【SICP练习】127 练习3.58

练习3-58

原文

Exercise 3.58. Give an interpretation of the stream computed by the following procedure:

(define (expand num den radix) (cons-stream (quotient (* num radix) den) (expand (remainder (* num radix) den) den radix)))

(Quotient is a primitive that returns the integer quotient of two integers.) What are the successive elements produced by (expand 1 7 10) ? What is produced by (expand 3 8 10) ?

分析

(expand 1 7 10) => (quotient (* 1 10) 7) => 1 => (expand (remainder 10 7) 7 10) => (quotient (* 3 10) 7) => 4 => (expand (remainder 30 7) 7 10) => (quotient (* 2 10) 7) => 2
……
…… => 1 4 2 8 5 7 4 2 8 5 7 ...

(expand 3 8 10)
……
…… => 3 7 5 0 0 0 ...

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