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euler11.clj
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euler11.clj
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; What is the greatest product of four adjacent numbers in the same
; direction (up down left right 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 diagonals
"for an h*w matrix of the form [& rows], returns all downward diagonals that start on the top row and are h long."
[colls]
(apply map vector
(map-indexed (fn [i coll] (drop i coll)) colls)))
(def runs
(lazy-cat (mapcat #(partition 4 1 %)
grid) ;horizontals
(mapcat #(partition 4 1 %)
(apply map vector grid)) ; verticals
(mapcat diagonals
(partition 4 1 grid)) ;diagonals going down
(mapcat diagonals
(partition 4 1 (reverse grid))))) ; diags going up
(defn products [input]
(map #(apply * %) ;; made this "apply" to make the time comparison
;; more fair!
(partition 4 1 (keep identity input))))
(def adjacents
(lazy-cat grid
(for [i (range 20)]
(lazy-cat
(for [x (range 20)] (get (get grid x) i))
(for [x (range 20)] (get (get grid x) (+ x i)))
(for [x (range 20)] (get (get grid x) (- x i)))
(for [x (range 20)] (get (get grid (- 19 x)) (+ x i)))
(for [x (range 20)] (get (get grid (- 19 x)) (- x i)))))))
(time
(reduce max (map #(apply * %) runs)))
(time
(reduce max (flatten (map products adjacents))))
(time (concat grid
(for [i (range 20)]
(concat
(for [x (range 20)] (get (get grid x) i))
(for [x (range 20)] (get (get grid x) (+ x i)))
(for [x (range 20)] (get (get grid x) (- x i)))
(for [x (range 20)] (get (get grid (- 19 x)) (+ x i)))
(for [x (range 20)] (get (get grid (- 19 x)) (- x i)))))))
(time (concat (mapcat #(partition 4 1 %)
grid) ;horizontals
(mapcat #(partition 4 1 %)
(apply map vector grid)) ; verticals
(mapcat diagonals
(partition 4 1 grid)) ;diagonals going down
(mapcat diagonals
(partition 4 1 (reverse grid)))))