leetcode441. Arranging Coins

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.

解法

利用公式，x*(x+1)/2 = n,求出x取整数。注意8＊n会超过范围，所以n转为long。

public class Solution {    public int arrangeCoins(int n) {        return (int)((-1 + Math.sqrt(1 + 8 * (long)n)) / 2);    }}