C++ Programming Code Examples
C++ > Arrays and Matrices Code Examples
Program to Compute Combinations using Matrix Multiplication
/* Program to Compute Combinations using Matrix Multiplication
1. This algorithm computes the combination using matrix multiplication method.
2. The time complexity to compute this is O(n*n*n).
3. This algorithm is very expensive to compute a combination.
This is a 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 x, 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(x = 0; x < n+1; x++)
{
for(j = 0; j < n+1; j++)
{
if(j == x+1)
matA[x][j] = x+1;
else
matA[x][j] = 0;
// Assign matB[][] equal to initially to compute square.
matB[x][j] = matA[x][j];
matC[x][j] = 0;
}
}
flag:
// Multiply matA[][] and matB[][] and store the data into matC[][].
for(x = 0; x < n+1; x++)
{
for(j = 0; j < n+1; j++)
{
for(k = 0; k < n+1; k++)
{
matC[x][j] += matA[x][k]*matB[k][j];
}
}
}
// Assign matB as the result matrix matC[][] and then assign matC[x][j] element to zero again.
for(x = 0; x < n+1; x++)
{
for(j = 0; j < n+1; j++)
{
matB[x][j] = matC[x][j];
matC[x][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;
}
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