SICP的一些练习题

1.3 较大两个数之和

(define (MaxSum x y z)
  (+ (cond ((or (> x y) (> x z)) x)
           (else 0))
     (cond ((or (> y x) (> y z)) y)
           (else 0))
     (cond ((or (> z x) (> z y)) z)
           (else 0))))
(MaxSum 5 3 10)

牛顿迭代

(define (Abs x)
  (cond ((> x 0) x)
        ((= x 0) 0)
        ((< x 0) (- x))))
(define (Square x) (* x x))
(define (Average x y)
  (/ (+ x y) 2))
(define (Improve guess x)
  (Average guess (/ x guess)))
(define (GoodEnough? guess x)
  (< (Abs (- (Square guess) x)) 0.001))
(define (SqrtIter guess x)
  (if (GoodEnough? guess x)
      guess
      (SqrtIter (Improve guess x)
                x)))
(SqrtIter 1 2)

一个表的最后一个表

(define (last-pair lst) 
  (if (<= (length lst) 1)
      lst
      (last-pair (cdr lst))))

集合操作

(define (element-of-set? x set)
  (cond ((null? set) false)
        ((equal? x (car set)) true)
        (else (element-of-set? x (cdr set)))))

(define (adjoin-set x set)
  (if (element-of-set? x set)
      set
      (cons x set)))

(define (intersection-set set1 set2)
  (cond ((or (null? set1) (null? set2)) '())
        ((element-of-set? (car set1) set2)
         (cons (car set1)
               (intersection-set (cdr set1) set2)))
        (else (intersection-set (cdr set1) set2))))

(define (union-set set1 set2)
  (cond ((null? set1) set2)
        ((null? set2) set1)
        ((element-of-set? (car set1) set2)
         (union-set (cdr set1) set2))
        (else (cons (car set1) (union-set (cdr set1) set2)))))


(define set1 (list 1 2 3 4))
(define set2 (list 3 4 5 6))
(element-of-set? 3 set1)
(element-of-set? 0 set1)
(intersection-set set1 set2)
(union-set set1 set2)