441. Arranging Coins

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.

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.

Solution

Math, time O(1)

利用二次方程求解公式：

image.png

注意要将n cast to long，否则8 * n会overflow！

class Solution {
    public int arrangeCoins(int n) {
        return (int) (Math.sqrt(1 + 8 * (long) n) - 1) / 2;
    }
}