Allocation-free UnionFind library for bare metal environments

Budi Syahiddin

Last update: Dec 10, 2022

Overview

Allocation-free UnionFind library for bare metal environments

The library provides the following algorithms that is used with UnionFind.

QuickFind
QuickUnion
Weighted QuickUnion
Weighted QuickUnion With Path Compression (Default)

Setup

Cargo.toml setup

[dependencies]
pulau-rs = "0.1.0"

Asymptotic Complexity

Algorithm	Struct	Init	Union	Find	Connected
QuickFind	`QuickFind`	`O(N)`	`O(N)`	`O(1)`	`O(1)`
QuickUnion	`QuickUnion`	`O(N)`	`O(N)`	`O(N)`	`O(N)`
Weighted (Rank) QuickUnion With Path Compression	`QuickUnion`	`O(N)`	`Amortized O(α(N))`	`Amortized O(α(N))`	`Amortized O(α(N))`
Weighted (Size) QuickUnion With Path Compression	`QuickUnion`	`O(N)`	`Amortized O(α(N))`	`Amortized O(α(N))`	`Amortized O(α(N))`

*Where α is the inverse Ackermann function

Applications of UnionFind

Checking for connected components in a graph
Checking for cycles in a graph
Searching for connected components in an image
Finding minimum spanning tree using Kruskal

Example Usage

use pulau_rs::{UnionFind, QuickFind, QuickUnion, BySize};
fn make_uf_quickfind() {
    // construct with quickfind algorithm with fixed size 10
    let mut uf = UnionFind::<QuickFind, u32, 10, 0>::new();
}

fn make_uf_quickunion() {
    // construct weighted quickunion with path compression algorithm with fixed size 10
    let mut uf = UnionFind::<QuickUnion, u32, 10>::new();
    // construct weighted quickunion with path compression using size heuristics and fixed size 10
    let mut uf_with_sz = UnionFind::<QuickUnion<BySize>, u8, 10>::new();
    uf.union_sets(1,2);
    uf.union_sets(2,3);
    uf.union_sets(2,3);
    assert!(uf.connected(1, 3));
}

License

pulau-rs is licensed under MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)

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