Knight's Shortest Path Problem

This repository contains a Python solution to the Knight's Shortest Path Problem, which calculates all possible shortest paths a knight can take to travel from a start position to an end position on a standard 8x8 chessboard. The solution uses Breadth-First Search (BFS) to ensure efficiency and correctness.

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Table of Contents

• Problem Description
• Features
• Example
• Directory Structure
• Setup and Usage
  • Running with Docker
  • Using Configurations
  • Command-Line Input
  • Interactive Mode
• Extensions and Future Enhancements
• Development Notes
• Dependencies
• License

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Problem Description

In chess, the knight moves in an "L" shape, meaning it can jump two squares in one direction and one square in a perpendicular direction. The challenge is to find all possible shortest paths from a given start position to an end position, using the rules of the knight's movement.

Example

For the start position a1 and the end position h7, the program finds all shortest paths, including:

• Shortest Paths Output: Paths are printed in algebraic notation, e.g., a1 -> c2 -> b4 -> d5 -> f6 -> h7. And other equivalent shortest paths.
• Graph Visualization: Generates a visualization based on matplotlib and a graph image showing all shortest paths (knight_paths.png).

Example Output

Matplotlib visual representation in python:

Output of runningn the program, Graphviz representation:

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Features

• Finds all shortest paths using Breadth-First Search (BFS).
• Outputs a visual representation of paths using Matplotlib.
• Outputs a visual representation of paths using Graphviz.
• Configurable start and end positions via CLI or config.json.
• Containerized with a Dockerfile for ease of deployment.

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Directory Structure

knight-shortest-path/
├── config.json            # Configuration file for defining start and end positions
├── dockerfile             # Dockerfile for containerizing the solution
├── knight_tour.py         # Main script implementing the solution
├── knight_paths.png       # Example output showing a graphical visualization of paths
├── requirements.txt       # Python dependencies
└── README.md              # Repository documentation

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Setup and Usage

Running with Docker

1. Build the Docker image:

   docker build -t knight-shortest-path .

2. Run the container:

   docker run --rm -v "$(pwd):/app" knight-shortest-path

Using Configurations

You can specify start and end positions in the provided config.json file:

{
  "start": "a1",
  "end": "h7"
}

Run the script:

python knight_tour.py --config config.json

Command-Line Input

Run the script and specify positions directly:

python knight_tour.py --start a1 --end h7

Interactive Mode

Run the program without arguments to input positions interactively:

python knight_tour.py

You will be prompted to enter positions in algebraic notation (e.g., a1 and h7).

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Extensions and Future Enhancements

1. Heuristic Optimization: Warnsdorff's Rule

The script can be enhanced with Warnsdorff's Rule, a heuristic that prioritizes moves with fewer onward options. This improves the algorithm’s efficiency by reducing unnecessary recursive calls, making it faster in finding solutions.

2. Generalization

The algorithm can be generalized to support:

• Custom board sizes: Extend to chessboards of dimensions other than 8x8 (e.g., NxM).
• Arbitrary start/end positions: Allow users to provide any start and end position, with validation to ensure feasibility.

3. Visualization

For a better user experience:

• Implement an interactive chessboard for exploring paths and configurations.

4. AI and Machine Learning Integration

• Use Reinforcement Learning to predict optimal knight paths.
• Generate training data from the current script for machine learning research.

5. Obstacles and Dynamic Boards

• Add support for obstacles or restricted squares.
• Modify the algorithm to dynamically navigate around these constraints.

6. Cloud Deployment

Deploy the solution as a REST API using Flask or FastAPI:

• Accept board configurations remotely.
• Return solutions as JSON or visual representations.

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Development Notes

Introduction

The Knight's Tour problem involves moving a knight across a chessboard such that it visits every square exactly once. This Python script implements a solution using Breadth-First Search (BFS), ensuring that all minimum-length paths from the starting to the ending position are found. The program includes various options for execution, such as through configuration files, command-line arguments, or interactive mode.

Summary

The current script is a solid foundation for solving the Knight's Tour problem. By adding features like heuristic optimization, visualization, machine learning, and cloud deployment, this project can be transformed into a powerful tool for learning, research, and experimentation.

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Dependencies

• Python 3.8 or later
• Required Python libraries (see requirements.txt):
  • matplotlib
  • graphviz
  • argparse
  • json

Install the dependencies with:

pip install -r requirements.txt

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License

This project is licensed under the MIT License. See the LICENSE file for details.