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Rat in a Maze Problem

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The rat in a maze problem is a path finding puzzle in which our objective is to find an optimal path from a starting point to an exit point. In this puzzle, there is a rat which is trapped inside a maze represented by a square matrix. The maze contains different cells through which that rat can travel in order to reach the exit of maze.

Rat in a Maze Problem using Backtracking Approach

Suppose the maze is of size NxN, where cells can either be marked as 1 or 0. A cell marked as 1 indicates a valid path, whereas a cell marked as 0 indicates a wall or blocked cell. Remember, the rat can move in up, down, left, or right directions, but it can only visit each cell once. The source and destination locations are the top-left and bottom-right cells, respectively.

Rat in a Maze Problem

The goal is to find all possible paths for the rat to reach the destination cell (N-1, N-1) from the starting cell (0, 0). The algorithm will display a matrix, from which we can find the path of the rat to reach the destination point. The figure below illustrates the path −

Rat in a Maze output

The backtracking process systematically explores all possible paths by marking visited cells and backtracking from dead ends. This approach guarantees to find all possible solutions if they exist for the given problem.

To solve the rat in a maze problem using the backtracking approach, follow the below steps −

  • First, mark the starting cell as visited.

  • Next, explore all directions to check if a valid cell exists or not.

  • If there is a valid and unvisited cell is available, move to that cell and mark it as visited.

  • If no valid cell is found, backtrack and check other cells until the exit point is reached.

Example

Following is the example illustrating how to solve the Rat in a Maze problem in various programming languages.

C C++ Java Python 
#include <stdio.h>
#define N 5
// Original maze
int maze[N][N] = {
   {1, 0, 0, 0, 0},
   {1, 1, 0, 1, 0},
   {0, 1, 1, 1, 0},
   {0, 0, 0, 1, 0},
   {1, 1, 1, 1, 1}
};
// To store the final solution of the maze path
int sol[N][N];
void showPath() {
   printf("The solution maze:\n");
   for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++)
         printf("%d ", sol[i][j]);
      printf("\n");
   }
}
// Function to check if a place is inside the maze and has value 1
int isValidPlace(int x, int y) {
   if (x >= 0 && x < N && y >= 0 && y < N && maze[x][y] == 1)
      return 1;
   return 0;
}
int solveRatMaze(int x, int y) {
   // When (x,y) is the bottom right room
   if (x == N - 1 && y == N - 1) {
      sol[x][y] = 1;
      return 1;
   }
   // Check whether (x,y) is valid or not
   if (isValidPlace(x, y)) {
      // Set 1 when it is a valid place
      sol[x][y] = 1;
      // Find path by moving in the right direction
      if (solveRatMaze(x + 1, y))
         return 1;
      // When the x direction is blocked, go for the bottom direction
      if (solveRatMaze(x, y + 1))
         return 1;
      // If both directions are closed, there is no path
      sol[x][y] = 0;
      return 0;
   }
   return 0;
}
int findSolution() {
   if (solveRatMaze(0, 0) == 0) {
      printf("There is no path\n");
      return 0;
   }
   showPath();
   return 1;
}
int main() {
   findSolution();
   return 0;
}

#include<iostream>
#define N 5
using namespace std;
// original maze
int maze[N][N]  =  {
   {1, 0, 0, 0, 0},
   {1, 1, 0, 1, 0},
   {0, 1, 1, 1, 0},
   {0, 0, 0, 1, 0},
   {1, 1, 1, 1, 1}
};
 // to store the final solution of the maze path 
int sol[N][N];        
void showPath() {
   cout << "The solution maze: " << endl;   
   for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++)
         cout << sol[i][j] << " ";
      cout << endl;
   }
}
// function to check place is inside the maze and have value 1
bool isValidPlace(int x, int y) {     
   if(x >= 0 && x < N && y >= 0 && y < N && maze[x][y] == 1)
      return true;
   return false;
}
bool solveRatMaze(int x, int y) {
   // when (x,y) is the bottom right room
   if(x == N-1 && y == N-1) {       
      sol[x][y] = 1;
      return true;
   }
   //check whether (x,y) is valid or not
   if(isValidPlace(x, y) == true) {     
      //set 1, when it is valid place
      sol[x][y] = 1; 
       //find path by moving right direction
      if (solveRatMaze(x+1, y) == true)      
         return true;
      //when x direction is blocked, go for bottom direction     
      if (solveRatMaze(x, y+1) == true)         
         return true;
      //if both are closed, there is no path     
      sol[x][y] = 0;         
      return false;
   }  
   return false;
}
bool findSolution() {
   if(solveRatMaze(0, 0) == false) {
      cout << "There is no path";
      return false;
   }
   showPath();
   return true;
}
int main() {
   findSolution();
}

