c3viche / knights-tour

Algorithm that solves Knight's Tour problem

Knight's Tour Problem Visual Solver

Two approaches for an open tour of a knight on a chess board

This project was something I built out of curiosity after I stumbled upon the Knight's Tour problem. The scripts provided, each in their own way find a valid path for an open tour for a knight chess piece. Provided are a bruteforce approach and a more heuristic solution using Warnsdorff's rule. Both approaches employ backtracking.

How to use

Instructions assume that the user has Git installed. If not installed, the documentation may help. All is done on the terminal.

1. Create or navigate to a directory to clone the repository, and then clone it with this terminal command.

git clone https://github.com/C3viche/Knights-Tour.git

2. Provided should be the up-to-date executable. Navigate to "Heuristic" or "Bruteforce" directory and run the executable.

cd Heuristic 
./knights_tour_op.exe

OR

cd Bruteforce
./knights_tour.exe

3. The following input is required for each:

   Heuristic Solution (RECOMMENDED)

   • Dimensions of the abstract "chess board" (m x n)
   • The starting position of the knight in number coordinates
     • This is done because not all chess boards have letter indications
     • (0, 0) is the the top left corner, y increases going down the board, and x increases going right

   Brute Force

   Very unpolished. This was my beta version for the project so I highly recommend using the other program provided instead (Heuristic Solution using Warnsdorff's rule). However this program still does work for small chess boards like 5x5 and 6x6.

   • The starting position of the knight in number coordinates:
     • must be entered as x, y
     • not input validation, so very error prone

Keep in Mind...

Some boards and some starting positions may lead to impossible tours or long computing time for the computer so cancel the program with Ctrl + C if solution is not computed in under a minute. I am currently working on a script that automatically ends the program if not finished in time.

Visuals

Here are some resources I found interesting!

• Numberphile Video about interesting patterns in the knight's tour
• Article on an optimized solution