marhicjeromegit / exact_cover

Implementation of the dancing link algorithm to find the exact cover subset of rows for a given matrix

ExactCover

This gem is a ruby implementation of D.Knuth's paper "Dancing Link" : https://arxiv.org/abs/cs/0011047 It implements a solver for the "exact cover of a matrix" problem. For a given matrix of 0s and 1s, it finds a set of rows that contains exactly one "1" in each column. This can be used to implement a tetramino or a sudoku solver.

Installation

Add this line to your application's Gemfile:

gem 'exact_matrix_cover'

And then execute:

$ bundle

Or install it yourself as:

$ gem install exact_matrix_cover

Usage

Basic usage

require "exact_cover"

matrix =
  [
    [0, 0, 1, 0, 1, 1, 0],
    [1, 0, 0, 1, 0, 0, 1],
    [0, 1, 1, 0, 0, 1, 0],
    [1, 0, 0, 1, 0, 0, 0],
    [0, 1, 0, 0, 0, 0, 1],
    [0, 0, 0, 1, 1, 0, 1]
  ]

solutions = ExactCover::CoverSolver.new(matrix).call
solutions.count
# => 1
solutions.first
# => [[1, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1], [0, 0, 1, 0, 1, 1, 0]]
# this corresponds to the 4th, 5th and first rows of the given matrix

You can iterate through all the solutions

require "exact_cover"

matrix =
  [
    [1, 1],
    [0, 1],
    [1, 0]
  ]

solutions = ExactCover::CoverSolver.new(matrix).call
solutions.count
# => 2
solutions.next
# => [[1, 1]]
solutions.next
# => [[1, 0], [0, 1]]

You can also pass a time limit to the cover solver. It will stop searching the solution space and raise a TimeLimitReached exception after the time limit has elapsed.

Raises an exception after 10 seconds

begin
  solutions = ExactCover::CoverSolver.new(matrix, 10).call
rescue ExactCover::CoverSolver::TimeLimitReached
end

Development

After checking out the repo, run bin/setup to install dependencies. Then, run rake spec to run the tests. You can also run bin/console for an interactive prompt that will allow you to experiment.

To install this gem onto your local machine, run bundle exec rake install. To release a new version, update the version number in version.rb, and then run bundle exec rake release, which will create a git tag for the version, push git commits and tags, and push the .gem file to rubygems.org.

Contributing

Bug reports and pull requests are welcome on GitHub at https://github.com/[USERNAME]/exact_cover.

License

The gem is available as open source under the terms of the MIT License.