java求最大公约数（分解质因数）

标签：java   算法   最大公约数   分解质因数   

以下是四种用java语言编程实现的求最大公约数的方法：

package gcd;

import java.util.ArrayList;
import java.util.List;

public class gcd {
	public static void main(String[] args) {
		long startTime;
		long endTime;
		long durationTime;
		
		int[] testArray1 = new int[]{784, 988, 460, 732, 548, 998, 672, 1024, 888, 512};
		int[] testArray2 = new int[]{1024, 82, 92, 128, 58, 2014, 512, 88, 582, 788};
		
		for (int i = 0; i < 10; i++) {
			startTime = System.nanoTime();
			System.out.println("欧几里得方法：" + Euclid(testArray1[i],testArray2[i]));
			endTime = System.nanoTime();
			durationTime = endTime - startTime;
			System.out.println("欧几里得算法耗时：" + durationTime + "\n");
			
			startTime = System.nanoTime();
			System.out.println("连续整数检测法：" + consecutiveIntegersTest(testArray1[i], testArray2[i]));
			endTime = System.nanoTime();
			durationTime = endTime - startTime;
			System.out.println("连续整数检测算法耗时：" + durationTime + "\n");
			
			startTime = System.nanoTime();
			System.out.println("辗转相减法：" + consecutiveSubstract(testArray1[i], testArray2[i]));
			endTime = System.nanoTime();
			durationTime = endTime - startTime;
			System.out.println("辗转相减算法耗时：" + durationTime + "\n");
			
			startTime = System.nanoTime();
			System.out.println("分解质因数法：" + primeFactors(testArray1[i], testArray2[i]));
			endTime = System.nanoTime();
			durationTime = endTime - startTime;
			System.out.println("分解质因数算法耗时：" + durationTime);
		}
		
	}

	/**
	 * 欧几里得算法求最大公约数
	 * @param no1
	 * @param no2
	 * @return
	 */
	public static int Euclid(int no1, int no2) {
		int remainder;
		remainder = no1%no2;
		while(remainder != 0) {
			no1 = no2;
			no2 = remainder;
			remainder = no1%no2;
		}
		return no2;
	}
	
	/**
	 * 连续整数检测法
	 * @param m
	 * @param n
	 * @return
	 */
	public static int consecutiveIntegersTest(int m, int n) {
		int t;
		if (m > n) 
			t = n;
		else
			t = m;
		while(true) {
			if (m%t == 0 && n%t == 0)
				break;
			else
				t = t - 1;
		}
		return t;
	}
	
	/**
	 * 辗转相减法
	 * @param num1
	 * @param num2
	 * @return
	 */
	public static int consecutiveSubstract(int num1, int num2) {
		while(true) {
			if (num1 > num2)
				num1 -= num2;
			else if (num1 < num2)
				num2 -= num1;
			else
				return num1;
		}
	}
	
	/**
	 * 分解质因数法
	 * @param primeNum1
	 * @param primeNum2
	 * @return
	 */
	public static int primeFactors(int primeNum1, int primeNum2) {
		int prime_gcd = 1;
		int compareListSize;
		int temp1, temp2;
		int pn1 = primeNum1, pn2 = primeNum2;
		List<Integer> num1List = new ArrayList<Integer>();
		List<Integer> num2List = new ArrayList<Integer>();
		List<Integer> sameNumList = new ArrayList<Integer>();
		//求出质因数
		for (int i = 2; i < pn1/2;) {		//注意此处用的是pn1，而不是primeNum1，primeNum1的值在下面的执行过程会不断减小
			if (primeNum1%i == 0) {		//求余数，如果能被整除，返回true
				temp1 = primeNum1 / i;		//求商
				primeNum1 = temp1;		//将商赋值给primeNum1，重新判断余数是否为0
				num1List.add(i);		//将质因数放入num1List
			} else if (primeNum1%i != 0) {
				i = i + 1;		//如果余数不等于0，除数i加1，继续求余数
			}
		}
		
		for (int i = 2; i < pn2/2;) {
			if (primeNum2%i == 0) {
				temp2 = primeNum2 / i;
				primeNum2 = temp2;
				num2List.add(i);
			} else if (primeNum2%i != 0) {
				i = i + 1;
			}
		}
		int num1ListSize = num1List.size();
		int num2ListSize = num2List.size();
		if (num1ListSize < num2ListSize) {
			for (int i = 0; i < num1List.size();) {
				if (num2List.contains(num1List.get(i))) {
					prime_gcd *= num1List.get(i);
					num2List.remove(num2List.indexOf(num1List.get(i)));
					num1List.remove(i);
					if (num1List.size() == 0 || num2List.size() == 0)
						break;
				} else {
					i = i + 1;
				}
			}
		} else {
			for (int i = 0; i < num2List.size(); ) {
				if (num1List.contains(num2List.get(i))) {
					prime_gcd *= num2List.get(i);
					num1List.remove(num1List.indexOf(num2List.get(i)));
					num2List.remove(i);
					if (num1List.size() == 0 || num2List.size() == 0)
						break;
				} else {
					i = i + 1;
				}
			}
		}
		return prime_gcd;
	}
}

java求最大公约数（分解质因数）

标签：java   算法   最大公约数   分解质因数   

原文地址：http://blog.csdn.net/yxdayd/article/details/44774015