Maximum Height of Triangular Arrangement of Array Values in C++

Problem statement

Given an array, we need to find the maximum height of the triangle which we can form, from the array values such that every (i+1)^th level contain more elements with the larger sum from the previous level.

Example

If input array is {40, 100, 20, 30 } then answer is 2 as −

We can have 100 and 20 at the bottom level and either 40 or 30 at the upper level of the pyramid

Algorithm

Our solution just lies on the logic that if we have maximum height h possible for our pyramid then ( h * (h + 1) ) / 2 elements must be present in the array

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
int getMaximumHeight(int *arr, int n) {
   int result = 1;
   for (int i = 1; i <= n; ++i) {
      long long y = (i * (i + 1)) / 2;
      if (y < n) {
         result = i;
      } else {
         break;
      }
   }
   return result;
}
int main() {
   int arr[] = {40, 100, 20, 30};
   int n = sizeof(arr) / sizeof(arr[0]);
   cout << "Result = " << getMaximumHeight(arr, n) << endl;
   return 0;
}

Output

When you compile and execute above program. It generates following output −

Result = 2