# LeetCode 441. Arranging Coins

## Description

https://leetcode.com/problems/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.```

## Explanation

The total number of coins needed to fulfil k rows is: 1 + 2 + … + k = (1 + k) * k / 2.

Therefore, we can use binary search to find what is the largest number of rows we can fulfill with n coins.

## Python Solution

``````class Solution:
def arrangeCoins(self, n: int) -> int:
start = 0
end = n

while start + 1 < end:
mid = start + (end - start) // 2

if mid * (mid + 1) // 2 <= n:
start = mid
else:
end = mid

if end * (end + 1) // 2 <= n:
return end

return start``````
• Time Complexity: O(logN).
• Space Complexity: O(1).