] (- x y))
(defn group-by-vals [f coll] (vals (group-by f coll)))
(defn get-cell-values [coll] (map (fn [[x y z]] z) coll))
(defn diagonals [grid] (map get-cell-values (group-by-vals right-diagonal? (grid-with-indexes grid))))

(defn all-adjecent-cells [grid] (concat grid (verticals) (diagonals grid) (diagonals (flip grid))))

(defn split-at-zeros [coll] (partition-by #(= 0 %) coll))
(defn four-element-subsets [coll] (if (< (count coll) 4) [coll] (partition 4 1 coll)))

(defn valid-combinations [] (mapcat split-at-zeros (all-adjecent-cells grid)))
(defn four-element-combinations [] (mapcat four-element-subsets (valid-combinations)))
(defn products [] (map #(apply * %) (four-element-combinations)))
(defn euler11 [] (apply max (products)))

(println (euler11))