[LeetCode] 441. Arranging Coins_Easy tag: Math

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.


利用 x(x+1)/2 <= n 求得x = (sqrt(8*n+1) -1)/2

Code O(1)

class Solution:
    def arrageCoins(self, n):
        return (int(math.sqrt(8*n +1) -1)//2)