441. Arranging Coins .java

/*
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 3rd row is incomplete, we return 2.
Example 2:


Input: n = 8
Output: 3
Explanation: Because the 4th row is incomplete, we return 3.
 

Constraints:

1 <= n <= 231 - 1
*/

//Solution:
class Solution {
    public int arrangeCoins(int n) {
        long start = 1;
        long end = n;
        while(start <= end){
            long mid =  start + (end  - start) / 2;
            if(n >= (mid*(mid + 1)/2))
                start = mid + 1;
            else
                end = mid - 1;
        }
        return (int)start-1;
    }
    
    
}