https://github.com/amirabdollahi/knight-tour
This repository provides a C# solution to the classic Knight's Tour problem using the backtracking algorithm. It supports customizable chessboard sizes and starting positions, offering a practical example of recursion and backtracking in problem-solving.
https://github.com/amirabdollahi/knight-tour
algorithms backtracking-algorithm c-sharp chessboard-game depth-first-search graphics2d knight-tour knights-tour pathfinding-algorithm recursion
Last synced: 29 days ago
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This repository provides a C# solution to the classic Knight's Tour problem using the backtracking algorithm. It supports customizable chessboard sizes and starting positions, offering a practical example of recursion and backtracking in problem-solving.
- Host: GitHub
- URL: https://github.com/amirabdollahi/knight-tour
- Owner: AmirAbdollahi
- Created: 2025-04-13T07:57:03.000Z (8 months ago)
- Default Branch: master
- Last Pushed: 2025-04-14T06:55:05.000Z (8 months ago)
- Last Synced: 2025-04-15T15:16:29.082Z (8 months ago)
- Topics: algorithms, backtracking-algorithm, c-sharp, chessboard-game, depth-first-search, graphics2d, knight-tour, knights-tour, pathfinding-algorithm, recursion
- Language: C#
- Homepage:
- Size: 61.5 KB
- Stars: 2
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Knight's Tour Problem
The Knight's Tour is a classic problem in computer science and mathematics, where the objective is to move a knight across a chessboard such that it visits every square exactly once. This repository offers an implementation of this problem in C#, utilizing the backtracking algorithm to find a solution.
## Features
- **Backtracking Algorithm**: Employs a depth-first search approach to explore all possible knight moves, backtracking when a move leads to a dead end.
- **Chessboard Size Flexibility**: Allows users to define the dimensions of the chessboard, supporting various sizes beyond the standard 8x8.
- **Customizable Starting Position**: Enables users to set the knight's initial position on the board.
## Screenshots
## Technical Explanation
### How the Algorithm Works
The knight moves in an L-shape: two squares in one direction and then one square perpendicular to that. There are 8 possible moves from any position on the board.
To simplify and generalize the movement logic, two arrays are used:
```csharp
int[] horizontal = { 2, 1, -1, -2, -2, -1, 1, 2 };
int[] vertical = { -1, -2, -2, -1, 1, 2, 2, 1 };
```
These arrays represent the relative x and y changes for each of the knight’s 8 possible moves. For example:
- `horizontal[0] = 2` and `vertical[0] = -1` means moving two steps right and one step up.
- Each index corresponds to a specific knight move. Indexes 0 through 7 cover all the move patterns.
### Board Representation
The chessboard is represented as a 2D array:
```csharp
int[,] board = new int[8, 8];
```
Each cell on the board stores the move number when it was visited by the knight. A value of `false` means the cell has not yet been visited.
### Move Selection
For each position, the algorithm checks all possible knight moves using the `horizontal` and `vertical` arrays and selects the move that leads to the cell with the fewest onward options — that's Warnsdorff’s rule in action.
## Getting Started
To run the Knight's Tour program:
1. **Clone the Repository**:
```bash
git clone https://github.com/AmirAbdollahi/knight-tour.git
```
2. **Open the Solution**:
Navigate to the cloned directory and open `Knight Tour.sln` using Visual Studio or your preferred C# development environment.
3. **Build the Solution**:
Compile the project to restore dependencies and build the executable.
4. **Run the Program**:
Execute the program within your development environment or run the compiled executable from the command line.
## Usage
Upon running the program, it will prompt you to enter the dimensions of the chessboard and the starting position of the knight. The program will then attempt to find a solution to the Knight's Tour problem using the backtracking algorithm.
## License
This project is open-source and available under the MIT License.