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Maze With N doors and 1 Key
  • Difficulty Level : Medium
  • Last Updated : 07 Jun, 2021

Given an N * N binary maze where a 0 denotes that the position can be visited and a 1 denotes that the position cannot be visited without a key, the task is to find whether it is possible to visit the bottom-right cell from the top-left cell with only one key along the way. If possible then print “Yes” else print “No”.

Example: 

Input: maze[][] = { 
{0, 0, 1}, 
{1, 0, 1}, 
{1, 1, 0}} 
Output: Yes 
 

Approach: This problem can be solved using recursion, for every possible move, if the current cell is 0 then without altering the status of the key check whether it is the destination else move forward. If the current cell is 1 then the key must be used, now for the further moves the key will be set to false i.e. it’ll never be used again on the same path. If any path reaches the destination then print Yes else print No.



Below is the implementation of the above approach: 

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Recursive function to check whether there is 
// a path from the top left cell to the 
// bottom right cell of the maze
bool findPath(vector<vector<int>> maze,
              int xpos, int ypos, bool key)
{
     
    // Check whether the current cell is
    // within the maze
    if (xpos < 0 || xpos >= maze.size() ||
        ypos < 0 || ypos >= maze.size())
        return false;
 
    // If key is required to move further
    if (maze[xpos][ypos] == '1')
    {
         
        // If the key hasn't been used before
        if (key == true)
 
            // If current cell is the destination
            if (xpos == maze.size() - 1 &&
                ypos == maze.size() - 1)
                return true;
 
        // Either go down or right
        return findPath(maze, xpos + 1,
                        ypos, false) ||
               findPath(maze, xpos,
                        ypos + 1, false);
 
        // Key has been used before
        return false;
    }
     
    // If current cell is the destination
    if (xpos == maze.size() - 1 &&
        ypos == maze.size() - 1)
        return true;
 
    // Either go down or right
    return findPath(maze, xpos + 1,
                    ypos, key) ||
           findPath(maze, xpos,
                    ypos + 1, key);
}
 
bool mazeProb(vector<vector<int>> maze,
              int xpos, int ypos)
{
    bool key = true;
    if (findPath(maze, xpos, ypos, key))
        return true;
         
    return false;
}
 
// Driver code
int main()
{
    vector<vector<int>> maze = { { '0', '0', '1' },
                                 { '1', '0', '1' },
                                 { '1', '1', '0' } };
    int n = maze.size();
 
    // If there is a path from the cell (0, 0)
    if (mazeProb(maze, 0, 0))
        cout << "Yes";
    else
        cout << "No";
}
 
// This code is contributed by grand_master

Java




// Java implementation of the approach
import java.io.*;
import java.util.ArrayList;
 
class GFG{
 
// Recursive function to check whether there
// is a path from the top left cell to the
// bottom right cell of the maze
static boolean findPath(
    ArrayList<ArrayList<Integer>> maze,
    int xpos, int ypos, boolean key)
{
     
    // Check whether the current cell is
    // within the maze
    if (xpos < 0 || xpos >= maze.size() ||
        ypos < 0 || ypos >= maze.size())
        return false;
 
    // If key is required to move further
    if (maze.get(xpos).get(ypos) == '1')
    {
         
        // If the key hasn't been used before
        if (key == true)
         
            // If current cell is the destination
            if (xpos == maze.size() - 1 &&
                ypos == maze.size() - 1)
                return true;
 
        // Either go down or right
        return findPath(maze, xpos + 1, ypos, false) ||
               findPath(maze, xpos, ypos + 1, false);
    }
 
    // If current cell is the destination
    if (xpos == maze.size() - 1 &&
        ypos == maze.size() - 1)
        return true;
 
    // Either go down or right
    return findPath(maze, xpos + 1, ypos, key) ||
           findPath(maze, xpos, ypos + 1, key);
}
 
static boolean mazeProb(
    ArrayList<ArrayList<Integer>> maze,
    int xpos, int ypos)
{
    boolean key = true;
     
    if (findPath(maze, xpos, ypos, key))
        return true;
 
    return false;
}
 
// Driver code
public static void main(String[] args)
{
    int size = 3;
    ArrayList<ArrayList<Integer>> maze =
    new ArrayList<ArrayList<Integer>>(size);
     
    for(int i = 0; i < size; i++)
    {
        maze.add(new ArrayList<Integer>());
    }
 
    // We are making these
    //{ { '0', '0', '1' },
    //  { '1', '0', '1' },
    //  { '1', '1', '0' } };
    maze.get(0).add(0);
    maze.get(0).add(0);
    maze.get(0).add(1);
    maze.get(1).add(1);
    maze.get(1).add(0);
    maze.get(1).add(1);
    maze.get(2).add(1);
    maze.get(2).add(1);
    maze.get(2).add(0);
     
    // If there is a path from the cell (0, 0)
    if (mazeProb(maze, 0, 0))
        System.out.print("Yes");
    else
        System.out.print("No");
}
}
 
// This code is contributed by sujitmeshram

Python3




# Python3 implementation of the approach
 
# Recursive function to check whether there is
# a path from the top left cell to the
# bottom right cell of the maze
def findPath(maze, xpos, ypos, key):
 
