练习3-66

原文

Exercise 3.66. Examine the stream (pairs integers integers). Can you make any general comments about the order in which the pairs are placed into the stream? For example, about how many pairs precede the pair (1,100)? the pair (99,100)? the pair (100,100)? (If you can make precise mathematical statements here, all the better. But feel free to give more qualitative answers if you find yourself getting bogged down.)

分析

对于序对(m,n)有两种情况：
1） m = n
(m,n)=2^m-2
2） m < n
(m,n)=2^m*(n-1) + 2^(m-1)-2

(1,100)=2^1*99+2^0-2=198-1=197

代码

(define (stream-take-while pred? stream)
    (if (stream-null? stream)
        '()
        (if (pred? (stream-car stream))
            (cons-stream (stream-car stream)
                         (stream-take-while pred? (stream-cdr stream)))
            '())))

(define before-1-100 (stream->list
             (stream-take-while
                    (lambda (pair)
                            (not (equal? pair '(1 100))))
                   (pairs integers integers))))

;Value: before-1-100

before-1-100

;Value 13: ((1 1) (1 2) (2 2) (1 3) (2 3) (1 4) (3 3) (1 5) (2 4) (1 6) (3 4) (1 7) (2 5) (1 8) (4 4) (1 9) (2 6) (1 10) (3 5) (1 11) (2 7) (1 12) (4 5) (1 13) (2 8) (1 14) (3 6) (1 15) (2 9) (1 16) (5 5) (1 17) (2 10) (1 18) (3 7) (1 19) (2 11) (1 20) (4 6) (1 21) (2 12) (1 22) (3 8) (1 23) (2 13) (1 24) (5 6) (1 25) (2 14) (1 26) (3 9) (1 27) (2 15) (1 28) (4 7) (1 29) (2 16) (1 30) (3 10) (1 31) (2 17) (1 32) (6 6) (1 33) (2 18) (1 34) (3 11) (1 35) (2 19) (1 36) (4 8) (1 37) (2 20) (1 38) (3 12) (1 39) (2 21) (1 40) (5 7) (1 41) (2 22) (1 42) (3 13) (1 43) (2 23) (1 44) (4 9) (1 45) (2 24) (1 46) (3 14) (1 47) (2 25) (1 48) (6 7) (1 49) (2 26) (1 50) (3 15) (1 51) (2 27) (1 52) (4 10) (1 53) (2 28) (1 54) (3 16) (1 55) (2 29) (1 56) (5 8) (1 57) (2 30) (1 58) (3 17) (1 59) (2 31) (1 60) (4 11) (1 61) (2 32) (1 62) (3 18) (1 63) (2 33) (1 64) (7 7) (1 65) (2 34) (1 66) (3 19) (1 67) (2 35) (1 68) (4 12) (1 69) (2 36) (1 70) (3 20) (1 71) (2 37) (1 72) (5 9) (1 73) (2 38) (1 74) (3 21) (1 75) (2 39) (1 76) (4 13) (1 77) (2 40) (1 78) (3 22) (1 79) (2 41) (1 80) (6 8) (1 81) (2 42) (1 82) (3 23) (1 83) (2 43) (1 84) (4 14) (1 85) (2 44) (1 86) (3 24) (1 87) (2 45) (1 88) (5 10) (1 89) (2 46) (1 90) (3 25) (1 91) (2 47) (1 92) (4 15) (1 93) (2 48) (1 94) (3 26) (1 95) (2 49) (1 96) (7 8) (1 97) (2 50) (1 98) (3 27) (1 99) (2 51))

(length before-1-100)

;Value: 197

（注：代码来源于网络）