libdoc.md

pulau-rs

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)

Asymptotic Complexity

Algorithm	Struct	Init	Union	Find	Connected
QuickFind	[QuickFind]	O(N)	O(N)	O(1)	O(1)
QuickUnion	[QuickUnion<false, false>]	O(N)	O(N)	O(N)	O(N)
Weighted QuickUnion	[QuickUnion<ByRank, false>]	O(N)	O(lg N)	O(lg N)	O(lg N)
Weighted (Rank) QuickUnion With Path Compression	[QuickUnion<ByRank, true>]	O(N)	Θ(α(N))	Θ(α(N))	Θ(α(N))
Weighted (Size) QuickUnion With Path Compression	[QuickUnion<BySize, true>]	O(N)	Θ(α(N))	Θ(α(N))	Θ(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>::default();
}

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