Project Euler Problem 11 Common Lisp

Project Euler Problem 11

(defparameter *data*
  '((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)))

(defun multiply-first-4 (lst)
  (if (> 4 (length lst))
      0
      (reduce #'* (subseq lst 0 4))))

(defun all-multiples (lst)
  (maplist #'multiply-first-4 lst))

(defun all-horizontals (lst)
  (mapcan #'all-multiples lst))

(defun all-verticals (lst)
  (all-horizontals (apply #'mapcar #'list lst)))

(defun %all-left-diagonals (lst &optional (n 0))
  (if (< n 4)
      (cons (nthcdr n (car lst))
            (%all-left-diagonals (cdr lst) (1+ n)))
      nil))

(defun all-left-diagonals (lst)
  (mapcon #'(lambda (x) (all-verticals (%all-left-diagonals x)))
          lst))

(defun all-right-diagonals (lst)
  (all-left-diagonals (reverse lst)))

(defun problem11 ()
  (reduce #'max (append (all-horizontals *data*)
                        (all-verticals *data*)
                        (all-left-diagonals *data*)
                        (all-right-diagonals *data*))))


Function multiply-first-4 returns the multiplication of the first 4 elements of a list, or it returns 0 if the list has less than 4 elements--otherwise the function will error out.  Better to just simply return 0 then the code complexity for handling a list with less than 4 elements.

Function all-multiples takes a list of say (1 2 3 4 5 6 7) turning it into ((1 2 3 4 5 6 7) (2 3 4 5 67) (3 4 5 6 7) (4 5 6 7) (5 6 7) (6 7) (7)).  It then takes that and applies multiply-first-4 to each of the lists within, resulting in (24 120 360 840 0 0 0).

Function all-horizontals applies all-multiples to a list of list, like *data* above, returning a flat list of all multiplications of 4 elements from left to right (and right to left simultaneously).

Function all-verticals takes a list of list and transposes it.  For example ((1 2 3) (4 5 6) ( 7 8 9)) becomes ((1 4 7) (2 5 8) (3 6 9)).  all-verticals applies that transposed list to all-horizontals.  The result is a flat list of all multiplications of 4 elements going up and down.  Transposing the list is a trick taken from Stackoverflow.

Function all-left-diagonals uses %all-left-diagonals to turn a list like ((1 2 3) (4 5 6) (7 8 9)) into ((1 2 3) (5 6) (9)) and applies it to all-verticals.  The result is a flat list of all multiplications of 4 elements going diagonal, from upper left to lower right.

Function all-right-diagonals reverses a list of lists, ((1 2 3) (4 5 6) (7 8 9)) becoming ((7 8 9) (4 5 6) (1 2 3)), and applies it to all-left-diagonals.  Thus resulting in a flat list of all multiplications of 4 elements going diagonal, from lower left to upper right.

Function problem11 takes all of these flat lists, appends them, and then finds the maximum.