Dancing links algorithm implementation

Introduction

An implementation of Knuth's dancing links algorithm for exact cover search.

Dancing links, Donald E. Knuth, Submitted on 15 Nov 2000 (see http://en.wikipedia.org/wiki/Dancing_Links, http://arxiv.org/abs/cs/0011047 and https://arxiv.org/pdf/cs/0011047v1.pdf).

In computer science, Dancing Links, also known as DLX, is the technique suggested by Donald Knuth to efficiently implement his Algorithm X. Algorithm X is a recursive, nondeterministic, depth-first, backtracking algorithm that finds all solutions to the exact cover problem.

Some of the better-known exact cover problems include tiling, the n queens problem, and Sudoku. The name Dancing Links comes from the way the algorithm works, as iterations of the algorithm cause the links to "dance" with partner links so as to resemble an "exquisitely choreographed dance."

Knuth credits Hiroshi Hitotsumatsu and Kohei Noshita with having invented the idea in 1979, but it is his paper which has popularized it.

See also http://en.wikipedia.org/wiki/Exact_cover and http://en.wikipedia.org/wiki/Exact_cover#Sudoku for more.

dancing_links.h and dancing_links.c are used to build a static library libdlx.a.

• For details of the interface of this library, read comments in dancing_links.h.
• For details of the implementation, read comments in dancing_links.c.

Documentation (HTML and PDF) can also be generated by doxygen using command make doc.

For usage of the library, look at examples in main.c, which is intented for unit testing purpose only (tests include sudoku solver and pentomino).

Code compiles with C compiler clang only as it makes use of __attribute__ ((overloadable)) which is a C language extension (see http://clang.llvm.org/docs/AttributeReference.html#overloadable).

Usage

1. Create a universe of elements with dlx_universe_create.

2. Create subsets of elements with successive calls to dlx_subset_define.

3. Optionally enforce one or several subsets to be included in every solution with successive calls to dlx_subset_require_in_solution.

4. Optionally declare a callback function to be called for every solution found with dlx_displayer_set.

5. Search for all sets of subsets exactly covering the universe with dlx_exact_cover_search.

6. Release the universe with dlx_universe_destroy.

All functions are declared in the header file dancing_links.h.

Have fun and let me know !