2.19.rkt

#lang sicp
;; Exercise 2.19:
;; Consider the change-counting program of 1.2.2.
;; It would be nice to be able to easily change the currency used by the program,
;; so that we could compute the number of ways to change a British pound, for example.
;; As the program is written, t
;; he knowledge of the currency is distributed partly into the procedure first-denomination and partly into the procedure count-change
;; (which knows that there are five kinds of U.S. coins).
;; It would be nicer to be able to supply a list of coins to be used for making change.
;;
;; We want to rewrite the procedure cc so that its second argument is a list of the values of the coins to use
;; rather than an integer specifying which coins to use. We could then have lists that defined each kind of currency:

(define us-coins
  (list 50 25 10 5 1))

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

;; We could then call cc as follows:
;;
;; (cc 100 us-coins)
;; 292

;; To do this will require changing the program cc somewhat.
;; It will still have the same form, but it will access its second argument differently, as follows:

(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 the procedures first-denomination, except-first-denomination and no-more?
;; in terms of primitive operations on list structures.
;; Does the order of the list coin-values affect the answer produced by cc? Why or why not?

(define (first-denomination coin-values)
    (car coin-values))

(define (except-first-denomination coin-values)
    (cdr coin-values))

(define (no-more? coin-values)
    (null? coin-values))