Java implementation LeetCode 441 coins arrangement

441. The arrangement coins

You have a total of n coins, you need to put them into the shape of a ladder, the k-th row must have exactly k coins.

Given a number n, to find the full number of rows can be formed in a stepped line.

n is a nonnegative integer, and in the range of 32-bit signed integer in.

Example 1:

n = 5

Coins can be arranged in the following lines:

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¤ ¤
¤ ¤

Because the third row is not complete, so the return 2.
Example 2:

n = 8

Coins can be arranged in the following lines:

¤
¤ ¤
¤ ¤ ¤
¤ ¤

Because the fourth row is not complete, it returns 3.

PS:
According to the mathematical formula, k (k + 1) / 2 = n, which can be interpreted as a positive number: k = sqrt (2n + 1 /4) - 1/2. Then ask the whole can.
The only problem is that, where 2n + 1/4 may exceed sqrt function parameters.
Thus, what we can transform, k = sqrt (2) * sqrt (n + 1/8) - 1/2, so that it will not overrun the square root.
So, we have such a line of code

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