šŸ­ Robot Mouse Maze Solver

Navigate through a maze using backtracking algorithm ā€” find the path from start to exit.

šŸ­ The Robot Mouse Challenge

šŸŽÆ The Mission:

A small robot mouse is placed in a square maze. It must navigate from the top-left corner (entrance) to the bottom-right corner (exit) using only open paths.

šŸ“‹ Rules:

  • Maze is N Ɨ N grid of tiles (1 = open, 0 = blocked)
  • Robot starts at [0][0], goal is [N-1][N-1]
  • Can move: Down, Right, Up, Left (no diagonals)
  • Cannot pass through walls (0) or revisit cells
  • Find any valid path or report "No path found"

Problem Specifications

  • Input: N (maze size), followed by NƗN matrix (0s and 1s)
  • Output: Solution matrix showing path with 1s, rest 0s
  • Algorithm: Backtracking with recursion
  • No Solution: Print "No path found"

Example: 4Ɨ4 Maze

Start
Goal
Path
Wall

Input Maze

šŸ­
0
0
0
1
1
0
1
0
1
0
0
1
1
1
šŸŽÆ

Solution Path

1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1

šŸ”„ Backtracking Strategy

Backtracking Algorithm

  1. Start: Place robot at [0][0], mark as part of path
  2. Base Case: If at [N-1][N-1], path found!
  3. Try Moves: For each direction (down, right, up, left):
    • Check if move is valid (in bounds, open, not visited)
    • If valid, mark cell and recursively explore from there
    • If that path succeeds, return true
  4. Backtrack: If no direction works, unmark cell and return false
  5. Result: Either solution matrix or "No path found"

Key Concepts

  • Recursion: Function calls itself to explore paths
  • Backtracking: Undo choices that don't lead to solution
  • State Tracking: Solution matrix marks valid path
  • Move Validation: Check bounds, walls, visited cells

Time Complexity

O(2^(NĀ²))
Worst case: explore all possible paths

Space Complexity

O(NĀ²)
Solution matrix + recursion stack

Why Backtracking?

Backtracking is ideal for this problem because:

  • We need to explore all possible paths until solution found
  • Dead ends require going back and trying different routes
  • Recursive structure naturally models the maze exploration
  • Solution emerges from successful path exploration

šŸ” Step-by-Step Maze Solving

Ready. Load a maze to start demo.

Maze Visualization

Load maze to begin

Progress Tracker

1. Parse maze input
2. Initialize solution matrix
3. Start at [0][0]
4. Explore paths recursively
5. Backtrack when stuck
6. Found path or no solution

šŸŽ® Solve Your Own Maze

Enter maze and press Solve Maze

Test Cases

Sample Input
4Ɨ4 maze with valid path
No Solution
Maze with no possible path
Easy Path
3Ɨ3 maze with simple route

šŸ“Š Algorithm Analysis

Time

O(2^(NĀ²))

Worst case explores all paths

Space

O(NĀ²)

Matrix + recursion depth

Complexity Breakdown

  • Time: Each cell can be visited or not (2 choices), NĀ² cells ā†’ O(2^(NĀ²))
  • Space: O(NĀ²) for solution matrix + O(NĀ²) recursion stack depth
  • Practical: Much faster than worst case due to pruning dead ends
  • Optimization: Can add heuristics (A*, BFS) for better performance

Backtracking Characteristics

  • āœ… Complete: Finds solution if one exists
  • āœ… Simple to implement: Clean recursive structure
  • āœ… Memory efficient: Only one path explored at a time
  • āŒ Can be slow: Exponential worst-case time
  • āŒ Not optimal: May not find shortest path

Alternative Approaches

  • BFS: Finds shortest path, O(NĀ²) time but needs queue
  • DFS: Similar to backtracking, explores depth-first
  • A* Search: Uses heuristics for optimal path finding
  • Dijkstra: Weighted graph shortest path algorithm

Real-World Applications

  • Robotics: Path planning for autonomous navigation
  • Games: AI pathfinding in grid-based games
  • Puzzles: Sudoku, N-Queens, maze solving
  • Network Routing: Finding paths through networks
  • Circuit Design: PCB trace routing