## 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).