SICP sicp 135: 3.66 exercises 1353.66 and

SICP sicp 135: 3.66 exercises 1353.66 and
Exercise 3-66 Original

Exercise 3.66. Examine the stream (pairs 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 .)

Analysis

There are two cases of order (m, n:
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

Code

(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

(Note: The Code comes from the Network)