441. Arranging Coins

• Difficulty: Easy

• Topics: Math, Binary Search

• Similar Questions:

Problem:

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:
¤
¤ ¤
¤ ¤

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

Example 2:

n = 8

The coins can form the following rows: ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤

Because the 4th row is incomplete, we return 3. </pre> </p>

Solutions:

class Solution {
public:
    int arrangeCoins(int n) {
        long left = 0;
        long right = INT_MAX / 4;

        while (left < right) {
            long mid = right - (right - left) / 2;
            if ( (mid + 1) * mid / 2 > n)  {
                right = mid - 1;
            } else {
                left = mid;
            }
        }

        return left;
    }
};