# 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++

 `// C++ program to traverse the matrix recursively ` ` `  `#include ` `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; ` `} `

## Java

 `// 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 `

## C#

 `// 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 `

## Python3

 `# 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 `

Output:

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

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