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| 1 | +/// A Disjoint Set Union (Union-Find) structure using 0..n indices. |
| 2 | +/// |
| 3 | +/// Uses path compression and union by size (attach smaller tree under larger). |
| 4 | +#[derive(Debug, Clone)] |
| 5 | +pub struct UnionFind { |
| 6 | + parent: Vec<usize>, |
| 7 | + size: Vec<usize>, |
| 8 | + components: usize, |
| 9 | +} |
| 10 | + |
| 11 | +impl UnionFind { |
| 12 | + /// Create a `UnionFind` with `n` elements (0..n-1), each in its own set. |
| 13 | + #[must_use] |
| 14 | + pub fn new(n: usize) -> Self { |
| 15 | + Self { |
| 16 | + parent: (0..n).collect(), |
| 17 | + size: vec![1; n], |
| 18 | + components: n, |
| 19 | + } |
| 20 | + } |
| 21 | + |
| 22 | + /// Returns the number of elements. |
| 23 | + #[must_use] |
| 24 | + pub const fn len(&self) -> usize { |
| 25 | + self.parent.len() |
| 26 | + } |
| 27 | + |
| 28 | + /// Returns true if no elements. |
| 29 | + #[must_use] |
| 30 | + pub const fn is_empty(&self) -> bool { |
| 31 | + self.parent.is_empty() |
| 32 | + } |
| 33 | + |
| 34 | + /// Find the representative (root) of `mut x` with path compression. |
| 35 | + /// |
| 36 | + /// # Panics |
| 37 | + /// Panics if `x` is out of bounds. |
| 38 | + pub fn find(&mut self, mut x: usize) -> usize { |
| 39 | + let n = self.len(); |
| 40 | + assert!(x < n, "index out of bounds in UnionFind::find"); |
| 41 | + |
| 42 | + // Find root |
| 43 | + let mut root = x; |
| 44 | + while self.parent[root] != root { |
| 45 | + root = self.parent[root]; |
| 46 | + } |
| 47 | + |
| 48 | + // Path compression |
| 49 | + while self.parent[x] != x { |
| 50 | + let next = self.parent[x]; |
| 51 | + self.parent[x] = root; |
| 52 | + x = next; |
| 53 | + } |
| 54 | + |
| 55 | + root |
| 56 | + } |
| 57 | + |
| 58 | + /// Returns true if `a` and `b` are in the same set. |
| 59 | + /// |
| 60 | + /// # Panics |
| 61 | + /// Panics if indices out of bounds. |
| 62 | + pub fn same(&mut self, a: usize, b: usize) -> bool { |
| 63 | + self.find(a) == self.find(b) |
| 64 | + } |
| 65 | + |
| 66 | + /// Unite the sets containing `a` and `b`. Returns `true` if they were separate (merge happened). |
| 67 | + /// |
| 68 | + /// # Panics |
| 69 | + /// Panics if indices out of bounds. |
| 70 | + pub fn unite(&mut self, a: usize, b: usize) -> bool { |
| 71 | + let mut ra = self.find(a); |
| 72 | + let mut rb = self.find(b); |
| 73 | + |
| 74 | + if ra == rb { |
| 75 | + return false; |
| 76 | + } |
| 77 | + |
| 78 | + // Union by size: ensure ra is the larger root |
| 79 | + if self.size[ra] < self.size[rb] { |
| 80 | + std::mem::swap(&mut ra, &mut rb); |
| 81 | + } |
| 82 | + |
| 83 | + // Attach rb under ra |
| 84 | + self.parent[rb] = ra; |
| 85 | + self.size[ra] += self.size[rb]; |
| 86 | + self.components -= 1; |
| 87 | + true |
| 88 | + } |
| 89 | + |
| 90 | + /// Size of the set containing `x`. |
| 91 | + /// |
| 92 | + /// # Panics |
| 93 | + /// Panics if `x` out of bounds. |
| 94 | + pub fn set_size(&mut self, x: usize) -> usize { |
| 95 | + let r = self.find(x); |
| 96 | + self.size[r] |
| 97 | + } |
| 98 | + |
| 99 | + /// Number of connected components (disjoint sets) |
| 100 | + #[must_use] |
| 101 | + pub const fn component_count(&self) -> usize { |
| 102 | + self.components |
| 103 | + } |
| 104 | +} |
| 105 | + |
| 106 | +#[cfg(test)] |
| 107 | +mod tests { |
| 108 | + use super::UnionFind; |
| 109 | + |
| 110 | + #[test] |
| 111 | + fn basic_union_find() { |
| 112 | + let mut uf = UnionFind::new(5); |
| 113 | + assert_eq!(uf.component_count(), 5); |
| 114 | + assert!(!uf.same(0, 1)); |
| 115 | + assert!(uf.unite(0, 1)); |
| 116 | + assert!(uf.same(0, 1)); |
| 117 | + assert_eq!(uf.set_size(0), 2); |
| 118 | + assert_eq!(uf.component_count(), 4); |
| 119 | + |
| 120 | + // idempotent union returns false |
| 121 | + assert!(!uf.unite(0, 1)); |
| 122 | + |
| 123 | + // connect remaining |
| 124 | + uf.unite(1, 2); |
| 125 | + uf.unite(3, 4); |
| 126 | + assert_eq!(uf.component_count(), 2); |
| 127 | + assert!(uf.same(0, 2)); |
| 128 | + assert!(uf.same(3, 4)); |
| 129 | + assert!(!uf.same(2, 3)); |
| 130 | + } |
| 131 | + |
| 132 | + #[test] |
| 133 | + #[should_panic] |
| 134 | + fn find_out_of_bounds() { |
| 135 | + let mut uf = UnionFind::new(3); |
| 136 | + let _ = uf.find(10); |
| 137 | + } |
| 138 | +} |
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