README.md

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:
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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.

Solutions (Python)

1. Simulation

class Solution:
    def arrangeCoins(self, n: int) -> int:
        k = 1
        while True:
            n -= k
            if n < 0:
                return k - 1
            k += 1

2. Mathematical

class Solution:
    def arrangeCoins(self, n: int) -> int:
        return int(((1 + 8 * n) ** .5 - 1) / 2)