Matrix Multiplication | Recursive

Given two matrices A and B. The task is to multiply matrix A and matrix B recursively. If matrix A and matrix B are not multiplicative compatible, then generate output “Not Possible”.

Examples :

Input: A = 12 56
           45 78
       B = 2 6
           5 8
Output: 304 520
        480 894

Input: A = 1 2 3
           4 5 6
           7 8 9
       B = 1 2 3
           4 5 6
           7 8 9

Output: 30  36  42  
        66  81  96  
       102 126 150  

It is recommended to first refer Iterative Matrix Multiplication.

First check if multiplication between matrices is possible or not. For this, check if number of columns of first matrix is equal to number of rows of second matrix or not. If both are equal than proceed further otherwise generate output “Not Possible”.

In Recursive Matrix Multiplication, we implement three loops of Iteration through recursive calls. The inner most Recursive call of multiplyMatrix() is to iterate k (col1 or row2). The second recursive call of multiplyMatrix() is to change the columns and the outermost recursive call is to change rows.

Below is Recursive Matrix Multiplication code. 

Java

// Java recursive code for Matrix Multiplication

class GFG
{
    public static int MAX = 100;

    // Note that below variables are static
    // i and j are used to know current cell of
    // result matrix C[][]. k is used to know
    // current column number of A[][] and row
    // number of B[][] to be multiplied
    public static int i = 0, j = 0, k = 0;

    static void multiplyMatrixRec(int row1, int col1, int A[][],
                       int row2, int col2, int B[][],
                       int C[][])
    {
        // If all rows traversed
        if (i >= row1)
            return;

        // If i < row1
        if (j < col2)
        {
            if (k < col1)
            {
                C[i][j] += A[i][k] * B[k][j];
                k++;

                multiplyMatrixRec(row1, col1, A, row2, col2, B, C);
            }

            k = 0;
            j++;
            multiplyMatrixRec(row1, col1, A, row2, col2, B, C);
        }

        j = 0;
        i++;
        multiplyMatrixRec(row1, col1, A, row2, col2, B, C);
    }

    // Function to multiply two matrices A[][] and B[][]
    static void multiplyMatrix(int row1, int col1, int A[][],
                    int row2, int col2, int B[][])
    {
        if (row2 != col1)
        {
            System.out.println("Not Possible\n");
            return;
        }

        int[][] C = new int[MAX][MAX];

        multiplyMatrixRec(row1, col1, A, row2, col2, B, C);

        // Print the result
        for (int i = 0; i < row1; i++)
        {
            for (int j = 0; j < col2; j++)
                System.out.print(C[i][j]+" ");

            System.out.println();
        }
    }

    // driver program
    public static void main (String[] args)
    {
        int row1 = 3, col1 = 3, row2 = 3, col2 = 3;
        int A[][] = { {1, 2, 3},
                      {4, 5, 6},
                      {7, 8, 9}};

        int B[][] = { {1, 2, 3},
                      {4, 5, 6},
                      {7, 8, 9} };

        multiplyMatrix(row1, col1, A, row2, col2, B);
    }
}

// Contributed by Pramod Kumar

Python3

# Recursive code for Matrix Multiplication
MAX = 100
i = 0
j = 0
k = 0

def multiplyMatrixRec(row1, col1, A,
                      row2, col2, B, C):

    # Note that below variables are static
    # i and j are used to know current cell of
    # result matrix C[][]. k is used to know
    # current column number of A[][] and row
    # number of B[][] to be multiplied
    global i
    global j
    global k

    # If all rows traversed.
    if (i >= row1):
        return

    # If i < row1
    if (j < col2):
        if (k < col1):
            C[i][j] += A[i][k] * B[k][j]
            k += 1
            multiplyMatrixRec(row1, col1, A,
                              row2, col2,B, C)

        k = 0
        j += 1
        multiplyMatrixRec(row1, col1, A,
                          row2, col2, B, C)

    j = 0
    i += 1
    multiplyMatrixRec(row1, col1, A,
                      row2, col2, B, C)

# Function to multiply two matrices
# A[][] and B[][]
def multiplyMatrix(row1, col1, A, row2, col2, B):
    if (row2 != col1):
        print("Not Possible")
        return

    C = [[0 for i in range(MAX)]
            for i in range(MAX)]
    multiplyMatrixRec(row1, col1, A,
                      row2, col2, B, C)

    # Print the result
    for i in range(row1):
        for j in range(col2):
            print( C[i][j], end = " ")
        print()

# Driver Code
A = [[1, 2, 3],
     [4, 5, 6],
     [7, 8, 9]]
B = [[1, 2, 3],
     [4, 5, 6],
     [7, 8, 9]]

row1 = 3
col1 = 3
row2 = 3
col2 = 3
multiplyMatrix(row1, col1, A, row2, col2, B)

# This code is contributed by sahilshelangia

C#

// C# recursive code for
// Matrix Multiplication
using System;

class GFG
{
    public static int MAX = 100;

    // Note that below variables
    // are static i and j are used
    // to know current cell of result
    // matrix C[][]. k is used to
    // know current column number of
    // A[][] and row number of B[][]
    // to be multiplied
    public static int i = 0, j = 0, k = 0;

    static void multiplyMatrixRec(int row1, int col1,
                                  int [,]A, int row2,
                                  int col2, int [,]B,
                                  int [,]C)
    {
        // If all rows traversed
        if (i >= row1)
            return;

