leetcode 441. 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.
解法：
这是一道数学类的问题，意思是让求出给定的数字 N 可以构造出的满足阶梯型架构的最后一个整数行。
这个题可以用循环做，但是也可以直接使用求通向公式的方法做，解法如图：
大致也就是配完全平方式，求解 K
有了通项公式，我们写出代码就不算难了，还要注意一点这里要把 n 转成 长整型long否则会有溢出的问题
代码：
class Solution {
public:
int arrangeCoins(int n) {
return (int) (sqrt(2*(long)n+0.25) - 0.5);
}
};