Counting Change in Scheme using a list of denominations

Question

I am writing a function to count the number of ways to make change in scheme given a list of denominations and an amount. My code is as follows, but it does not work as intended. Should I be using cons instead of the + operator? Should the third line down's base case be the empty list?

(define (change k l)
 (cond ((= k 0) 1)
     ((or (< k 0) (null? l)) 0)
     (else (+ (change k (cdr l))
              (change (- k (car l))
                      (cdr l)))))) 

Test:

(change 11 (list 1 5 10 25))

Answer 1

If the returned value is just a number then forget about cons and '() for building the output, and only use car, cdr, null? for processing the input. Other than that, be aware that there's a small mistake in the last line of your code, here's the fixed version:

(define (change k l)
  (cond ((= k 0) 1)
        ((or (< k 0) (null? l)) 0)
        (else
         (+ (change k (cdr l))
            (change (- k (car l)) l))))) ; don't do (cdr l) here

Now it works as expected:

(change 11 (list 1 5 10 25))
=> 4