; ======================================================================
;
; 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.1.32
;; 递归版本
(define (accumulate-r combiner null-value term a next b)
(if (> a b)
null-value
(combiner (term a)
(accumulate-r combiner null-value term (next a) next b))))
;; 迭代版本
(define (accumulate-i combiner null-value term a next b)
(if (> a b)
null-value
(accumulate-i combiner
(combiner null-value (term a))
term (next a) next b)))
;; sum
(define (sum term a next b)
(accumulate-r + 0 term a next b))
;; product
(define (product term a next b)
(accumulate-i * 1 term a next b))
;; Test-it:
;; Welcome to MzScheme version 209, Copyright (c) 2004 PLT Scheme, Inc.
;;
;; ;; 我们已经用基于accumulate-i的product代替的原来的product
;; ;; factorial调用了product, 所得结果与以前一致
;; > (factorial 5)
;; 120
;;
;; ;; 我们已经用基于accumulate-r的sum代替的原来的sum
;; ;; integral调用了sum, 所得结果与以前一致
;; > (integral cube 0 1 0.01)
;; 0.24998750000000042
;; BTW, 我们甚至可以定义更高阶的函数，把比较函数也抽象出来
(define (accumulate-high compare combiner null-value term a next b)
(if (compare a b)
null-value
(accumulate-high compare combiner
(combiner null-value (term a))
term (next a) next b)))
