SICP-2.2.1节练习
练习 2.17 - 2.23
练习 2.17：
Define a procedure last-pair that returns the list that contains only the last element of a given (nonempty) list: (last-pair (list 23 72 149 34)) (34)
我的解答：
(define (last-pair xs)
(if (null? (cdr xs))
(car xs)
(last-pair (cdr xs))))
练习 2.18：
Define a procedure reverse that takes a list as argument and returns a list of the same elements in reverse order: (reverse (list 1 4 9 16 25)) (25 16 9 4 1)
我的解答：
(define (reverse1 xs)
(define (iter ans xs)
(if (null? xs)
ans
(iter (cons (car xs) ans) (cdr xs))))
(iter '() xs))
(define (reverse2 xs)
(if (null? xs)
'()
(append (reverse2 (cdr xs)) (list (car xs)))))
练习 2.19：
Consider the change-counting program of section 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, the 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?
我的解答：
(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))
练习 2.20：
The procedures +, *, and list take arbitrary numbers of arguments. One way to define such procedures is to use define with notation dotted-tail notation. In a procedure definition, a parameter list that has a dot before the last parameter name indicates that, when the procedure is called, the initial parameters (if any) will have as values the initial arguments, as usual, but the final parameter's value will be a list of any remaining arguments. For instance, given the definition (define (f x y . z) <body>) the procedure f can be called with two or more arguments. If we evaluate (f 1 2 3 4 5 6) then in the body of f, x will be 1, y will be 2, and z will be the list (3 4 5 6). Given the definition (define (g . w) <body>) the procedure g can be called with zero or more arguments. If we evaluate (g 1 2 3 4 5 6) then in the body of g, w will be the list (1 2 3 4 5 6).4 Use this notation to write a procedure same-parity that takes one or more integers and returns a list of all the arguments that have the same even-odd parity as the first argument. For example, (same-parity 1 2 3 4 5 6 7) (1 3 5 7) (same-parity 2 3 4 5 6 7) (2 4 6)
我的解答：
(define (same-parity . xs)
(define p? (if (even? (car xs))
even?
odd?))
(define (iter xs)
(cond ((null? xs) '())
((p? (car xs)) (cons (car xs)
(iter (cdr xs))))
(else (iter (cdr xs)))))
(iter xs))
练习 2.21：
The procedure square-list takes a list of numbers as argument and returns a list of the squares of
those numbers.
(square-list (list 1 2 3 4))
(1 4 9 16)
Here are two different definitions of square-list. Complete both of them by filling in the missing
expressions:
(define (square-list items)
(if (null? items)
nil
(cons <??> <??>)))
(define (square-list items)
(map <??> <??>))
我的解答：
(define (square-list-1 xs)
(if (null? xs)
'()
(cons (square (car xs))
(square-list-1 (cdr xs)))))
(define (square-list-2 xs)
(map square xs))
练习 2.22：
Louis Reasoner tries to rewrite the first square-list procedure of Exercise 2-21 so that it evolves
an iterative process:
(define (square-list items)
(define (iter things answer)
(if (null? things)
answer
(iter (cdr things)
(cons (square (car things))
answer))))
(iter items nil))
Unfortunately, defining square-list this way produces the answer list in the reverse order of the
one desired. Why?
Louis then tries to fix his bug by interchanging the arguments to cons:
(define (square-list items)
(define (iter things answer)
(if (null? things)
answer
(iter (cdr things)
(cons answer
(square (car things))))))
(iter items nil))
This doesn't work either. Explain.
我的解答：
直接给代码：
(define (square-list-3 xs)
(define (iter ans xs)
(if (null? xs)
ans
(iter (cons (square (car xs))
ans)
(cdr xs))))
(reverse (iter '() xs)))
练习 2.23：
The procedure for-each is similar to map. It takes as arguments a procedure and a list of
elements. However, rather than forming a list of the results, for-each just applies the procedure to
each of the elements in turn, from left to right. The values returned by applying the procedure to
the elements are not used at all—for-each is used with procedures that perform an action, such as
printing. For example,
(for-each (lambda (x) (newline) (display x))
(list 57 321 88))
57
321
88
The value returned by the call to for-each (not illustrated above) can be something arbitrary, such
as true. Give an implementation of for-each.
我的解答：
(define (for-each proc xs)
(if (not (null? xs))
(begin (proc (car xs))
(for-each proc (cdr xs)))))
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Apr 23, 2023 12:26:47 AM
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