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55 lines
1.7 KiB
55 lines
1.7 KiB
2 years ago
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Exercise 2.19: Consider the change-counting
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program of 1.2.2. It would be nice to be able to easily change
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the currency used by the program, so that we could compute the number of ways
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to change a British pound, for example. As the program is written, the
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knowledge of the currency is distributed partly into the procedure
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first-denomination and partly into the procedure count-change
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(which knows that there are five kinds of U.S. coins). It would be nicer to be
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able to supply a list of coins to be used for making change.
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We want to rewrite the procedure cc so that its second argument is a
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list of the values of the coins to use rather than an integer specifying which
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coins to use. We could then have lists that defined each kind of currency:
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(define us-coins
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(list 50 25 10 5 1))
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(define uk-coins
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(list 100 50 20 10 5 2 1 0.5))
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We could then call cc as follows:
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(cc 100 us-coins)
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292
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To do this will require changing the program cc somewhat. It will still
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have the same form, but it will access its second argument differently, as
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follows:
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(define (cc amount coin-values)
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(cond ((= amount 0)
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1)
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((or (< amount 0)
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(no-more? coin-values))
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0)
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(else
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(+ (cc
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amount
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(except-first-denomination
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coin-values))
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(cc
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(- amount
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(first-denomination
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coin-values))
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coin-values)))))
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Define the procedures first-denomination,
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except-first-denomination and no-more? in terms of primitive
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operations on list structures. Does the order of the list coin-values
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affect the answer produced by cc? Why or why not?
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