# 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.