# Knight's Shortest Path Solver

A Python-based algorithm that finds all shortest paths for a knight on an empty chessboard.

## Problem Description

Given two positions on a standard 8x8 chessboard, this program computes:

- **All minimum-length move sequences** to get a knight from the starting position to the destination
- **A graph visualization** (in GraphViz/DOT format) showing all shortest paths

## Features

- Finds all optimal solutions (not just one)
- Generates GraphViz DOT files for visualization
- Containerized execution for consistency
- Configurable output naming

## Prerequisites

- Docker (for containerized execution)
- Python 3.7+ (for running directly)
- GraphViz (optional, for rendering DOT files)

## Installation & Usage

### Using Docker (Recommended)

Build and run the algorithm:

```bash
./run.sh build <dest_x> <dest_y> <output_name>
```

Example:
```bash
./run.sh build 4 5 knight_paths
```

Or use an existing image:

```bash
./run.sh run <dest_x> <dest_y> <output_name>
```

### Parameters

- `<dest_x>`: X-coordinate of destination (0-7)
- `<dest_y>`: Y-coordinate of destination (0-7)
- `<output_name>`: Base name for output files (no extension)

### Output

The program generates:
- `<output_name>.txt`: All shortest paths in text format
- `<output_name>.dot`: GraphViz file for visualization

To visualize the graph:

```bash
dot -Tpng <output_name>.dot -o <output_name>.png
```

## Project Structure

```
├── README.md
├── run.sh              # Build and execution script
├── Dockerfile          # Container configuration
├── src/
│   └── knight_solver.py  # Main algorithm
└── requirements.txt    # Python dependencies
```

## Algorithm Details

The solver uses BFS (Breadth-First Search) to explore all possible knight moves, ensuring all minimum-length paths are found. It then constructs a directed graph of these paths and outputs the results in both human-readable and GraphViz formats.

## License

See LICENSE file for details.