LeetCode-in-Java

441. Arranging Coins

Easy

You have n coins and you want to build a staircase with these coins. The staircase consists of k rows where the ith row has exactly i coins. The last row of the staircase may be incomplete.

Given the integer n, return the number of complete rows of the staircase you will build.

Example 1:

Input: n = 5

Output: 2

Explanation: Because the 3^rd row is incomplete, we return 2.

Example 2:

Input: n = 8

Output: 3

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

Constraints:

• 1 <= n <= 231 - 1

Solution

public class Solution {
    public int arrangeCoins(int n) {
        if (n < 0) {
            throw new IllegalArgumentException(
                    "Input Number is invalid. Only positive numbers are allowed");
        }
        if (n <= 1) {
            return n;
        }
        if (n <= 3) {
            return n == 3 ? 2 : 1;
        }
        // Binary Search space will start from 2 to n/2.
        long start = 2;
        long end = n / 2;
        while (start <= end) {
            long mid = start + (end - start) / 2;
            long coinsFilled = mid * (mid + 1) / 2;
            if (coinsFilled == n) {
                return (int) mid;
            }
            if (coinsFilled < n) {
                start = mid + 1;
            } else {
                end = mid - 1;
            }
        }
        // Since at this point start > end, start will start pointing to a value greater
        // than the desired result. We will return end as it will point to the correct
        // int value.
        return (int) end;
    }
}

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