# Backtracking – Rat In A Maze Puzzle

Given a maze, NxN matrix. A rat has to find a path from source to destination. maze[0][0] (left top corner)is the source and maze[N-1][N-1](right bottom corner) is destination. There are few cells which are blocked, means rat cannot enter into those cells. Rat can move in any direction ( left, right, up and down).

Input: A 2D-matrix with 0’s and 1’s fill in it. 0 means that cell is blocked and 1 means rat can move to that cell.

Rat In A Maze Puzzle

Approach:

• Create a solution matrix of the same structure as maze.
• Whenever rat moves to cell in a maze, mark that particular cell in solution matrix.
• At the end print the solution matrix, follow that 1’s from the top left corner, it will be that path for the rat.

Algorithm:

1. If rat reaches the destination
• print the solution matrix.
• Else
• Mark the current cell in solution matrix as 1
• If previous step is not in vertical direction (upwards) then move forward in the vertical direction(downwards) and recursively check if this movement leads to solution.
• If movement in above step doesn’t lead to the solution and If previous step is not in horizontal direction (towards left) then move forward in the horizontal direction(towards right) and recursively check if this movement leads to solution.
2. If movement in above step doesn’t lead to the solution and If previous step is not in vertical direction (downwards) then move forward in the horizontal direction(upwards) and recursively check if this movement leads to solution.
3. If movement in above step doesn’t lead to the solution and If previous step is not in horizontal direction (towards right) then move forward in the horizontal direction(towards left) and recursively check if this movement leads to solution.
4. If none of the above solution works then BACKTRACK and mark the current cell as 0.

NOTE: It is important to check the previous direction in which the rat has moved because if rat will move in the opposite direction w.r.t its previous direction then rat might end up in infinite loop. Example: if rat has moved to its left in the previous direction then if in next moves to right then moving left option will be available again then rat will move to left again , then again right and so on

Code:

Output:

``` 1 0 1 1 1
1 1 1 0 1
0 0 0 1 1
0 0 0 1 0
0 0 0 1 1

```

Reference: http://www.geeksforgeeks.org/backttracking-set-2-rat-in-a-maze/

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If you find anything incorrect or you feel that there is any better approach to solve the above problem, please write comment.
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### 6 Responses

1. Nikhil Kumar says:

I think there is one step missed and it will not work where there is loop inside path e.g.
1 0 1 1 1
1 1 1 1 1
0 1 0 1 1
0 1 1 1 0
0 0 0 1 1
It has a loop and with above algorithm it will keep going in the inner 1’s forever. So we should also check if soln matrix is not already traversed for the next step.
if (isSafeToGo(maze, x, y, N) && soln[x][y] != 1)

• tutorialhorizon says:

yes you are right that is why it has been ordered in particular sequence, anyways the suggestion you provided can also be implemented.

• MURHY says:

What is the use of direction? It can work even without direction. Please explain.

2. Nikhil P says:

Your solution will not work if the maze has loops….
eg: https://ideone.com/WiC5KO

3. Rehmanali Momin says:

What if there are more than 1 steps?

4. Benoit Bst says:

Hi, thanks for sharing

If people have an interest in backtracking Algo in C++ :

I have a complete simple example on my github with backtracking into maze.
You can explore the Core library or play directly in the term.

The game : https://github.com/benoit-b