Racket Function for Changing 2 and 1 Euro with 10 Cents and 20 Cents

Question

Can somebody explain me a code in Racket in which I change 2 Euro and a 1 Euro Coin with 10 Cents and 20 Cents?

I can only change one time a 2 Euro coin and one time a 1 Euro coin. With 20 Cents and 10 Cents. Here is my code:

(define (change sum coins) 
  (if (< sum 200) 
    0 
    (if (= sum 200) 
      1 
      (if (and (> sum 0) 
               (<= (length coins) 0)) 
        0 
        (+ (change (- sum (car coins)) (cdr coins)) 
           (change sum (cdr coins))))))) 

(change 200'(20 10)) 
(change 100'(20 10)) 

So what I have to modify? Thanks for your help!

Answer 1

Since the 200 target is hardcoded, you should start with the current sum of 0, and count up, not down:

(define (change sum coins) 
  (if (> sum 200)             ; invalid solution
    0 
    (if (= sum 200)              ; good solution
      1 
      (if (= (length coins) 0)     ; no more coins to use
        0 
        (+ (change (+ sum (car coins))  ; use first coin,
                   coins)               ; _increasing_ the sum
           (change sum 
                   (cdr coins)))))))      ; don't use first coin any more

Now we have

> (change 0 '(10))
1
> (change 0 '(20 10))
11
> (change 0 '(7))
0
> 

Now you can abstract away the target value of 200, making it a parameter in a new function which will have to make this function its inner definition so it has access to its parameter:

(define (coin-change-ways target coins)
  (define (change sum coins) 
     ....
     ....)
  (change 0 coins))

See this for more explanations.