8-Puzzle-Problem

Solving the 8-Puzzle Problem Using BFS

Overview

This code demonstrates solving the 8-puzzle problem using Breadth-First Search (BFS) as a state-space search technique. The 8-puzzle is a classic problem that involves sliding tiles in a 3x3 grid to match a desired goal configuration.

The algorithm explores the shortest path from an initial configuration to the goal state and visualizes the steps involved in solving the puzzle.

What is the 8-Puzzle Problem?

The 8-puzzle consists of:

• A 3x3 grid with 8 numbered tiles (1 to 8) and one blank space (0).
• A goal to rearrange the tiles from a starting configuration to the desired target state by sliding adjacent tiles into the blank space.

Example

• Initial State

1  2  3
4  5  6
0  7  8

• Goal State

1  2  3
4  5  6
7  8  0

How the Code Works

Breadth-First Search (BFS)

BFS is used to find the shortest solution path:

1. Start from the initial state.
2. Explore all possible moves (Up, Down, Left, Right) from the current state.
3. Add new states to a queue and mark visited states to avoid loops.
4. Stop when the goal state is reached.

Visualization

Each step of the solution path is visualized using Matplotlib to show how the tiles are rearranged until the goal state is achieved.

Key Functions

1. bfs_solve:

• Implements BFS to find the solution path.
• Returns a list of states from the initial to the goal configuration.

2. visualize_puzzle:

• Visualizes the solution path as a sequence of grids, showing how the tiles move.

Output

• Visualization: Displays the step-by-step solution in a series of grids.
• Textual Output: If no solution exists, the program prints No solution found.

Why BFS?

• Guarantees Shortest Path: BFS explores all states level-by-level.
• Complete: Ensures that a solution is found if one exists.

Use Cases

• Understanding search algorithms in AI.
• Practicing state-space search problems.
• Visualizing problem-solving processes.

Enjoy solving puzzles programmatically! 🎉