将真分数分解为埃及分数

描述	分子为1的分数称为埃及分数。现输入一个真分数(分子比分母小的分数，叫做真分数)，请将该分数分解为埃及分数。如：8/11 = 1/2+1/5+1/55+1/110。 接口说明  /*  功能: 将分数分解为埃及分数序列  输入参数：      String pcRealFraction:真分数(格式“8/11”)  返回值：      String pcEgpytFraction:分解后的埃及分数序列(格式“1/2+1/5+1/55+1/100”)  */  public static String  ConvertRealFractToEgpytFract(String pcRealFraction)  {   return null;  }
知识点	字符串
运行时间限制	10M
内存限制	128
输入	输入一个真分数，String型
输出	输出分解后的string
样例输入	8/11
样例输出	1/2+1/5+1/55+1/110

 

package com.oj5;

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

public class Test {
	static class FractionNum{
		int up;
		int down;
		public FractionNum() {
		}
		public FractionNum(int up, int down) {
			this.up = up;
			this.down = down;
		}
		public int getUp() {
			return up;
		}
		public void setUp(int up) {
			this.up = up;
		}
		public int getDown() {
			return down;
		}
		public void setDown(int down) {
			this.down = down;
		}
	}
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		String inputStr = in.nextLine();
		FractionNum input = new FractionNum(Integer.parseInt(inputStr.split("\/")[0]),Integer.parseInt(inputStr.split("\/")[1]));
		FractionNum temp = new FractionNum(input.getUp(),input.getDown());
		FractionNum num = new FractionNum();
		StringBuilder sb = new StringBuilder();
		while(isEgpyFraction(temp)){
			for(int i = 2;;i++){
				
				int gbs = getGBS(temp.getDown(),i);
				int bs = gbs/temp.getDown();
				int bs2 = gbs/i;
				int result = bs*temp.getUp()-bs2*1;
				//System.out.println(result+" "+i);
				if(result>0){
					sb.append(1+"/"+i+"+");
					int gys = getGYS(result,gbs);
					temp.setUp(result/gys);
					temp.setDown(gbs/gys);
					//System.out.println(result/gys+"/"+gbs/gys+"  "+gys+" "+i);
					break;
				}
			}
		}
		sb.append(temp.getUp()+"/"+temp.getDown());
		System.out.println(sb.toString());
	}
	private static boolean isEgpyFraction(FractionNum num) {
		if(num.getUp()==1)
			return false;
		return true;
	}
	private static int getGYS(int a, int b) {
		if(b>a){
			int temp = b;
			b = a;
			a = temp;
		}
		while(b!=0){
			int c = a%b;
			a = b;
			b = c;
		}
		return a;
	}
	private static int getGBS(int a, int b) {
		int min,max;
		if(b>a){
			int temp = b;
			b = a;
			a = temp;
		}
		min = b;
		max = a;
		while(b!=0){
			int c = a%b;
			a = b;
			b = c;
		}
		//System.out.println(min*max+" "+a);
		return (min*max)/a;
	}
	private static boolean isEgpyFraction() {
		// TODO Auto-generated method stub
		return false;
	}
}