tcyang-md / knight-board

Knight's tour implemented in java using stacks and backtracking to find a single solution for 3x3 - 8x8 sized boards

Knight's Tour ♟️

The knight's tour is a sequence of moves of a knight on a chessboard such that the knight visits every square once. If the knight is able to visit every square and ends up on the beginning square as its last move, this is a complete knight tour.

My program written in Java and implements Stacks and Backtracking in order to find a solution for boards between 3x3 and 8x8.

Instructions

Download both KnightTour.java and KnightBoard.java. The knight tour can be run by calling $ java KnightTour n where n is an n x n size board.

$ java KnightTour 5
Possible Knight Tour with max #squares visited in this (5x5) board:
+--+--+--+--+--+
| 1|10| 5|16|25|
+--+--+--+--+--+
| 4|17| 2|11| 6|
+--+--+--+--+--+
| 9|20|13|24|15|
+--+--+--+--+--+
|18| 3|22| 7|12|
+--+--+--+--+--+
|21| 8|19|14|23|
+--+--+--+--+--+

(Time to find this solution = 70.3757 milliseconds)

Breakdown

• KnightBoard: Chessboard class is a 2D array that has n size, keeps track of the number of moves in moveCount, and current position of the knight in currentX and currentY. There are also some helper methods such as printChessBoard, copyBoard, and move (checks if a knights move to a specific position is valid). There are also setters and getters to modify moveCount, currentX, and currentY positions.
• KnightTour: Implements and prints a valid knight tour. This does not print all valid knight tours as the valid number of tours for a 6x6 board is 6,637,920 and the it only gets exponentially larger. The program essentially has all 8 moves of a knight listed out in two separate arrays possibleRow and possibleCol. It only adds valid moves from the current position to the stack. This for every single space that the knight can occupy until a board is found where currentBoard.getMoveCount() == n * n or if n == 3 || n == 4 there is no solution where every space is visited so a solution with all but one space visited is valid.

Solution Times

Size	Time in ms
3x3	0.771277
4x4	10.917376
5x5	55.889333
6x6	236.791035
7x7	90.314049
8x8	94947.098818

Visualization of the Stack

$ java KnightTour 3
Stack: Round 1
+--+--+--+
| 1|  |  |
+--+--+--+
|  |  |  |
+--+--+--+
|  |  |  |
+--+--+--+
Stack: Round 2 (two more possible moves are added to the stack)
+--+--+--+      +--+--+--+
| 1|  |  |      | 1|  |  |
+--+--+--+      +--+--+--+
|  |  | 2|      |  |  |  |
+--+--+--+      +--+--+--+
|  |  |  |      |  | 2|  |
+--+--+--+      +--+--+--+
Stack: Round 3 (explores all possible moves from the last board added to the stack)
+--+--+--+
| 1|  |  |
+--+--+--+
|  |  | 2|
+--+--+--+
| 3|  |  |
+--+--+--+
Stack: Round 4
+--+--+--+
| 1| 4|  |
+--+--+--+
|  |  | 2|
+--+--+--+
| 3|  |  |
+--+--+--+
Stack: Round 5
...
Stack: Round 6
...
Stack: Round 7
...
Stack: Round 8
+--+--+--+
| 1| 4| 7|
+--+--+--+
| 6|  | 2|
+--+--+--+
| 3| 8| 5|
+--+--+--+