011.clj

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

(use '(incanter core))

(def *test-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
   ])

; get an element from array at (x,y) using the number of columns
(defn get_element [array x y ncol]
  (get array (+ (* x ncol) y)))

; function to work out the direction to move in
; fnx and fny are how we change the x, y coordinates
; span is the number of numbers to consider (note recursive decreasing)
(defn select_dir [array x y ncol span fnx fny]
  (when (not (zero? span))
    (cons
      (get_element array x y ncol)
      (select_dir array (fnx x) (fny y) ncol (dec span) fnx fny))))

; horizontal line
(defn horiz [array ncol span]
  (for [x (range ncol) y (range (inc (- ncol span)))]
    (select_dir array x y ncol span identity inc)))

(defn vert [array ncol span]
  (for [x (range (inc (- ncol span))) y (range ncol)]
    (select_dir array x y ncol span inc identity)))

(defn diag_down [array ncol span]
  (for [x (range (inc (- ncol span))) y (range (inc (- ncol span)))]
    (select_dir array x y ncol span inc inc)))

(defn diag_up [array ncol span]
  (for [x (range (dec span) ncol) y (range (inc (- ncol span)))]
    (select_dir array x y ncol span dec inc)))

; join all quads together
(defn get_quads [array ncol span]
  (concat (horiz array ncol span) (vert array ncol span) (diag_down array ncol span) (diag_up array ncol span)))

(defn euler011 []
  (apply max (map #(reduce * %1) (get_quads *test-grid* 20 4))) )