        // If i < row1
        if (j < col2)
        {
            if (k < col1)
            {
                C[i, j] += A[i, k] * B[k, j];
                k++;

                multiplyMatrixRec(row1, col1, A,
                                  row2, col2, B, C);
            }

            k = 0;
            j++;
            multiplyMatrixRec(row1, col1, A,
                              row2, col2, B, C);
        }

        j = 0;
        i++;
        multiplyMatrixRec(row1, col1, A,
                          row2, col2, B, C);
    }

    // Function to multiply two
    // matrices A[][] and B[][]
    static void multiplyMatrix(int row1, int col1,
                               int [,]A, int row2,
                               int col2, int [,]B)
    {
        if (row2 != col1)
        {
            Console.WriteLine("Not Possible\n");
            return;
        }

        int[,]C = new int[MAX, MAX];

        multiplyMatrixRec(row1, col1, A,
                          row2, col2, B, C);

        // Print the result
        for (int i = 0; i < row1; i++)
        {
            for (int j = 0; j < col2; j++)
                Console.Write(C[i, j] + " ");

            Console.WriteLine();
        }
    }

    // Driver Code
    static public void Main ()
    {
        int row1 = 3, col1 = 3,
            row2 = 3, col2 = 3;
        int [,]A = {{1, 2, 3},
                    {4, 5, 6},
                    {7, 8, 9}};

        int [,]B = {{1, 2, 3},
                    {4, 5, 6},
                    {7, 8, 9}};

        multiplyMatrix(row1, col1, A,
                       row2, col2, B);
    }
}

// This code is contributed by m_kit

Javascript

<script>
    // Javascript recursive code for Matrix Multiplication

    let MAX = 100;

    // Note that below variables are static
    // i and j are used to know current cell of
    // result matrix C[][]. k is used to know
    // current column number of A[][] and row
    // number of B[][] to be multiplied
    let i = 0, j = 0, k = 0;

    function multiplyMatrixRec(row1, col1, A, row2, col2, B, C)
    {
        // If all rows traversed
        if (i >= row1)
            return;

        // If i < row1
        if (j < col2)
        {
            if (k < col1)
            {
                C[i][j] += A[i][k] * B[k][j];
                k++;

                multiplyMatrixRec(row1, col1, A, row2, col2, B, C);
            }

            k = 0;
            j++;
            multiplyMatrixRec(row1, col1, A, row2, col2, B, C);
        }

        j = 0;
        i++;
        multiplyMatrixRec(row1, col1, A, row2, col2, B, C);
    }

    // Function to multiply two matrices A[][] and B[][]
    function multiplyMatrix(row1, col1, A, row2, col2, B)
    {
        if (row2 != col1)
        {
            document.write("Not Possible" + "</br>");
            return;
        }

        let C = new Array(MAX);
        for(let i = 0; i < MAX; i++)
        {
            C[i] = new Array(MAX);
            for(let j = 0; j < MAX; j++)
            {
                C[i][j] = 0;
            }
        }

        multiplyMatrixRec(row1, col1, A, row2, col2, B, C);

        // Print the result
        for (let i = 0; i < row1; i++)
        {
            for (let j = 0; j < col2; j++)
                document.write(C[i][j]+" ");

            document.write("</br>");
        }
    }

    let row1 = 3, col1 = 3, row2 = 3, col2 = 3;
    let A = [ [1, 2, 3],
              [4, 5, 6],
              [7, 8, 9] ];

    let B = [ [1, 2, 3],
              [4, 5, 6],
              [7, 8, 9] ];

    multiplyMatrix(row1, col1, A, row2, col2, B);

</script>

C++

// Recursive code for Matrix Multiplication
#include <stdio.h>

const int MAX = 100;

void multiplyMatrixRec(int row1, int col1, int A[][MAX],
                       int row2, int col2, int B[][MAX],
                       int C[][MAX])
{
    // Note that below variables are static
    // i and j are used to know current cell of
    // result matrix C[][]. k is used to know
    // current column number of A[][] and row
    // number of B[][] to be multiplied
    static int i = 0, j = 0, k = 0;

    // If all rows traversed.
    if (i >= row1)
        return;

    // If i < row1
    if (j < col2) {
        if (k < col1) {
            C[i][j] += A[i][k] * B[k][j];
            k++;

            multiplyMatrixRec(row1, col1, A, row2, col2, B,
                              C);
        }

        k = 0;
        j++;
        multiplyMatrixRec(row1, col1, A, row2, col2, B, C);
    }

    j = 0;
    i++;
    multiplyMatrixRec(row1, col1, A, row2, col2, B, C);
}

// Function to multiply two matrices A[][] and B[][]
void multiplyMatrix(int row1, int col1, int A[][MAX],
                    int row2, int col2, int B[][MAX])
{
    if (row2 != col1) {
        printf("Not Possible\n");
        return;
    }

    int C[MAX][MAX] = { 0 };

    multiplyMatrixRec(row1, col1, A, row2, col2, B, C);

    // Print the result
    for (int i = 0; i < row1; i++) {
        for (int j = 0; j < col2; j++)
            printf("%d  ", C[i][j]);

        printf("\n");
    }
}

// Driven Program
int main()
{
    int A[][MAX]
        = { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 } };

    int B[][MAX]
        = { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 } };

    int row1 = 3, col1 = 3, row2 = 3, col2 = 3;
    multiplyMatrix(row1, col1, A, row2, col2, B);

    return 0;
}

// This code is contributed by Aarti_Rathi

Output

30 36 42 
66 81 96 
102 126 150 

Time Complexity: O(row1 * col2)
Auxiliary Space: O(log (max(row1,col2)), As implicit stack is used due to recursion

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