441. Arranging Coins

1. Description

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.

2. Example

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

3. Solutions

Math

Time complexity: O(1)
Space complexity: O(1)

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// TODO

class Solution
{
public:
    // int arrangeCoins(int n)
    int arrangeCoins(int number)
    {
        return (sqrt(2 * (long)number + 0.25) - 0.5);
    }
};