問題描述：

You have a total ofncoins that you want to form in a staircase shape, where everyk-th row must have exactlykcoins.

Givenn, find the total number offullstaircase rows that can be formed.

nis a non-negative integer and fits within the range of a 32-bit signed integer.

n = 5

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

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

n = 8

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

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

主要是考察了等差數列的求和公式1+2+3+4+..+n = (1+n)*n / 2.

可以有兩種做法：

1.二分查詢法

2.利用數學公式推導求解

以下程式碼給出了兩種求解方式：

1.二分查詢：

class Solution {
public:
    int arrangeCoins(int n) {
        long long left = 1,right = n, mid;
        while(left <= right)
        {
        	mid = left + (right - left) / 2;
        	long long temp = mid * (mid + 1) / 2;
			if(temp == n) return mid;
			else if(temp < n) left = mid + 1;
			else right = mid - 1;			
		}
		return left - 1;
    }
};
 

class Solution {
public:
    int arrangeCoins(int n) {
        return (int) floor((-1 + sqrt(1+8L*n))/2.0);
    }
};