import java.util.Arrays;
public class MazeSolverClass {
   private static final int N = 5;
   // Original maze
   private static int[][] maze = {
      {1, 0, 0, 0, 0},
      {1, 1, 0, 1, 0},
      {0, 1, 1, 1, 0},
      {0, 0, 0, 1, 0},
      {1, 1, 1, 1, 1}
   };
   // To store the final solution of the maze path
   private static int[][] sol = new int[N][N];
   // to display path
   private static void showPath() {
      System.out.println("The solution maze:");
      for (int i = 0; i < N; i++) {
         System.out.println(Arrays.toString(sol[i]));
      }
   }
   // Function to check if a place is inside the maze and has value 1
   private static boolean isValidPlace(int x, int y) {
      return x >= 0 && x < N && y >= 0 && y < N && maze[x][y] == 1;
   }
   private static boolean solveRatMaze(int x, int y) {
      // When (x,y) is the bottom right room
      if (x == N - 1 && y == N - 1) {
         sol[x][y] = 1;
         return true;
      }
      // Check whether (x,y) is valid or not
      if (isValidPlace(x, y)) {
         // Set 1 when it is a valid place
         sol[x][y] = 1;
         // Find path by moving in the right direction
         if (solveRatMaze(x + 1, y)) {
            return true;
         }
         // When the x direction is blocked, go for the bottom direction
         if (solveRatMaze(x, y + 1)) {
            return true;
         }
         // If both directions are closed, there is no path
         sol[x][y] = 0;
         return false;
      }
      return false;
   }
   private static boolean findSolution() {
      return solveRatMaze(0, 0);
   }
   // main method
   public static void main(String[] args) {
      if (findSolution()) {
         showPath();
      } else {
         System.out.println("There is no path");
      }
   }
}

N = 5
# Original maze
maze = [
    [1, 0, 0, 0, 0],
    [1, 1, 0, 1, 0],
    [0, 1, 1, 1, 0],
    [0, 0, 0, 1, 0],
    [1, 1, 1, 1, 1]
]
# To store the final solution of the maze path
sol = [[0] * N for _ in range(N)]
def showPath():
    print("The solution maze:")
    for row in sol:
        print(*row)

def isValidPlace(x, y):
    return 0 <= x < N and 0 <= y < N and maze[x][y] == 1

def solveRatMaze(x, y):
    # When (x,y) is the bottom right room
    if x == N - 1 and y == N - 1:
        sol[x][y] = 1
        return True

    # Check whether (x,y) is valid or not
    if isValidPlace(x, y):
        # Set 1 when it is a valid place
        sol[x][y] = 1

        # Find path by moving in the right direction
        if solveRatMaze(x + 1, y):
            return True

        # When the x direction is blocked, go for the bottom direction
        if solveRatMaze(x, y + 1):
            return True

        # If both directions are closed, there is no path
        sol[x][y] = 0
        return False

    return False
def findSolution():
    if not solveRatMaze(0, 0):
        print("There is no path")
        return False
    showPath()
    return True

if __name__ == "__main__":
    findSolution()

Output

The solution maze:
1 0 0 0 0 
1 1 0 0 0 
0 1 1 1 0 
0 0 0 1 0 
0 0 0 1 1
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