SICP 1章 - メモ帳

ex 1.16

逐次平方なら

反復プロセスなら

(define (square x) (* x x))
(define (even? n) (= (remainder n 2) 0))
(define (fast-expt2 b n)
  (define (iter b n a)
    (cond ((= n 0) a)
          ((even? n) (iter (square b) (/ n 2) a))
          (else (iter b (- n 1) (* a b)))))
  (iter b n 1))

gosh> (fast-expt2 2 3)
8

ex 1.17

multipleの逐次平方

(define (double x) (* x 2))
(define (halve x) (/ x 2))
(define (even? n) (= (remainder n 2) 0))
(define (fast-mult a b)
  (cond ((= b 0) 0)
        ((even? b) (double (fast-mult a (halve b))))
        (else (+ a (fast-mult a (- b 1))))))

gosh> (fast-mult 2 4)
8

ex 1.18

multipleの反復プロセス

(define (double x) (* x 2))
(define (halve x) (/ x 2))
(define (even? n) (= (remainder n 2) 0))
(define (fast-mult2 a b)
  (define (iter a b total)
    (cond ((= b 0) total)
          ((even? b) (iter (double a) (halve b) total))
          (else (iter a (- b 1) (+ total a)))))
   (iter a b 0))

ex 1.30

穴埋め問題

(define (sum term a next b)
  (define (iter a result)
    (if (> a b) 
      result
      (iter (next a) (+ (term a) result))))
  (iter a 0))

ex 1.31

(define (even? n) (= (remainder n 2) 0))
(define (product term a next b)
  (if (> a b) 
    1
    (* (term a)
       (product term (next a) next b))))
(define (pi n)
  (define (term x)
    (if (even? x)
      (/ (+ x 2.0) (+ x 3.0))
      (/ (+ x 3.0) (+ x 2.0))))
    (* 4.0 (product term 0 (lambda (x) (+ x 1)) n )))

gosh> (pi 1)
3.5555555555555554
gosh> (pi 10)
3.023170192001359
gosh> (pi 100)
3.1263793980429804
gosh> (pi 1000)
3.1400269461050057
gosh> (pi 10000)
3.1414356249916424
gosh> (pi 100000)
3.14157694613687