;; 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)))

;; EXERCISE 2.19
;; The order of the coin values doesn't matter because we recurse
;; over all coins.
(define us-coins (list 50 25 10 5 1))

(define uk-coins (list 100 50 20 10 5 2 1 0.5))

;: (cc 100 us-coins)

(define (cc amount coin-values)
  (cond ((= amount 0) 1)
        ((or (< amount 0) (no-more? coin-values)) 0)
        (else
         (+ (cc amount
                (except-first-denomination coin-values))
            (cc (- amount
                   (first-denomination coin-values))
                coin-values)))))

(define (first-denomination coins) (car coins))

(define (except-first-denomination coins) (cdr coins))

(define (no-more? coins) (null? coins))