Arranging Coins in C++

Suppose we have n coins that we want to form in a staircase shape, every k-th row must have exactly k coins. So if we have n, then we have to find the total number of full staircase rows that can be formed.

So, if the input is like 5, then the output will be 2, as using 5 coins we can make two full starecase rows, the last one needs three, but we have to remain 2 −

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This can be done directly by using this formula −

$$\frac{\sqrt{(8n+1)}-1}{2}$$

Example 

Let us see the following implementation to get a better understanding −

 Live Demo

#include <bits/stdc++.h>
using namespace std;
class Solution {
public:
   int arrangeCoins(int n) {
      return (sqrt(8*(long long)n+1)-1)/2;
   }
};
main(){
   Solution ob;
   cout << (ob.arrangeCoins(13));
}

Input

13

Output

4