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Number of non-negative integral solutions of sum equation in C++
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 solutions for the equation. Let's see an example.
Input
2
Output
6
Solutions are
0 0 2 0 1 1 0 2 0 1 0 1 1 1 0 2 0 0
Algorithm
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.
Implementation
Following is the implementation of the above algorithm in C++
#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.
66
Updated on: 26-Oct-2021
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