"SICP Exercise" 135 Exercise 3.66

Exercise 3-66 Original

Exercise 3.66. Examine the stream (pairs integers integers). Can you do any general comments about the order in which the pairs is 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 this, all the better. But feel-give more qualitative answers if you find yourself getting bogged down.)

Analysis

There are two scenarios for order pairs (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-whilePred?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)))) (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 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 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 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) ( 3) (1) (2) (1) (7 8) (1) (2) (1 98) (3) (1) (2)) (length before-1-100); value:197

(Note: The code originates from the network)

"SICP Exercise" 135 Exercise 3.66