[LeetCode] 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 kcoins.

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.

其实有规律可循，如果将硬币返回恰好满足的行数，则硬币需要1，3，6，10，15...即硬币的总数满足x(x+1) = 2n

只要求解这个方程中的x，也就是行数即可。

class Solution {
public:
    int arrangeCoins(int n) {
        return sqrt(static_cast<double>(n) * 2 + 0.25) - 0.5;
    }
};
// 25 ms