SICP的一些练习题

1.3 较大两个数之和

1 (define (MaxSum x y z)

2   (+ (cond ((or (> x y) (> x z)) x)

3            (else 0))

4      (cond ((or (> y x) (> y z)) y)

5            (else 0))

6      (cond ((or (> z x) (> z y)) z)

7            (else 0))))

8 (MaxSum 5 3 10)

较大两个数之和

牛顿迭代

 1 (define (Abs x)

 2   (cond ((> x 0) x)

 3         ((= x 0) 0)

 4         ((< x 0) (- x))))

 5 (define (Square x) (* x x))

 6 (define (Average x y)

 7   (/ (+ x y) 2))

 8 (define (Improve guess x)

 9   (Average guess (/ x guess)))

10 (define (GoodEnough? guess x)

11   (< (Abs (- (Square guess) x)) 0.001))

12 (define (SqrtIter guess x)

13   (if (GoodEnough? guess x)

14       guess

15       (SqrtIter (Improve guess x)

16                 x)))

17 (SqrtIter 1 2)

牛顿迭代

一个表的最后一个表

1 (define (last-pair lst) 

2   (if (<= (length lst) 1)

3       lst

4       (last-pair (cdr lst))))

最后一个表

集合操作

 1 (define (element-of-set? x set)

 2   (cond ((null? set) false)

 3         ((equal? x (car set)) true)

 4         (else (element-of-set? x (cdr set)))))

 5 

 6 (define (adjoin-set x set)

 7   (if (element-of-set? x set)

 8       set

 9       (cons x set)))

10 

11 (define (intersection-set set1 set2)

12   (cond ((or (null? set1) (null? set2)) '())

13         ((element-of-set? (car set1) set2)

14          (cons (car set1)

15                (intersection-set (cdr set1) set2)))

16         (else (intersection-set (cdr set1) set2))))

17 

18 (define (union-set set1 set2)

19   (cond ((null? set1) set2)

20         ((null? set2) set1)

21         ((element-of-set? (car set1) set2)

22          (union-set (cdr set1) set2))

23         (else (cons (car set1) (union-set (cdr set1) set2)))))

24 

25 

26 (define set1 (list 1 2 3 4))

27 (define set2 (list 3 4 5 6))

28 (element-of-set? 3 set1)

29 (element-of-set? 0 set1)

30 (intersection-set set1 set2)

31 (union-set set1 set2)

集合