Transpose a matrix in racket (list of lists

Question

I got a list of lists in racket and have to transpose them.

(: transpose ((list-of(list-of %a)) -> (list-of (list-of %a))))

(check-expect (transpose (list (list 1 2 3)
                               (list 4 5 6)))
              (list (list 1 4)
                    (list 2 5)
                    (list 3 6)))

(define transpose
  (lambda (xs)
    (cond
      ((empty? xs)empty)
      ((pair? xs)(make-pair  (make-pair (first(first xs))  (make-pair (first(first(rest xs)))empty)) (transpose (rest(rest xs))))))))

That's my code at the moment. I think the problem is in the recursive call (correct me if I'm wrong please).

The actual outcome is (list (list 1 4)). The rest seems kinda ignored.

It would really help me, if somebody knows the problem, or has a tip.

Answer 1

The simplest definition of transpose is:

(define (transpose xss)
  (apply map list xss))

Why does it work?

  (apply map list '((a b) (d e))
= (apply map List '((a b) (d e))    ; use List rather than list
= (map List '(a b) '(d e))
= (list (List 'a 'd) (List 'b e))
= '((a d) (b e))

Here List is spelled with capital letters only to show which list was given by the user and which was produced by map.

Here is a less "clever" solution. It uses that the first column of a matrix becomes the first row in the transposed matrix.

(define transpose
  (lambda (xss)
    (cond
      [(empty? xss)         empty]
      [(empty? (first xss)) empty]
      [else                 (define first-column   (map first xss))
                            (define other-columns  (map rest  xss))
                            (cons first-column
                                  (transpose other-columns))])))

Answer 2

for/list can be used sequentially to create a list of lists with transposed items:

(define (transpose_ lol)                    ; lol is list of lists
  (for/list ((i (length (list-ref lol 0)))) ; loop for length of first inner list
    (for/list ((il lol))                    ; for each inner list (il)
      (list-ref il i))))                    ; get its item

Testing:

(transpose_ (list (list 1 2 3)
                  (list 4 5 6)))

Output:

'((1 4) (2 5) (3 6))