An online Knight's tour visualizer using divide and conquer algorithm
This project uses Emscripten to compile C code into JavaScript.
For an online version, see https://sgalal.github.io/knights-tour-visualization/.
- Source files:
src - For test:
test - For web pages:
index.html,index.js,index.css
- Prerequisite: Emscripten
- 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
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.
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.
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:
Then connect the parts together. Since all the parts are structured, we can combine them by substitute the directions on the corners:
Since every point is connected with other two points, and there are only 8 possible directions (from 0 to 7):
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.