0441._arranging_coins.md

441. Arranging Coins

难度: Easy

刷题内容

原题连接

• https://leetcode.com/problems/arranging-coins/

内容描述

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.

解题方案

思路 1 - 时间复杂度: O(lgN)- 空间复杂度: O(1)******

直接模拟，beats 48.90%

class Solution(object):
    def arrangeCoins(self, n):
        """
        :type n: int
        :rtype: int
        """
        cnt = 1
        while n > 0:
            n -= cnt
            cnt += 1
        return cnt - 1 if n == 0 else cnt - 2

思路 2 - 时间复杂度: O(1)- 空间复杂度: O(1)******

可以直接公式：

i(i+1)/2 = n

解i

i = ( sqrt(8*n+1) -1 )/ 2 

时间复杂度是O(1)是因为sqrt函数时间复杂度可以看成O(1)，参考这里的讨论

beats 100%

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