data_beans/alg/union_find.rs
1//! Disjoint-set union (DSU) with union-by-rank and path halving.
2//!
3//! Kept in-tree (not delegated to `petgraph`/`disjoint_sets`) because callers
4//! need the per-root **size** (member count) for weighted centroid merging — a
5//! field none of the ecosystem crates expose.
6
7/// Union-Find (disjoint set) with path halving and union by rank.
8pub struct UnionFind {
9 parent: Vec<usize>,
10 rank: Vec<usize>,
11 size: Vec<usize>,
12}
13
14impl UnionFind {
15 pub fn new(n: usize) -> Self {
16 Self {
17 parent: (0..n).collect(),
18 rank: vec![0; n],
19 size: vec![1; n],
20 }
21 }
22
23 #[inline]
24 pub fn find(&mut self, mut x: usize) -> usize {
25 while self.parent[x] != x {
26 self.parent[x] = self.parent[self.parent[x]];
27 x = self.parent[x];
28 }
29 x
30 }
31
32 /// Union the sets containing `a` and `b`; returns the surviving root.
33 #[inline]
34 pub fn union(&mut self, a: usize, b: usize) -> usize {
35 let ra = self.find(a);
36 let rb = self.find(b);
37 if ra == rb {
38 return ra;
39 }
40 let (big, small) = if self.rank[ra] >= self.rank[rb] {
41 (ra, rb)
42 } else {
43 (rb, ra)
44 };
45 self.parent[small] = big;
46 self.size[big] += self.size[small];
47 if self.rank[big] == self.rank[small] {
48 self.rank[big] += 1;
49 }
50 big
51 }
52
53 /// Member count of the set whose root is `x` (caller passes a root, typically
54 /// `uf.find(...)` — accepting any node index would require an extra find).
55 #[inline]
56 pub fn size(&self, x: usize) -> usize {
57 self.size[x]
58 }
59
60 /// Direct parent pointer — valid as a final representative only after
61 /// `flatten` has been called. Used in multilevel extraction hot loops to
62 /// avoid per-call `find` after a batch of unions.
63 #[inline]
64 pub fn parent(&self, x: usize) -> usize {
65 self.parent[x]
66 }
67
68 /// Path-compress every node so `parent[i]` is its final representative.
69 /// Call after a batch of unions if subsequent lookups use [`Self::parent`] directly.
70 pub fn flatten(&mut self) {
71 for i in 0..self.parent.len() {
72 self.parent[i] = self.find(i);
73 }
74 }
75}