Write a program in C/C++ to find the maximum height when coins are arranged in a triangle.

In this section, we will see an interesting problem. There are N coins. We have to find out what is the maximum height we can reach if we arrange the coins in a pyramid shape. In this way, 1 coin will be placed in the first row, 2 coins in the second row, and so on.

In the given diagram, we can see that to build a pyramid with a height of 3, we need at least 6 coins. We cannot build a pyramid with a height of 4 until we have 10 coins. Now let's see how to check the maximum height.

We can use the following formula to determine the height.

Example

Real-time demonstration

#include<iostream>
#include<cmath>
using namespace std;
int getMaxHeight(int n) {
   int height = (-1 + sqrt(1 + 8 * n)) / 2;
   return height;
}
main() {
   int N;
   cout << "Enter number of coins: " ;
   cin >> N;
   cout << "Height of pyramid: " << getMaxHeight(N);
}

Output

Enter number of coins: 13
Height of pyramid: 4

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