题解 | 将真分数分解为埃及分数

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        while (in.hasNextLine()) {
            String[] s = in.nextLine().split("/");
            long a = Long.parseLong(s[0]);
            long b = Long.parseLong(s[1]);
            StringBuilder sb = new StringBuilder();
            if (a > b - a) {
                sb.append("1/2+");
                if (b % 2 != 0) {
                    b = b * 2;
                    a = a * 2 - b / 2;
                } else {
                    a = a - b / 2;
                }
            }
            complete(sb, a, b);
            System.out.println(sb);
        }
    }

    private static void complete(StringBuilder sb, long a, long b) {
        if (a == 1) {
            sb.append("1/").append(b);
            return;
        }
        if (b % a == 0) {
            sb.append("1/").append(b / a);
            return;
        }
        if (b % (a - 1) == 0) {
            sb.append("1/").append(b / (a - 1)).append("+1/").append(b);
            return;
        }
        long x = b / a + 1;
        sb.append("1/").append(x).append("+");
        complete(sb, a * x - b, b * x);
    }
}