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:
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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:

class Solution {
    public int arrangeCoins(int n) {
        int left = 1, right = n;
        long target = (long) n;
        while (left <= right) {
            int mid = left + (right - left) / 2;
            if ((1 + mid) * (long) mid / 2 <= target) {
                left = mid + 1;
            } else {
                right = mid - 1;
            }
        }
        return right;
    }
}