euler11.clj

; Problem 11
;
; What is the greatest product of four adjacent numbers in any direction (up,
; down, left, right, or diagonally) in the 2020 grid?

(def grid20 [[ 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 02 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 grid-get [grid x y] ; get value at x,y from grid
     (-> (nth grid y) (nth x)))

(defn get-string [grid xstart ystart xstep ystep length] ; get string of values from grid
  (loop [x xstart y ystart sofar []]
    (cond (= length (count sofar))
	  sofar
	  :else
	  (recur (+ x xstep) (+ y ystep) (conj sofar (grid-get grid x y))))))

; horizontal strings
(def horiz-string (for [x (range 17) y (range 20)]
		    (get-string grid20 x y 1 0 4)))

; vertical strings
(def vertical-string (for [x (range 20) y (range 17)]
		       (get-string grid20 x y 0 1 4)))

; diagonal-down
(def diag-down-string (for [x (range 17) y (range 17)]
		       (get-string grid20 x y 1 1 4)))

; diagonal-up
(def diag-up-string (for [x (range 0 17) y (range 3 20)]
		       (get-string grid20 x y 1 -1 4)))

(def answer
     (last (sort
	    (map #(reduce * %)
		 (concat horiz-string
			 vertical-string
			 diag-down-string
			 diag-up-string)))))