Arranging Coins : LeetCode

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) {
        long start =0;
        long end = n;
        while(start<=end){
            long k = start+(end-start)/2;
            long total = k*(k+1)/2;
            if(total==n){
                return (int)k;
            }
            if(n<total){
                end = k-1;
            }else{
                start = k+1;
            }
        }
        return (int)end;
    }
}