Number of non-negative integral solutions of sum equation in C++

C++Server Side ProgrammingProgramming

In this tutorial, we are going to write a program that finds the number non-negative integral solution of sum equation.

The sum equation is x + y + z = n. You are given the number n, you need to find the number of solution for the equation.

Let's see the steps to solve the problem.

  • Initialise the number m.

  • Initialise the count to 0.

  • Write three nested loops to get all the combinations of three numbers.

    • Check the validation of the equation.

    • If the current numbers satisfies the equation, then increment the count.

  • Return the count.

Example

Let's see the code.

 Live Demo

#include <bits/stdc++.h>
using namespace std;
int getEquationSolutionCount(int n) {
   int count = 0;
   for (int i = 0; i <= n; i++) {
      for (int j = 0; j <= n - i; j++) {
         for (int k = 0; k <= n - i - j; k++) {
            if (i + j + k == n) {
               count++;
            }
         }
      }
   }
   return count;
}
int main() {
   int n = 10;
   cout << getEquationSolutionCount(n) << endl;
   return 0;
}

Output

If you run the above code, then you will get the following result.

10

Conclusion

If you have any queries in the tutorial, mention them in the comment section.

raja
Published on 03-Jul-2021 08:21:10
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