Problem:
Score : 300 points

Problem Statement

You are given an integer N.

Find a triple of positive integers h, n and w such that 4/N = 1/h + 1/n + 1/w.

If there are multiple solutions, any of them will be accepted.

Constraints

It is guaranteed that, for the given integer N, there exists a solution such that h,n,w \leq 3500.

Inputs

Input is given from Standard Input in the following format:

N

Outputs

Print a triple of positive integers h, n and w that satisfies the condition, in the following format:

h n w

Sample Input 1

2

Sample Output 1

1 2 2

4/2 = 1/1 + 1/2 + 1/2.

Sample Input 2

3485

Sample Output 2

872 1012974 1539173474040

It is allowed to use an integer exceeding 3500 in a solution.

Sample Input 3

4664

Sample Output 3

3498 3498 3498

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)


import java.util.HashMap;
import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        long N = (long) scanner.nextInt();
        int[] theOne = new int[3500];
        for (int i = 0; i < 3500; i++) theOne[i] = i+1;

        for (long j = 1; j <= 3500; j++) {
            for (long k = 1; k <= 3500;k++) {
                long x = (j * k * N);
                long y = 4 * j * k - N * (j + k);
                if (y != 0) {
                    int thatOne = binarySearch(theOne, x, y, 0, theOne.length - 1);
                    if (thatOne > 0) {
                        System.out.println(j + " " + k + " " + thatOne);
                        return;
                    }
                }
            }
        }
    }

    private static int binarySearch(int[] field, long x, long y, int start, int end) {
        if (start > end || start >= field.length || end < 0) return -1;
        int mid = (start + end) / 2;
        if (field[mid] * y < x) return binarySearch(field, x, y, mid + 1, end);
        else if (field[mid] * y > x) return binarySearch(field, x, y, start, mid - 1);
        else return field[mid];
    }

}