Problem:
Score : 200 points

Problem Statement

There is a kangaroo at coordinate 0 on an infinite number line that runs from left to right, at time 0.
During the period between time i-1 and time i, the kangaroo can either stay at his position, or perform a jump of length exactly i to the left or to the right.
That is, if his coordinate at time i-1 is x, he can be at coordinate x-i, x or x+i at time i.
The kangaroo's nest is at coordinate X, and he wants to travel to coordinate X as fast as possible.
Find the earliest possible time to reach coordinate X.

Constraints

X is an integer.

1≤X≤10^9

Input

The input is given from Standard Input in the following format:

X

Output

Print the earliest possible time for the kangaroo to reach coordinate X.

Sample Input 1

6

Sample Output 1

3

The kangaroo can reach his nest at time 3 by jumping to the right three times, which is the earliest possible time.

Sample Input 2

2

Sample Output 2

2

He can reach his nest at time 2 by staying at his position during the first second, and jumping to the right at the next second.

Sample Input 3

11

Sample Output 3

5

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.*;
import java.util.*;

public class Main {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int x = in.nextInt();
		
		Queue<PosT> queue = new LinkedList<>();
		queue.add(new PosT(0,0));
		while(queue.size() > 0){
			PosT cur = queue.remove();
			if(cur.pos == x){
				System.out.println(cur.time);
				return;
			}
			queue.add(new PosT(cur.pos+cur.time+1,cur.time+1));
			queue.add(new PosT(cur.pos-cur.time-1,cur.time+1));
			queue.add(new PosT(cur.pos,cur.time+1));
		}
	}
}

class PosT{
	public int pos;
	public int time;
	
	public PosT(int _pos, int _time){
		pos = _pos;
		time = _time;
	}
}