Construction and interpretation of SICP computer program 1.16 Iterative method logarithmic calculation of n-square of B



The 1.16 iteration method calculates the n-th square of B

First, the Java implementation of the recursive and iterative method:

public class Test {public    static void Main (String args[]) {        int ex,ey;        ex = EXPT (122,4);        EY = Expt_iter (122, 4, 1);        System.out.println (EY);        System.out.println (ex);    }    recursive    static int expt (int b,int n) {        int sum;        if (n = = 0)            return 1;        else        {            sum = (EXPT (b, (n-1))) * (b);            return sum;        }    }    Iterate    static int expt_iter (int b, int counter,int product) {        int sum;        if (counter = = 0) {            return product;        }        else        {            sum = Expt_iter (b, (counter-1), (b*product));            return sum;}}    }

Again is the logarithmic iteration of scheme:

#lang racket;; N is even: B^n = (b^ (N/2)) ^2 (define (square x) (* x x)), defines the product function (define (FAST-EXPT b N), filter  (expt-iter B N 1)) (Define (expt-ite R b N A)  (cond (= n 0) a), when n= 0, the value is 1       ((even N) (Expt-iter (square B) (/n 2) a), and whether it is an even number (odd  N) (Expt-iter b (-N 1) (* b a)))); Determine if it is an odd number (define (even n)  (= (remainder n 2) 0)) (FAST-EXPT 2 15); N is odd: B^n = b*b^ (n-1)

Construction and interpretation of SICP computer program 1.16 Iterative method logarithmic calculation of n-square of B