Algorithm: Euclid's Algorithm

最新推荐文章于 2024-08-19 20:50:30 发布

d3y1

最新推荐文章于 2024-08-19 20:50:30 发布

阅读量664

点赞数

CC 4.0 BY-SA版权

分类专栏： Algorithm 文章标签： Euclid algorithm

本文链接：https://blog.youkuaiyun.com/IOIO_/article/details/46287359

Algorithm 专栏收录该内容

151 篇文章

订阅专栏

本文介绍了一种使用欧几里得算法求两个正整数最大公约数的方法。该算法通过不断取余数并交换数值的方式，直至余数为零，此时的除数即为两数的最大公约数。文章提供了详细的算法步骤及Java实现代码。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

Algorithm E

Algorithm E (Euclid’s algorithm). Given two positive integers m and n, find
their greatest common divisor, that is, the largest positive integer that evenly
divides both m and n.
E1. [Find remainder.] Divide m by n and let r be the remainder. (We will have
0<= r < n.)
E2. [Is it zero?] If r = 0, the algorithm terminates; n is the answer.
E3. [Reduce.] Set m <– n, n <– r, and go back to step E1. |

Flow diagram

这里写图片描述

Java program

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

/**
 * Created with IntelliJ IDEA.
 * User: 1O1O
 * Date: 12/15/13
 * Time: 6:52 PM
 * :)~
 * Euclid's Algorithm:ALGORITHMS
 */
public class Main {

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        System.out.print("Please input a positive integer for m:");
        int m = Integer.parseInt(br.readLine());

        System.out.print("Please input a positive integer for n:");
        int n = Integer.parseInt(br.readLine());

        int r;

        do{
            r = m%n;
            if(r == 0){
                System.out.println("The greatest common divisor of m and n is:"+n);
                break;
            }else {
                m = n;
                n = r;
            }
        }while (true);
    }
}

Inputs & Outputs

Please input a positive integer for m:12
Please input a positive integer for n:45
The greatest common divisor of m and n is:3

Reference

<< The Art of Computer Programming: Fundamental Algorithms>> VOLUME 1, DONALD E. KNUTH