    # Check whether the current cell is
    # within the maze
    if xpos < 0 or xpos >= len(maze) or ypos < 0 \
                            or ypos >= len(maze):
        return False
 
    # If key is required to move further
    if maze[xpos][ypos] == '1':
 
        # If the key hasn't been used before
        if key == True:
 
            # If current cell is the destination
            if xpos == len(maze)-1 and ypos == len(maze)-1:
                return True
 
            # Either go down or right
            return findPath(maze, xpos + 1, ypos, False) or \
            findPath(maze, xpos, ypos + 1, False)
 
        # Key has been used before
        return False
 
    # If current cell is the destination
    if xpos == len(maze)-1 and ypos == len(maze)-1:
        return True
 
    # Either go down or right
    return findPath(maze, xpos + 1, ypos, key) or \
           findPath(maze, xpos, ypos + 1, key)
 
 
def mazeProb(maze, xpos, ypos):
    key = True
    if findPath(maze, xpos, ypos, key):
        return True
    return False
 
# Driver code
if __name__ == "__main__":
 
    maze = [['0', '0', '1'],
            ['1', '0', '1'],
            ['1', '1', '0']]
    n = len(maze)
     
    # If there is a path from the cell (0, 0)
    if mazeProb(maze, 0, 0):
        print("Yes")
    else:
        print("No")

C#




// C# implementation of the approach
using System;
using System.Collections.Generic;
 
class GFG{
 
// Recursive function to check whether there
// is a path from the top left cell to the
// bottom right cell of the maze
static bool findPath(List<List<int>> maze,
                     int xpos, int ypos, bool key)
{
     
    // Check whether the current cell is
    // within the maze
    if (xpos < 0 || xpos >= maze.Count ||
        ypos < 0 || ypos >= maze.Count)
        return false;
 
    // If key is required to move further
    if (maze[xpos][ypos] == '1')
    {
         
        // If the key hasn't been used before
        if (key == true)
         
            // If current cell is the destination
            if (xpos == maze.Count - 1 &&
                ypos == maze.Count - 1)
                return true;
 
        // Either go down or right
        return findPath(maze, xpos + 1, ypos, false) ||
               findPath(maze, xpos, ypos + 1, false);
    }
 
    // If current cell is the destination
    if (xpos == maze.Count - 1 &&
        ypos == maze.Count - 1)
        return true;
 
    // Either go down or right
    return findPath(maze, xpos + 1, ypos, key) ||
           findPath(maze, xpos, ypos + 1, key);
}
 
static bool mazeProb(List<List<int>> maze,
                     int xpos, int ypos)
{
    bool key = true;
     
    if (findPath(maze, xpos, ypos, key))
        return true;
 
    return false;
}
 
// Driver code
public static void Main(String[] args)
{
    int size = 3;
    List<List<int>> maze =
    new List<List<int>>(size);
     
    for(int i = 0; i < size; i++)
    {
        maze.Add(new List<int>());
    }
 
    // We are making these
    //{ { '0', '0', '1' },
    //  { '1', '0', '1' },
    //  { '1', '1', '0' } };
    maze[0].Add(0);
    maze[0].Add(0);
    maze[0].Add(1);
    maze[1].Add(1);
    maze[1].Add(0);
    maze[1].Add(1);
    maze[2].Add(1);
    maze[2].Add(1);
    maze[2].Add(0);
     
    // If there is a path from the cell (0, 0)
    if (mazeProb(maze, 0, 0))
        Console.Write("Yes");
    else
        Console.Write("No");
}
}
 
// This code is contributed by gauravrajput1

Javascript




<script>
 
// JavaScript implementation of the approach
 
// Recursive function to check whether there is 
// a path from the top left cell to the 
// bottom right cell of the maze
function findPath(maze, xpos, ypos, key)
{
     
    // Check whether the current cell is
    // within the maze
    if (xpos < 0 || xpos >= maze.length ||
        ypos < 0 || ypos >= maze.length)
        return false;
 
    // If key is required to move further
    if (maze[xpos][ypos] == '1')
    {
         
        // If the key hasn't been used before
        if (key == true)
 
            // If current cell is the destination
            if (xpos == maze.length - 1 &&
                ypos == maze.length - 1)
                return true;
 
        // Either go down or right
        return findPath(maze, xpos + 1,
                        ypos, false) ||
               findPath(maze, xpos,
                        ypos + 1, false);
 
        // Key has been used before
        return false;
    }
     
    // If current cell is the destination
    if (xpos == maze.length - 1 &&
        ypos == maze.length - 1)
        return true;
 
    // Either go down or right
    return findPath(maze, xpos + 1,
                    ypos, key) ||
           findPath(maze, xpos,
                    ypos + 1, key);
}
 
function mazeProb(maze, xpos, ypos)
{
    let key = true;
    if (findPath(maze, xpos, ypos, key))
        return true;
         
    return false;
}
 
// Driver code
    let maze = [ [ '0', '0', '1' ],
                 [ '1', '0', '1' ],
                 [ '1', '1', '0' ] ];
    let n = maze.length;
 
    // If there is a path from the cell (0, 0)
    if (mazeProb(maze, 0, 0))
        document.write("Yes");
    else
        document.write("No");
         
</script>
Output: 
Yes

 

Time Complexity: O(2N)
 

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