[441]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 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.

思路

万能公式

Code

Python

class Solution(object):
    def arrangeCoins(self, n):
        """
        :type n: int
        :rtype: int
        """
        return int(((8*n+1)**0.5-1)/2)

Runtime: 85ms