Print all possible paths from the first row to the last row in a 2D array

Given a 2D array of characters with M rows and N columns. The task is to print all the possible paths from top (first row) to bottom (last row).

Examples:

Input: arr[][] = {
{‘a’, ‘b’, ‘c’},
{‘d’, ‘e’, ‘f’},
{‘g’, ‘h’, ‘i’}}
Output:
adg adh adi aeg aeh aei afg afh afi
bdg bdh bdi beg beh bei bfg bfh bfi
cdg cdh cdi ceg ceh cei cfg cfh cfi

Input: arr[][] = {
{‘a’, ‘b’},
{‘d’, ‘e’}, }
Output:
ad ae
bd be

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

Approach:

This problem can be solved using Depth First Traversal of an array with a slight modification.
The modification here is to only iterate through the columns in the array until the target row is reached.

Below is the implementation of the above approach:

C++

// C++ implementation of the approach  
#include<bits/stdc++.h> 
using namespace std; 
  
void dfs(char inputchar[][2], string res,  
                int i, int j, int R, int C)  
{ 
      
    // If the current row index equals to R, it  
    // indicates we have reached the bottom of  
    // the array and hence we print the result  
    if (i == R)  
    { 
        cout << res << " "; 
        return;  
    } 
  
    res = res + (inputchar[i][j]);  
  
    // Iterate over each of the columns  
    // in the array  
    for (int k = 0; k < C ; k++) 
    { 
        dfs(inputchar, res, i + 1, k, R, C); 
        if (i + 1 == R)  
            break;  
    } 
} 
  
// Function to print all the possible paths  
void printPaths(char inputchar[][2], int R, int C) 
{ 
    for (int i = 0; i < C; i++) 
    { 
        dfs(inputchar, "", 0, i, R, C); 
        cout<<endl; 
    } 
          
    /* 
    * Depth first traversal of the array  
    *  
    * @param input array of characters  
    * @param res to be printed in console  
    * @param i current row index  
    * @param j current column index  
    * @param R number of rows in the input array  
    * @param C number of rows in the output array  
    *  
*/
} 
  
  
// Driver code  
int main() 
{ 
      
    char inputchar[][2] = { 
            { 'a', 'b' },  
            { 'd', 'e' } 
            }; 
              
    int R = sizeof(inputchar)/sizeof(inputchar[0]); 
    int C = sizeof(inputchar[0])/sizeof(char); 
  
    printPaths(inputchar, R, C);  
} 
  
// This code is contributed by chitranayal 

Java

// Java implementation of the approach 
public class GFG { 
  
    // Function to print all the possible paths 
    private static void printPaths(char[][] input, 
                                   int R, int C) 
    { 
        for (int i = 0; i < C; i++) { 
            dfs(input, "", 0, i, R, C); 
            System.out.println(); 
        } 
    } 
  
    /** 
    * Depth first traversal of the array 
    * 
    * @param input array of characters 
    * @param res to be printed in console 
    * @param i     current row index 
    * @param j     current column index 
    * @param R     number of rows in the input array 
    * @param C     number of rows in the output array 
    */
    private static void dfs(char[][] input, String res, 
                            int i, int j, int R, int C) 
    { 
        // If the current row index equals to R, it 
        // indicates we have reached the bottom of 
        // the array and hence we print the result 
        if (i == R) { 
            System.out.print(res + " "); 
            return; 
        } 
  
        res = res + input[i][j]; 
  
        // Iterate over each of the columns 
        // in the array 
        for (int k = 0; k < C; k++) { 
            dfs(input, res, i + 1, k, R, C); 
            if (i + 1 == R) { 
                break; 
            } 
        } 
    } 
  
    // Driver code 
    public static void main(String[] args) 
    { 
        char[][] input = { 
            { 'a', 'b' }, 
            { 'd', 'e' } 
        }; 
        int R = input.length; 
        int C = input[0].length; 
        printPaths(input, R, C); 
    } 
} 

Python3

# Python3 implementation of the approach  
  
# Function to print all the possible paths  
def printPaths(inputchar, R, C) : 
    for i in range(C) : 
        dfs(inputchar, "", 0, i, R, C); 
        print() 
          
    """ 
    * Depth first traversal of the array  
    *  
    * @param input array of characters  
    * @param res to be printed in console  
    * @param i current row index  
    * @param j current column index  
    * @param R number of rows in the input array  
    * @param C number of rows in the output array  
    * """
def dfs(inputchar, res, i, j, R, C) : 
      
    # If the current row index equals to R, it  
    # indicates we have reached the bottom of  
    # the array and hence we print the result  
    if (i == R) : 
        print(res, end = " "); 
        return;  
  
    res = res + inputchar[i][j];  
  
    # Iterate over each of the columns  
    # in the array  
    for k in range(C) : 
        dfs(inputchar, res, i + 1, k, R, C); 
        if (i + 1 == R) : 
            break;  
  
# Driver code  
if __name__ == "__main__" : 
      
    inputchar = [ 
            [ 'a', 'b' ],  
            [ 'd', 'e' ]  
            ]; 
              
    R = len(inputchar); 
    C = len(inputchar[0]); 
      
    printPaths(inputchar, R, C);  
  
# This code is contributed by AnkitRai01 

C#

// C# implementation of the approach  
using System; 
  
class GFG  
{  
  
    // Function to print all the possible paths  
    private static void printPaths(char[,] input,  
                                int R, int C)  
    {  
        for (int i = 0; i < C; i++) 
        {  
            dfs(input, "", 0, i, R, C);  
            Console.WriteLine();  
        }  
    }  
  
    /**  
    * Depth first traversal of the array  
    *  
    * @param input array of characters  
    * @param res to be printed in console  
    * @param i current row index  
    * @param j current column index  
    * @param R number of rows in the input array  
    * @param C number of rows in the output array  
    */
    private static void dfs(char[,] input, string res,  
                            int i, int j, int R, int C)  
    {  
        // If the current row index equals to R, it  
        // indicates we have reached the bottom of  
        // the array and hence we print the result  
        if (i == R)  
        {  
            Console.Write(res + " ");  
            return;  
        }  
  
        res = res + input[i,j];  
  
        // Iterate over each of the columns  
        // in the array  
        for (int k = 0; k < C; k++)  
        {  
            dfs(input, res, i + 1, k, R, C);  
            if (i + 1 == R)  
            {  
                break;  
            }  
        }  
    }  
  
    // Driver code  
    public static void Main()  
    {  
        char[,] input = {  
            { 'a', 'b' },  
            { 'd', 'e' }  
        };  
        int R = input.GetLength(0);  
        int C = input.GetLength(1);  
        printPaths(input, R, C);  
    }  
}  
  
// This code is contributed by AnkitRai01 

Output:

ad ae 
bd be

Time Complexity: O(R * C)
Space Complexity: O(1)

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My Personal Notes

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

C++

Java

Python3

C#

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