How to use map with a list of lists

Question

I am needed to use map on a list of lists in Scheme (Racket).

What I want specifically is something like (map-lists add1 '((3 1) (2 8))) => '((4 2) (3 9)).

I know how to solve this recursively, like so:

(define map-lists 
  (lambda (f A)
    (if (null? A)
    '()
    (if (pair? (car A))
        (cons (map f (car A)) (map-lists f (cdr A)))
        (if (null? (car A))
           (cons (car A) (map-lists f (cdr A)))
           (cons (f (car A)) (map-lists f (cdr A))))))))

But am needing to solve this without recursion! I know (map add1 '(3 1)) will give '(4 2) which is part of the solution, but this doesn't work for a list of lists.

Please help.

Answer 1

You are reimplementing one map and use another inside it.

You can just use two maps for the two levels of the nested lists. Consider this:

(map 1+ (list 2 3)) ==> (3 4)

(lambda (x) (map 1+ (list 2 3))) #f ==> (3 4)

(lambda (x) (map 1+ x)) (list 2 3) ==> (3 4)

(lambda (x) (map 1+ x)) (list 7 8) ==> (8 9)

(map (lambda (x) (1+ x)) (list 2 3)) ==> (3 4)

(map (lambda (x) (map 1+ x)) (list (list 2 3) (list 7 8))) ==> ....

Hopefully you can complete the rest.