Disjoint Sets

# Disjoint Sets

Some algorithms, such as finding connected components in undirected graph and Kruskal's method of finding minimum spanning tree, require a data structure that can efficiently represent a collection of disjoint subsets. A widely used data structure for this purpose is the Disjoint set forest.

Usage:

``````a = IntDisjointSets(10)  # creates a forest comprised of 10 singletons
union!(a, 3, 5)          # merges the sets that contain 3 and 5 into one and returns the root of the new set
root_union!(a, x, y)     # merges the sets that have root x and y into one and returns the root of the new set
find_root(a, 3)          # finds the root element of the subset that contains 3
in_same_set(a, x, y)     # determines whether x and y are in the same set
elem = push!(a)          # adds a single element in a new set; returns the new element
# (this operation is often called MakeSet)``````

One may also use other element types:

``````a = DisjointSets{AbstractString}(["a", "b", "c", "d"])
union!(a, "a", "b")
in_same_set(a, "c", "d")
push!(a, "f")``````

Note that the internal implementation of `IntDisjointSets` is based on vectors, and is very efficient. `DisjointSets{T}` is a wrapper of `IntDisjointSets`, which uses a dictionary to map input elements to an internal index. Note for `DisjointSets`, `union!`, `root_union!` and `find_root` return the index of the root.