Arranging Coins

Problem

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.

Constraints

• 1 <= n <= 231 - 1

Solution

The problem Arranging Coins can be solved using a simple equation. Sum of all integers between [1, n] is n * (n + 1) / 2. Therefore, the result can be calculated by finding the largest integer x where x * (x + 1) / 2 <= n. Based on Quadratic formula, x can be gained using the following equation.

Implementation

class Solution
{
  public:
    int arrangeCoins(int n) { return (sqrt(1 + 8.0 * n) - 1) / 2; }
};