gistfile1.scm

;; integer, integer -> (Listof integer)
;; 
;; Produces the starting indeces of all the diagonals of a board with the provided dimensions.
(define (list-starter-indeces width height)
  (list-starter-indeces-helper 0 0 width height))

;; integer, integer, integer, integer -> (Listof integer)
;;
;; Produces the starting indeces of all the diagonals of a board with the provided dimensions, starting at the provided index.
(define (list-starter-indeces-helper x y width height)
  (cond [(and (= x (sub1 width))
              (= y (sub1 height))) ; in the lower right corner
         (list (list x y))] 
        [(= y (sub1 height)) ; along the bottom
         (cons (list x y)
               (list-starter-indeces-helper (add1 x)
                                            y
                                            width
                                            height))]
        [(= x 0) ; along the left side
         (cons (list x y)
               (list-starter-indeces-helper x
                                            (add1 y)
                                            width
                                            height))]))

(check-expect (list-starter-indeces 1 1)
              '((0 0)))
(check-expect (list-starter-indeces 3 3)
              '((0 0)
                (0 1)
                (0 2)
                (1 2)
                (2 2)))