; ======================================================================
;
;          Structure and Interpretation of Computer Programs
;                  (trial answer to excercises)
;
;                  计算机程序的构造和解释(习题试解)
;
;                                             created: code17 03/05/05
;                                             modified:
; (保持内容完整不变前提下，可以任意转载)
; ======================================================================

;; SICP No.1.31

;; 递归版本
(define (product-r term a next b)
  (if (> a b)
      1
      (* (term a)
         (product-r term (next a) next b))))

;; 迭代版本
(define (product-i term a next b)
  (define (iter a result)
    (if (> a b)
        result
        (iter (next a) (* result (term a)))))
  (iter a 1))

;; 阶乘
(define (factorial n)
  (define (term i) i)
  (define (next i) (+ i 1))
  (product-i term 1 next n))

;; 求pi
(define (john-wallis-pi n)
  (define (term i) (/ (* (* 2 i) (* 2 (+ i 1)))
                      (square (+ 1 (* 2 i)))))
  (define (next i) (+ i 1))
  (* (product-i term 1 next n) 4.0))


;; Test-it:
;; Welcome to MzScheme version 209, Copyright (c) 2004 PLT Scheme, Inc.
;; > (factorial 5)
;; 120
;; > (factorial 10)
;; 3628800
;; > (john-wallis-pi 10)
;; 3.2137849402931895
;; > (john-wallis-pi 100)
;; 3.1493784731686008
;; > (john-wallis-pi 1000)
;; 3.142377365093878
;; > (john-wallis-pi 10000)
;; 3.1416711865344635
;; > (john-wallis-pi 100000)
;; 3.1416005075027056