# Java Program to Implement Strassen Algorithm

This is a Java Program to Implement Strassen Matrix Multiplication Algorithm. This is a program to compute product of two matrices using Strassen Multiplication algorithm. Here the dimensions of matrices must be a power of 2.

Here is the source code of the Java Program to Implement Strassen Matrix Multiplication Algorithm. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

/**
** Java Program to Implement Strassen Algorithm
**/

import java.util.Scanner;

/** Class Strassen **/
public class Strassen
{
/** Function to multiply matrices **/
public int[][] multiply(int[][] A, int[][] B)
{
int n = A.length;
int[][] R = new int[n][n];
/** base case **/
if (n == 1)
R[0][0] = A[0][0] * B[0][0];
else
{
int[][] A11 = new int[n/2][n/2];
int[][] A12 = new int[n/2][n/2];
int[][] A21 = new int[n/2][n/2];
int[][] A22 = new int[n/2][n/2];
int[][] B11 = new int[n/2][n/2];
int[][] B12 = new int[n/2][n/2];
int[][] B21 = new int[n/2][n/2];
int[][] B22 = new int[n/2][n/2];

/** Dividing matrix A into 4 halves **/
split(A, A11, 0 , 0);
split(A, A12, 0 , n/2);
split(A, A21, n/2, 0);
split(A, A22, n/2, n/2);
/** Dividing matrix B into 4 halves **/
split(B, B11, 0 , 0);
split(B, B12, 0 , n/2);
split(B, B21, n/2, 0);
split(B, B22, n/2, n/2);

/**
M1 = (A11 + A22)(B11 + B22)
M2 = (A21 + A22) B11
M3 = A11 (B12 - B22)
M4 = A22 (B21 - B11)
M5 = (A11 + A12) B22
M6 = (A21 - A11) (B11 + B12)
M7 = (A12 - A22) (B21 + B22)
**/

int [][] M2 = multiply(add(A21, A22), B11);
int [][] M3 = multiply(A11, sub(B12, B22));
int [][] M4 = multiply(A22, sub(B21, B11));
int [][] M5 = multiply(add(A11, A12), B22);
int [][] M6 = multiply(sub(A21, A11), add(B11, B12));
int [][] M7 = multiply(sub(A12, A22), add(B21, B22));

/**
C11 = M1 + M4 - M5 + M7
C12 = M3 + M5
C21 = M2 + M4
C22 = M1 - M2 + M3 + M6
**/
int [][] C12 = add(M3, M5);
int [][] C21 = add(M2, M4);

/** join 4 halves into one result matrix **/
join(C11, R, 0 , 0);
join(C12, R, 0 , n/2);
join(C21, R, n/2, 0);
join(C22, R, n/2, n/2);
}
/** return result **/
return R;
}
/** Funtion to sub two matrices **/
public int[][] sub(int[][] A, int[][] B)
{
int n = A.length;
int[][] C = new int[n][n];
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
C[i][j] = A[i][j] - B[i][j];
return C;
}
/** Funtion to add two matrices **/
public int[][] add(int[][] A, int[][] B)
{
int n = A.length;
int[][] C = new int[n][n];
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
C[i][j] = A[i][j] + B[i][j];
return C;
}
/** Funtion to split parent matrix into child matrices **/
public void split(int[][] P, int[][] C, int iB, int jB)
{
for(int i1 = 0, i2 = iB; i1 < C.length; i1++, i2++)
for(int j1 = 0, j2 = jB; j1 < C.length; j1++, j2++)
C[i1][j1] = P[i2][j2];
}
/** Funtion to join child matrices intp parent matrix **/
public void join(int[][] C, int[][] P, int iB, int jB)
{
for(int i1 = 0, i2 = iB; i1 < C.length; i1++, i2++)
for(int j1 = 0, j2 = jB; j1 < C.length; j1++, j2++)
P[i2][j2] = C[i1][j1];
}
/** Main function **/
public static void main (String[] args)
{
Scanner scan = new Scanner(System.in);
System.out.println("Strassen Multiplication Algorithm Test\n");
/** Make an object of Strassen class **/
Strassen s = new Strassen();

System.out.println("Enter order n :");
int N = scan.nextInt();
/** Accept two 2d matrices **/
System.out.println("Enter N order matrix 1\n");
int[][] A = new int[N][N];
for (int i = 0; i < N; i++)
for (int j = 0; j < N; j++)
A[i][j] = scan.nextInt();

System.out.println("Enter N order matrix 2\n");
int[][] B = new int[N][N];
for (int i = 0; i < N; i++)
for (int j = 0; j < N; j++)
B[i][j] = scan.nextInt();

int[][] C = s.multiply(A, B);

System.out.println("\nProduct of matrices A and  B : ");
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
System.out.print(C[i][j] +" ");
System.out.println();
}

}
}


Output:

Strassen Multiplication Algorithm Test

Enter order n :
4
Enter N order matrix 1

2 3 1 6
4 0 0 2
4 2 0 1
0 3 5 2
Enter N order matrix 2

3 0 4 3
1 2 0 2
0 3 1 4
5 1 3 2

Product of matrices A and  B :
39 15 27 28
22 2 22 16
19 5 19 18
13 23 11 30