A simple implementation of disjoint-set data structure with union-by-size and path halving. Works with any integral, unsigned type that fits in a std::size_t.

A disjoint-set data structure, also known as union-find or merge-find data structure, can help you store and quary and manipulate a collection of non-overlaping (disjoin) subsets of a set.

For example, you can use a disjoint-set data structure to determine connected components of a graph: start from every node being in it's own set. For each edge in the network, merge (union) the two sets the two ends of the edge belong to. The final collection of sets each detemine a connected component.

This package relies on cmake. Make sure a moderatly recent version (3.14 or newer) is already installed. You should also have a C++ compiler with C++14 support. We regularly test this with GCC 8.4 so anything more recent should do.

Here is how to build and run the tests:

$ git clone https://github.com/arashbm/disjoint_set.git
$ cd disjoint_set
$ mkdir build  # make directory to build in
$ cd build
$ cmake ..
$ cmake --build . --target disjoint_set_tests  # build the tests
$ ./disjoint_set_tests

At this point you should see "All tests passed" if all the steps are successful. You can continue by install the library on your system:

cmake --build . --target install

This final step might require admin previlages. It basically just copies the include/ directoy to its proper location on your system, e.g. to /usr/include on linux. It also copies the cmake files require by the cmake command find_package to their proper location, e.g. to /usr/share.

// in "example.cpp"

#include <iostream>
#include <ds/disjoint_set.hpp>

int main() {
  ds::disjoint_set<std::size_t> dis(10);

  dis.merge(1, 2);
  dis.merge(3, 2);
  dis.merge(0, 5);

  // get all the sets with their representative
  std::unordered_map<
    std::size_t,
    std::vector<std::size_t>> sets = dis.sets();
  std::cout << sets.size() << " disjoint sets" << std::endl;

  // get all the sets with their representative, except singleton sets
  auto sets_no_sing = dis.sets(false);
  std::cout << sets_no_sing.size() <<
    " sets without the singletons" << std::endl;

  // get representative of the set that 1 belongs to
  size_t rep = dis.rep(1);

  std::cout << "Members of the set containing 1:" << std::endl;
  for (auto&& i: sets[rep])
    std::cout << "- " << i << std::endl;

  return 0;
}

Assuming you cloned this library in /path/to/disjoint_set you can compile example.cpp with:

$ g++ -std=c++14 -I/path/to/disjoint_set/include -o example example.cpp

If you have installed the library as instructed previously, you skip -I option:

$ g++ -std=c++14 -o example example.cpp

$ ./example
7 disjoint sets
2 sets without the singletons
Members of the set containing 1:
- 1
- 2
- 3

Check out the tests (in src/disjoint_tests.cpp) for more examples.