Check if a Number can be Represented as a Sum of 2 Triangular Numbers in C++

In this section, we will see if we can express one number as the sum of two triangular numbers or not. The triangular numbers are like below −

From the example, we can see that 1, 3, 6, 10 are some triangular numbers. We need to express a number N (say 16) as sum of two triangular numbers (6, 10).

The approach is very simple. We have to get all triangular numbers less than N. Form a set from these values. Now we have to take a number say X from the set, and check whether N – X is present in the set, then X can be represented as sum of two triangular numbers.

Example

 Live Demo

#include <iostream>
#include <set>
using namespace std;
bool isSumTriangularNum(int n) {
   set<int> s;
   int i = 1;
   while (1) { //find and store all triangular numbers below n, and store into set
      int x = i * (i + 1) / 2;
      if (x >= n)
         break;
      s.insert(x);
      i++;
   }
   for (auto x : s)
   if (s.find(n - x) != s.end())
   return true;
   return false;
}
int main() {
   int num = 16;
   if(isSumTriangularNum(num)){
      cout << "Can be represented";
   }else{
      cout << "Cannot be represented";
   }
}

Output

Can be represented