/*
This is the java implementation of classic Coppersmith-Freivalds’ algorithm to check whether
the multiplication of matrix A and B equals the given matrix C. It does it by checking A*(B*r)-(C*r) where r
 is any random column vector consisting only 0/1 as its elements. If this value is zero algorithm prints Yes, No otherwise.
*/

//This is a sample program to check whether the matrix c is equal to the multiplication of a and b
//implementation of Coppersmith Freivalds Algorithm
import java.util.Random;
import java.util.Scanner;

public class Coppersmith_Freivalds_Algorithm
{
    public static void main(String args[])
    {
        System.out.println("Enter the dimesion of the matrices: ");
        Scanner input = new Scanner(System.in);
        int n = input.nextInt();
        System.out.println("Enter the 1st matrix: ");
        double a[][] = new double[n][n];
        for(int i=0; i<n; i++)
            {
                for(int j=0; j<n; j++)
                    {
                        a[i][j] = input.nextDouble();
                    }
            }
        System.out.println("Enter the 2st matrix: ");
        double b[][] = new double[n][n];
        for(int i=0; i<n; i++)
            {
                for(int j=0; j<n; j++)
                    {
                        b[i][j] = input.nextDouble();
                    }
            }
        System.out.println("Enter the result matrix: ");
        double c[][] = new double[n][n];
        for(int i=0; i<n; i++)
            {
                for(int j=0; j<n; j++)
                    {
                        c[i][j] = input.nextDouble();
                    }
            }
        //random generation of the r vector containing only 0/1 as its elements
        double [][]r = new double[n][1];
        Random random = new Random();
        for(int i=0; i<n; i++)
            {
                r[i][0] = random.nextInt(2);
            }
        //test A * (b*r) - (C*) = 0
        double br[][] = new double[n][1];
        double cr[][] = new double[n][1];
        double abr[][] = new double[n][1];
        br = multiplyVector(b, r, n);
        cr = multiplyVector(c, r, n);
        abr = multiplyVector(a, br, n);
        //check for all zeros in abr
        boolean flag = true;
        for(int i=0; i<n; i++)
            {
                if(abr[i][0] == 0)
                    continue;
                else
                    flag = false;
            }
        if(flag == true)
            System.out.println("Yes");
        else
            System.out.println("No");
        input.close();
    }

    public static double[][] multiplyVector(double[][] a, double[][] b, int n)
    {
        double result[][] = new double[n][1];
        for (int i = 0; i < n; i++)
            {
                for (int j = 0; j < 1; j++)
                    {
                        for (int k = 0; k < n; k++)
                            {
                                result[i][j] = result[i][j] + a[i][k] * b[k][j];
                            }
                    }
            }
        return result;
    }
}


/*
Output:
Enter the dimesion of the matrices:
2
Enter the 1st matrix:
2 3
3 4
Enter the 2st matrix:
1 0
1 2
Enter the result matrix:
6 5
8 7