C++ Program to Compute Combinations using Matrix Multiplication

#include<iostream>
 
using namespace std;
 
// A function to find the factorial of a given number using matrix multiplication method.
int MatFactorial(int n)
{
	int i, j, k, matA[n+1][n+1], matB[n+1][n+1], matC[n+1][n+1], count;
	count = n;
	// Assigning numbers from 1 to n to the super diagonal indexes of the matrix.
	// Assigning result matric matC[][] to zero initially.
	for(i = 0; i < n+1; i++)
	{
		for(j = 0; j < n+1; j++)
		{
			if(j == i+1)
				matA[i][j] = i+1;
			else
				matA[i][j] = 0;
 
			// Assign matB[][] equal to initially to compute square.	
			matB[i][j] = matA[i][j];
			matC[i][j] = 0;	
		}
	}
 
	flag:
	// Multiply matA[][] and matB[][] and store the data into matC[][].
	for(i = 0; i < n+1; i++)
	{
		for(j = 0; j < n+1; j++)
		{
			for(k = 0; k < n+1; k++)
			{
				matC[i][j] += matA[i][k]*matB[k][j];
			}	
		}
	}
 
	// Assign matB as the result matrix matC[][] and then assign matC[i][j] element to zero again.
	for(i = 0; i < n+1; i++)
	{
		for(j = 0; j < n+1; j++)
		{
			matB[i][j] = matC[i][j];
			matC[i][j] = 0;	
		}
	}
 
	count--;
	// We need to compute the matA[][] raise to the power of n so if count is more than 1 then increase the power of matA[][].
	if(count > 1)
		goto flag;
 
	// If matA[][] raise to n is calculated, then return the last element of the first row of matB[][], as the factorial of n.	
	return matB[0][n];
}
 
int main()
{
	int n, r,  result;
	cout<<"A program to find combination from nCr format using matrix multiplication method:-";
	cout<<"\n\n\tEnter the value of n: ";
	cin>>n;
	cout<<"\tEnter the value of r: ";
	cin>>r;
 
	// Get result using formulae to calculate combinations.
	result = MatFactorial(n)/(MatFactorial(r)*MatFactorial(n-r));
 
	cout<<"\nThe number of possible combinations is: "<<result;
 
	return 0;
}