原题链接在这里：https://leetcode.com/problems/arranging-coins/

题目：

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 = 5

The coins can form the following rows:
¤
¤ ¤
¤ ¤

Because the 3rd row is incomplete, we return 2. 

Example 2:

n = 8

The coins can form the following rows:
¤
¤ ¤
¤ ¤ ¤
¤ ¤

Because the 4th row is incomplete, we return 3.

题解：

1+2+...+x = n, 求和公式(1+x)*x/2 = n, x = (-b + Math.sqrt(b^2 - 4ac))/2a 或者 (-b - Math.sqrt(b^2 - 4ac))/2a. 

负值去掉保留正值.

Note: 不能用8*n, 可能overflow. 要用8.0*n自动转化成double型.

Time Complexity: O(1). Space: O(1).

AC Java:

1 public class Solution {
2     public int arrangeCoins(int n) {
3         return (int)((Math.sqrt(8.0*n+1) - 1)/2);
4     }
5 }

LeetCode Arranging Coins