pe011.lisp

(in-package :experimental)

(defparameter num-numbers* 4
  "The number of adjacent numbers needed for the problem.")

(defparameter grid*
"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"
  "A string representing the grid.")

(def parse-line (line)
  "Parses a line of the grid and returns a list of the numbers in
   that row."
  (map #'parse-integer (tokens line)))

(def parse-grid ()
  "Parses the entire grid and returns a list of every row. Each row
   is a list of the numbers in the row."
  (map #'parse-line (tokens grid* #\newline)))

(def transpose (grid)
  "Takes a list of lists and transposes it."
  (apply #'map #'list grid))

(def top-left-to-bottom-right-diags (grid)
  "Given a grid, returns all of the possible diagonals that go from 
   the top left to the bottom right."
  (accum a
    (up r-start (dec num-numbers*) (len grid)
      (up c-start (dec num-numbers* dec) (len+car grid)
        (a (accum b
             (up diff 0 num-numbers*
               (b (nth (- c-start diff)
                       (nth (- r-start diff) grid))))))))))

(def bottom-left-to-top-right-diags (grid)
  "Given a grid, returns all of the possible diagonals that go from
   the bottom left to the top right."
  (accum a
    (up r-start (dec num-numbers*) (len grid)
      (up c-start 0 (- (len+car grid) num-numbers* -1)
        (a (accum b
             (up diff 0 num-numbers*
               (b (nth (+ c-start diff)
                       (nth (- r-start diff) grid))))))))))

(def group-by-n (n xs)
  "Groups every N adjacent elements in XS."
  (let next (firstn n xs)
    (if (len< next n)
        '()
        (cons next (group-by-n n (cdr xs))))))

(def horizontals (grid)
  "Returns all of the possible horizontal adjacent numbers."
  (mappend [group-by-n num-numbers* _] grid))

(def verticals (grid)
  "Returns all of the possible vertical adjacent numbers."
  (horizontals (transpose grid)))

(def solve ()
  "Solves PE problem 11."
  (ado (parse-grid)
       (append (horizontals it)
               (verticals it)
               (bottom-left-to-top-right-diags it)
               (top-left-to-bottom-right-diags it))
       (map [reduce #'* _] it)
       (best #'> it)))