Fig.1 Algorithm Visualization
$ pip install -r requirements.txt
A knight's tour (See Fig.2) is a sequence of moves of a knight on a chessboard such that the knight visits every square only once. If the knight ends on a square that is one knight's move from the beginning square (so that it could tour the board again immediately, following the same path), the tour is closed, otherwise it is open.
Fig.2 Sample Knight's Tour
We can solve the knight's tour problem using warnsdorff's algorithm, which states that:-
- We can start from any initial position of the knight on the board.
- We can always move to an adjacent, unvisited square with minimal degree(minimum number of unvisited adjacent).
Fig.1 demonstrates a sample run of the visualizer when knight is placed at 0, 0, you can find other samples here.
| Symbol | Meaning |
|---|---|
| 0 | Unvisited Cell |
| 1 | Visited Cell |
| 2 | Knight's Position |
On an 8 × 8 board, there are exactly 26,534,728,821,064 directed closed tours (i.e. two tours along the same path that travel in opposite directions are counted separately, as are rotations and reflections). The number of undirected closed tours is half this number, since every tour can be traced in reverse!
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