List length in scheme

Question

Hi I am trying to write a program where given a list of lists check to see if they are equal in size and return #t if they are.

So for example if i were to write (list-counter? '((1 2 3) (4 5 6) (7 8 9))) the program would return #t, and (list-counter? '((1 2 3) (4 5 6) (7 8))) would return #f.

SO far this is what I have done:

 (define list-counter?
  (lambda (x)
    (if (list? x)
        (if (list?(car x))
      (let (l (length (car x))))
        (if (equal? l (length(car x))))
        (list-counter?(cdr x))
 ) ) ) ) ) 

I think where I am going wrong is after I set the length of l to the length of the first list. Any help would be appreciated.

Answer 1

There are several ways to solve this problem. For instance, by hand and going step-by-step:

(define (all-lengths lists)
  (if (null? lists)
      '()
      (cons (length (car lists))
            (all-lengths (cdr lists)))))

(define (all-equal? head lengths)
  (if (null? lengths)
      true
      (and (= head (car lengths))
           (all-equal? head (cdr lengths)))))

(define (list-counter? lists)
  (let ((lengths (all-lengths lists)))
    (all-equal? (car lengths) (cdr lengths))))

Let me explain the above procedures. I'm dividing the problem in two steps, first create a new list with the lengths of each sublist - that's what all-lengths does. Then, compare the first element in a list with the rest of the elements, and see if they're all equal - that's what all-equal? does. Finally, list-counter? wraps it all together, calling both of the previous procedures with the right parameters.

Or even simpler (and shorter), by using list procedures (higher-order procedures):

(define (list-counter? lists)
  (apply = (map length lists)))

For understanding the second solution, observe that all-lengths and all-equal? represent special cases of more general procedures. When we need to create a new list with the result of applying a procedure to each of the elements of another list, we use map. And when we need to apply a procedure (= in this case) to all of the elements of a list at the same time, we use apply. And that's exactly what the second version of list-counter? is doing.