package DivideAndConquer;

// Java Program to Implement Strassen Algorithm
 
// Class Strassen matrix multiplication
public class StrassenMatrixMultiplication {
 
    // Method 1
    // Function to multiply matrices
    public int[][] multiply(int[][] A, int[][] B)
    {
        int n = A.length;

        int[][] R = new int[n][n];
 
        if (n == 1)

            R[0][0] = A[0][0] * B[0][0];

        else {
            // Dividing Matrix into parts
            // by storing sub-parts to variables
            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 parts
            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 parts
            split(B, B11, 0, 0);
            split(B, B12, 0, n / 2);
            split(B, B21, n / 2, 0);
            split(B, B22, n / 2, n / 2);
 
            // Using Formulas as described in algorithm
 
            // M1:=(A1+A3)×(B1+B2)
            int[][] M1
                = multiply(add(A11, A22), add(B11, B22));
           
            // M2:=(A2+A4)×(B3+B4)
            int[][] M2 = multiply(add(A21, A22), B11);
           
            // M3:=(A1−A4)×(B1+A4)
            int[][] M3 = multiply(A11, sub(B12, B22));
           
            // M4:=A1×(B2−B4)
            int[][] M4 = multiply(A22, sub(B21, B11));
           
            // M5:=(A3+A4)×(B1)
            int[][] M5 = multiply(add(A11, A12), B22);
           
            // M6:=(A1+A2)×(B4)
            int[][] M6
                = multiply(sub(A21, A11), add(B11, B12));
           
            // M7:=A4×(B3−B1)
            int[][] M7
                = multiply(sub(A12, A22), add(B21, B22));
 
            // P:=M2+M3−M6−M7
            int[][] C11 = add(sub(add(M1, M4), M5), M7);
           
            // Q:=M4+M6
            int[][] C12 = add(M3, M5);
           
            // R:=M5+M7
            int[][] C21 = add(M2, M4);
           
            // S:=M1−M3−M4−M5
            int[][] C22 = add(sub(add(M1, M3), M2), M6);

            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 R;
    }
 
    // Method 2
    // Function to subtract 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;
    }
 
    // Method 3
    // Function 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;
    }
 
    // Method 4
    // Function 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];
    }
 
    // Method 5
    // Function to join child matrices
    // into (to) 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];
    }
 
    // Method 5
    // Main driver method
    public static void main(String[] args)
    {
        System.out.println("Strassen Multiplication Algorithm Implementation For Matrix Multiplication :\n");

        StrassenMatrixMultiplication s = new StrassenMatrixMultiplication();
 
        // Size of matrix
        // Considering size as 4 in order to illustrate
        int N = 4;
 
        // Matrix A
        // Custom input to matrix
        int[][] A = { { 1, 2, 5, 4 },
                      { 9, 3, 0, 6 },
                      { 4, 6, 3, 1 },
                      { 0, 2, 0, 6 } };
 
        // Matrix B
        // Custom input to matrix
        int[][] B = { { 1, 0, 4, 1 },
                      { 1, 2, 0, 2 },
                      { 0, 3, 1, 3 },
                      { 1, 8, 1, 2 } };
 
        // Matrix C computations
 
        // Matrix C calling method to get Result
        int[][] C = s.multiply(A, B);
 
        System.out.println("\nProduct of matrices A and  B : ");
 
        // Print the output
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++)
                System.out.print(C[i][j] + " ");
            System.out.println();
        }
    }
}