ch1-challenge-counting-change.scm

; challenge for section 1.2.2 - counting change

(define (count-change amount)
  (cc amount 5))

(define (cc amount kinds-of-coins)
  (cond ((= amount 0) 1)
        ((or (< amount 0) (= kinds-of-coins 0)) 0)
        (else (+ (cc amount
                     (- kinds-of-coins 1))
                 (cc (- amount
                        (first-denomination kinds-of-coins))
                     kinds-of-coins)))))

(define (first-denomination kinds-of-coins)
  (cond ((= kinds-of-coins 1) 1)
        ((= kinds-of-coins 2) 5)
        ((= kinds-of-coins 3) 10)
        ((= kinds-of-coins 4) 25)
        ((= kinds-of-coins 5) 50)))

; Challenge - design a better algorithm for computing the result.
; The above is a tree-recursive process.
; Can a tail recursive process be used instead?
; It would be good to test the results from the two as well.
; Maybe memoization would help even the recursive function improve.