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:
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¤ ¤
¤ ¤

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



Example 2:

n = 8

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

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

Source: leetcode | Difficulty: EASY
Tags: Sorting

Mathematics

Starter code: class Solution:
    def arrangeCoins(self, n: int) -> int:
        

Solutions:
class Solution:

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


class Solution:

	def arrangeCoins(self, n):
		return int(((8 * n + 1) ** 0.5 - 1) / 2)


class Solution:

	def arrangeCoins(self, n):
		return int((2 * n + 0.25) ** 0.5 - 0.5)


class Solution:

	def arrangeCoins(self, n):
		if n == 0:
			return 0
		upper = math.ceil(math.sqrt(2 * n))
		lower = math.floor(math.sqrt(2 * n)) - 2
		for k in range(lower + 1, upper):
			if (k + 1) * k <= 2 * n and (k + 2) * (k + 1) > 2 * n:
				return k


class Solution(object):

	def arrangeCoins(self, n):
		return int(math.sqrt(2 * n + 0.25) - 0.5)