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: Accepted)

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    static InputStream is;
    static PrintWriter out;
    static String INPUT = "";

    static void solve()
    {
        int x = ni();
        int t = 0;
        while (true) {
            if ((t * (t + 1) / 2) >= x) {
                out.println(t);
                break;
            }
            t++;
        }
    }

    public static void main(String[] args) throws Exception
    {
        long S = System.currentTimeMillis();
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);

        solve();
        out.flush();
        long G = System.currentTimeMillis();
        tr(G-S+"ms");
    }

    private static boolean eof()
    {
        if(lenbuf == -1)return true;
        int lptr = ptrbuf;
        while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;

        try {
            is.mark(1000);
            while(true){
                int b = is.read();
                if(b == -1){
                    is.reset();
                    return true;
                }else if(!isSpaceChar(b)){
                    is.reset();
                    return false;
                }
            }
        } catch (IOException e) {
            return true;
        }
    }

    private static byte[] inbuf = new byte[1024];
    static int lenbuf = 0, ptrbuf = 0;

    private static int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }

    private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }

    private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }

    private static double nd() { return Double.parseDouble(ns()); }
    private static char nc() { return (char)skip(); }

    private static String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private static char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private static char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }

    private static int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }

    private static int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }

        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private static long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }

        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }

    // https://algs4.cs.princeton.edu/15uf/UF.java.html
    public static class UnionFind {
        private int count = 0;
        private int[] parent, rank;

        public UnionFind(int n) {
            count = n;
            parent = new int[n];
            rank = new int[n];
            for (int i = 0; i < n; i++) {
                parent[i] = i;
            }
        }

        public int find(int p) {
            while (p != parent[p]) {
                parent[p] = parent[parent[p]];
                p = parent[p];
            }
            return p;
        }

        public void union(int p, int q) {
            int rootP = find(p);
            int rootQ = find(q);
            if (rootP ==rootQ) return;
            if (rank[rootQ] > rank[rootP]) {
                parent[rootP] = rootQ;
            } else {
                parent[rootQ] = rootP;
                if (rank[rootP] == rank[rootQ]) {
                    rank[rootP]++;
                }
            }
            count--;
        }

        public int count() {
            return count;
        }

        public void print() {
            out.println("Parent:");
            for (int i : parent) {
                out.print(i);
                out.print(" ");
            }
            out.println();
            out.println("Rank:");
            for (int i : rank) {
                out.print(i);
                out.print(" ");
            }
            out.println();
        }
    }
}