Traverse a given Matrix using Recursion

Given a matrix arr of size N x M, the task is to traverse this matrix using recursion.

Examples:

Input: arr[][] = {{1, 2, 3}, 
                  {4, 5, 6},
                  {7, 8, 9}} 
Output: 1, 2, 3, 4, 5, 6, 7, 8, 9

Input: M[][] = {{11, 12, 13}, 
                  {14, 15, 16}, 
                  {17, 18, 19}}
Output: 11, 12, 13, 14, 15, 16, 17, 18, 19

Approach: Below are the steps to traverse the Matrix recursively:

  • Base Case: If the current row or column exceeds the size N or M, respectively, the recursion is stopped.
    • If the current column exceeds the total number of columns M, then the next row is started.
      if (current_col >= M)
          This row ends.
          Start for next row
      
    • If the current row exceeds the total number of rows N, then the complete traversal is stopped.
      if (current_row >= N)
          Matrix has been
          traversed completely
      
  • Recursive Case: In each recursive call,
    1. The current element of the Matrix is printed.
    2. Two recursive calls are made:
      • One to traverse the next row, and
      • Another to traverse the next column.

    After we print all the elements of the row and when we move on to the next column, this again calls the row in recursion, thereby printing all the elements of the matrix.

Below is the implementation of the above approach:

C++

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// C++ program to traverse the matrix recursively
  
#include <iostream>
using namespace std;
  
#define N 2
#define M 3
  
// Function to traverse the matrix recursively
int traverseMatrix(int arr[N][M], int current_row,
                   int current_col)
{
    // If the entire column is traversed
    if (current_col >= M)
        return 0;
  
    // If the entire row is traversed
    if (current_row >= N)
        return 1;
  
    // Print the value of the current
    // cell of the matrix
    cout << arr[current_row][current_col] << ", ";
  
    // Recursive call to traverse the matrix
    // in the Horizontal direction
    if (traverseMatrix(arr, current_row,
                       current_col + 1)
        == 1)
        return 1;
  
    // Recursive call for changing the
    // Row of the matrix
    return traverseMatrix(arr,
                          current_row + 1,
                          0);
}
  
// Driver code
int main()
{
    int arr[N][M] = { { 1, 2, 3 },
                      { 4, 5, 6 } };
  
    traverseMatrix(arr, 0, 0);
    return 0;
}

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Java

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// Java program to traverse the matrix recursively
class GFG {
      
    final static int N = 2;
    final static int  M = 3;
      
    // Function to traverse the matrix recursively
    static int traverseMatrix(int arr[][], int current_row,
                       int current_col)
    {
        // If the entire column is traversed
        if (current_col >= M)
            return 0;
      
        // If the entire row is traversed
        if (current_row >= N)
            return 1;
      
        // Print the value of the current
        // cell of the matrix
        System.out.print(arr[current_row][current_col] + ", ");
      
        // Recursive call to traverse the matrix
        // in the Horizontal direction
        if (traverseMatrix(arr, current_row,
                           current_col + 1)
            == 1)
            return 1;
      
        // Recursive call for changing the
        // Row of the matrix
        return traverseMatrix(arr,
                              current_row + 1,
                              0);
    }
      
    // Driver code
    public static void main (String[] args)
    {
        int arr[][] = { { 1, 2, 3 },
                          { 4, 5, 6 } };
      
        traverseMatrix(arr, 0, 0);
    }
}
  
// This code is contributed by AnkitRai01

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C#

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// C# program to traverse the matrix recursively
  
using System;
  
public class GFG {
      
    static int N = 2;
    static int  M = 3;
      
    // Function to traverse the matrix recursively
    static int traverseMatrix(int [,]arr, int current_row,
                       int current_col)
    {
        // If the entire column is traversed
        if (current_col >= M)
            return 0;
      
        // If the entire row is traversed
        if (current_row >= N)
            return 1;
      
        // Print the value of the current
        // cell of the matrix
        Console.Write(arr[current_row,current_col] + ", ");
      
        // Recursive call to traverse the matrix
        // in the Horizontal direction
        if (traverseMatrix(arr, current_row,
                           current_col + 1)
            == 1)
            return 1;
      
        // Recursive call for changing the
        // Row of the matrix
        return traverseMatrix(arr,
                              current_row + 1,
                              0);
    }
      
    // Driver code
    public static void Main (string[] args)
    {
        int [,]arr = { { 1, 2, 3 },
                          { 4, 5, 6 } };
      
        traverseMatrix(arr, 0, 0);
    }
}
  
// This code is contributed by AnkitRai01

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Python3

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# Python3 program to traverse the matrix recursively 
N = 2 
M = 3 
  
# Function to traverse the matrix recursively 
def traverseMatrix(arr, current_row, current_col) : 
  
    # If the entire column is traversed 
    if (current_col >= M) :
        return 0
  
    # If the entire row is traversed 
    if (current_row >= N) :
        return 1
  
    # Print the value of the current 
    # cell of the matrix 
    print(arr[current_row][current_col],end= ", "); 
  
    # Recursive call to traverse the matrix 
    # in the Horizontal direction 
    if (traverseMatrix(arr, current_row, current_col + 1 ) == 1) : 
        return 1
          
    # Recursive call for changing the 
    # Row of the matrix 
    return traverseMatrix(arr, current_row + 1, 0); 
  
# Driver code 
if __name__ == "__main__"
    arr = [ [ 1, 2, 3 ], 
            [ 4, 5, 6 ] ]; 
  
    traverseMatrix(arr, 0, 0); 
  
# This code is contributed by AnkitRai01

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Output:

1, 2, 3, 4, 5, 6,

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