#lang racket


; If X = (x_0 x_1 ... x_n) and Y = (y_0 y_1 ... y_m) then
;       (fmap2lcm fn X Y)
; is the list (r_0 r_1 ... r_l) where where the element r_i
; in position i is (fn x_(i mod n) y_(i mod m))
; and l = lcm(m, n) where lcm - least common multiple.
;
; In other words the map is performed by reusing the lists X and Y until
; they both end at the same time.

; Example: (fmap2lcm list '(1 2) '(3 4 5)) is 
; ((1 3) (2 4) (1 5) (2 3) (1 4) (2 5))

; This is a very ugly implementation
; We have a seriously nested set of if-statments, and are dragging the
; original input lists through the recursion.

(define fmap2lcm-r
  (lambda (fn X-cur Y-cur X-orig Y-orig)
    (if (and (null? X-cur) (null? Y-cur))
        '()
        (if (null? X-cur)
            (fmap2lcm-r fn X-orig Y-cur X-orig Y-orig)
            (if (null? Y-cur)
                (fmap2lcm-r fn X-cur Y-orig X-orig Y-orig)
                (cons (fn (first X-cur) (first Y-cur))
                      (fmap2lcm-r fn (rest X-cur) (rest Y-cur) X-orig Y-orig)
                )
            )))))

(define fmap2lcm
  (lambda (fn X Y)
    ; handle special boundary case of empty input lists
    (if (or (null? X) (null? Y)) '() (fmap2lcm-r fn X Y X Y)))