https://github.com/sgalal/knights-tour-visualization

An online Knight's tour visualizer using divide and conquer algorithm
https://github.com/sgalal/knights-tour-visualization

algorithm divide-and-conquer emscripten html5 knight-tour knights-tour visualization visualizer

Last synced: 2 months ago
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An online Knight's tour visualizer using divide and conquer algorithm

• Host: GitHub
• URL: https://github.com/sgalal/knights-tour-visualization
• Owner: sgalal
• License: mit
• Created: 2018-05-25T02:54:01.000Z (about 7 years ago)
• Default Branch: master
• Last Pushed: 2020-07-09T02:17:07.000Z (almost 5 years ago)
• Last Synced: 2025-04-14T02:26:44.373Z (2 months ago)
• Topics: algorithm, divide-and-conquer, emscripten, html5, knight-tour, knights-tour, visualization, visualizer
• Language: C
• Homepage: https://sgalal.github.io/knights-tour-visualization/
• Size: 716 KB
• Stars: 19
• Watchers: 1
• Forks: 6
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Knight's Tour Visualization

[![Build status](https://ci.appveyor.com/api/projects/status/a3t55hc7dcxlwlg2?svg=true)](https://ci.appveyor.com/project/chromezh/knights-tour-visualization) [![Maintainability](https://api.codeclimate.com/v1/badges/31c1219b5c34c6108000/maintainability)](https://codeclimate.com/github/sgalal/knights-tour-visualization/maintainability)

_An online [Knight's tour](https://en.wikipedia.org/wiki/Knight%27s_tour) visualizer using divide and conquer algorithm_

This project uses [Emscripten](http://kripken.github.io/emscripten-site/) to compile C code into JavaScript.

For an online version, see .

![Knight's Tour on a 14\*14 board](demo/demo.gif)

## Project Structure

* Source files: `src`

* For test: `test`

* For web pages: `index.html`, `index.js`, `index.css`

## Build

* **Prerequisite**: [Emscripten](http://kripken.github.io/emscripten-site/)

* **Build**: `emcc -std=c11 -Weverything -Werror -Wno-unused-function -Wno-language-extension-token -O2 -s ASSERTIONS=1 -s EXPORTED_FUNCTIONS='["_getNextPointSerialize"]' -s EXTRA_EXPORTED_RUNTIME_METHODS='["ccall","cwrap"]' -o tour.js src/tour.c`

* **Test**: `clang -std=c11 -Weverything -Werror -Wno-language-extension-token -DDEBUG -o tour src/tour.c test/tour_tb.c && ./tour`

## Implementation

### Algorithm

The code is an implementation of _Parberry, Ian. "An efficient algorithm for the Knight's tour problem." Discrete Applied Mathematics 73.3(1997):251-260_.

A knight’s tour is called _**closed**_ if the last square visited is also reachable from the first square by a knight’s move.

A knight’s tour is said to be _**structured**_ if it includes the knight’s moves shown in Fig. 1.

![Fig. 1. Required moves for a structured knight's tour.](demo/Fig1.jpg)

An _n_ \* _n_ chessboard has a closed knight's tour iff _n_ ≥ 6 is even.

For board size of 6 \* 6, 6 \* 8, 8 \* 8, 8 \* 10, 10 \* 10, and 10 \* 12, we have already found **structured**, **closed** knight’s tours, which are shown in Fig. 2.

![Fig. 2. Structured knight’s tours for (in row-major order) 6 x 6, 6 x 8, 8 x 8, 8 x 10, 10 x 10, and 10 x 12 boards.](demo/Fig2.jpg)

This means the problem is already solved when _n_ ∈ {6, 8, 10}.

For larger _n_, divide the chess board into parts to meet the sizes above. For instance, a board with _n_ = 42 can be divided as follows:

![Divide example](demo/divide_example.svg)

Then connect the parts together. Since all the parts are structured, we can combine them by substitute the directions on the corners:

![Fig. 3. How to combine four structured knight’s tours into one.](demo/Fig3.jpg)

### Data Structure

Since every point is connected with other two points, and there are only 8 possible directions (from 0 to 7):

![8 directions](demo/direction.svg)

The 6 pre-defined tours are stored in 2-dimensional arrays.

There are 8 types of corners (as were shown in Fig. 3.), which are denoted by 0-7, is recorded in _**point attribute**_. Besides, the point attribute of ordinary points is 8.