数学方法，解一元二次方程，o(1)复杂度。

import java.util.Scanner;

public class Main {
    public static void main(String[] args){
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int k = (int) ((-1 + Math.sqrt(1 + 8 * n)) / 2);
        while (k * k + k - 2 * n < 0) {
            k++;
        }
        System.out.println(k);
    }
}