题解 | #将真分数分解为埃及分数#

import java.util.*;

import java.io.*;
public class Main {
    private static StringBuilder sb = null;
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String str = null;
        while ((str = br.readLine()) != null) {
            String[] arr = str.split("/");
            int a = Integer.parseInt(arr[0]);
            int b = Integer.parseInt(arr[1]);
            sb = new StringBuilder();
            //b=a*p+q, q<a; 故a/b最大可减去一个1/(p+1);
            //a/b-1/(p+1) = (a(p+1)-b)/b(p+1)=(ap+a-b)/b(p+1)=(b-q+a-b)/b(p+1)=(a-q)/b(p+1)
            boolean flag = true;
            while (a != 1) {
                int p = b / a;
                int q = b % a;
                if (q == 0) {
                    sb.append("1/" + p + "\n");
                    flag = false;
                    break;
                }
                //为什么要用a-1暂未理解，此处不加无法通过17/73的用例
                if (b % (a - 1) == 0) {
                    sb.append("1/" + (b / (a - 1)) + "+");
                    break;
                }
                sb.append("1/" + (p + 1) + "+");
                // System.out.println("1/" + (p + 1) + "+");
                b = b * (p + 1);
                a = a - q;
                // System.out.println("b:" + b + " a:" + a);
            }
            if (flag) {
                sb.append("1/" + b + "\n");
            }
        }
        System.out.println(sb.toString());
    }

}