【SICP練習】135 練習3.66，sicp練習1353.66

【SICP練習】135 練習3.66，sicp練習1353.66
練習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

對於序對(m,n)有兩種情況：
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

代碼

(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-1-100before-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

（註：代碼來源於網路）