A Disjoint-Set data structure (aka Union-Find w/ Rank)

What is Union-Find?

Suppose you have a collection S of elements e1, e2, ..., en, and wish to group them into different collections using operations:

• "put ei and ej into the same group" (union),
• "give me a representative of the group ei belongs to" (find).

Then a Union-Find data structure helps to store the underlying groups very efficiently and implements this API.

(Some) Applications

• Detect Cycles in Graph: Given a graph G, we can put the endpoints of edges into the same group (same connected component) unless there is a pair of endpoints (ei, ej) that share a group representative. If that happens, there was already a path existing between them, and adding this edge will add multiple paths, which cannot be the case for acyclic graphs.

• Number of connected components in Graph: Given a graph G, put the endpoints of edges into the same group (same connected component). Once all nodes are exhausted, the number of groups formed is the number of connected components in G.

Some interesting lecture notes regarding Union-Find.

Usage

Setup

In Cargo.toml, add this crate as a dependency.

[dependencies]
reunion = { version = "0.1" }

API

Example 1

Task: Create a UnionFind data structure of arbitrary size that contains usize at its elements. Then, union a few elements and capture the state of the data structure after that.

Solution:

use reunion::{UnionFind, UnionFindTrait};
use std::collections::HashSet;

fn main() {
    // Create a UnionFind data structure of arbitrary size that contains subsets of usizes.
    let mut uf1 = UnionFind::<usize>::new();

    // Note: Trivial subsets (i.e. singletons) are ignored in the data structure because they can always be calculated based on the state and the context.

    println!("Freshly created structure: {}", uf1);

    uf1.union(2, 1);
    uf1.union(4, 3);
    uf1.union(6, 5);
    uf1.union(1, 5);

    println!("After a few unions: {}", uf1);

    let mut hs1 = HashSet::new();
    hs1.insert(1);
    hs1.insert(2);
    hs1.insert(6);
    hs1.insert(5);

    let mut hs2 = HashSet::new();
    hs2.insert(3);
    hs2.insert(4);

    let subsets = uf1.subsets();

    assert_eq!(subsets.len(), 2);

    assert!(&subsets.contains(&hs1));
    assert!(&subsets.contains(&hs2));

    // Iterate over the subsets.

    for partition in uf1 {
        println!("{:?}", partition);
    }
}

Example 2

Task: Create a UnionFind data structure of size at least 10, that contains u16 at its elements.

Note: The size business only helps for reducing the number of memory reallocations required. Therefore, it is not too special and is totally optional.

Solution:

// Create a UnionFind data structure of a fixed size that contains subsets of u16.
let mut uf2 = UnionFind::<u16>::with_capacity(10);

println!("{}", uf2);