leetcode 441. Arranging Coins

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.

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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

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代码：

class Solution {
public:
    int arrangeCoins(int n) {
        return (int) (sqrt(2*(long)n+0.25) - 0.5);
    }
};