LeetCode 441. Arranging Coins

You have a total of n coins that you want to form in a staircase shape, where every k-th row must have exactly k coins.

Given n, find the total number of full staircase rows that can be formed.

n is a non-negative integer and fits within the range of a 32-bit signed integer.

Example 1:

n = 5The coins can form the following rows:¤¤ ¤¤ ¤Because the 3rd row is incomplete, we return 2.

Example 2:

n = 8The coins can form the following rows:¤¤ ¤¤ ¤ ¤¤ ¤Because the 4th row is incomplete, we return 3.

根据等差数列求和公式，1+2+3+...+x=(x*(x+1))/2<=n，则x<=sqrt(2n).

public class Solution {    public int arrangeCoins(int n) {        int res = (int)(Math.sqrt(n) * Math.sqrt(2));        while(res >= 0){            if(res * (res + 1) <= 2 * n) return res;            res --;        }        return res;    }}