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

Approach:



  1. This problem can be solved using Depth First Traversal of an array with a slight modification.
  2. 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++

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// 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

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Java

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// 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);
    }
}

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Python3

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# 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

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C#

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// 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

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Output:

ad ae 
bd be

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

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Improved By : AnkitRai01, chitranayal

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