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pub struct DisjointSetForest {
count: usize,
parent: Vec<usize>,
tree_size: Vec<usize>,
}
impl DisjointSetForest {
pub fn new(count: usize) -> DisjointSetForest {
let parent: Vec<usize> = (0..count).collect();
let tree_size = vec![1 as usize; count];
DisjointSetForest {
count,
parent,
tree_size,
}
}
pub fn num_trees(&self) -> usize {
self.parent
.iter()
.enumerate()
.fold(0, |acc, (i, p)| acc + if i == *p { 1 } else { 0 })
}
pub fn root(&mut self, i: usize) -> usize {
assert!(i < self.count);
let mut j = i;
loop {
unsafe {
let p = *self.parent.get_unchecked(j);
*self.parent.get_unchecked_mut(j) = *self.parent.get_unchecked(p);
if j == p {
break;
}
j = p;
}
}
j
}
pub fn find(&mut self, i: usize, j: usize) -> bool {
assert!(i < self.count && j < self.count);
self.root(i) == self.root(j)
}
pub fn union(&mut self, i: usize, j: usize) {
assert!(i < self.count && j < self.count);
let p = self.root(i);
let q = self.root(j);
if p == q {
return;
}
unsafe {
let p_size = *self.tree_size.get_unchecked(p);
let q_size = *self.tree_size.get_unchecked(q);
if p_size < q_size {
*self.parent.get_unchecked_mut(p) = q;
*self.tree_size.get_unchecked_mut(q) = p_size + q_size;
} else {
*self.parent.get_unchecked_mut(q) = p;
*self.tree_size.get_unchecked_mut(p) = p_size + q_size;
}
}
}
pub fn trees(&mut self) -> Vec<Vec<usize>> {
use std::collections::HashMap;
let mut root_sets: HashMap<usize, usize> = HashMap::new();
let mut sets: Vec<Vec<usize>> = vec![];
for i in 0..self.count {
let root = self.root(i);
match root_sets.get(&root).cloned() {
Some(set_idx) => {
sets[set_idx].push(i);
}
None => {
let idx = sets.len();
let set = vec![i];
sets.push(set);
root_sets.insert(root, idx);
}
}
}
sets
}
}
#[cfg(test)]
mod tests {
use super::DisjointSetForest;
use ::test;
use rand::{rngs::StdRng, SeedableRng};
use rand_distr::{Distribution, Uniform};
#[test]
fn test_trees() {
#[rustfmt::skip]
let mut forest = DisjointSetForest {
count: 8,
parent: vec![1, 3, 1, 3, 4, 4, 5, 4],
tree_size: vec![1, 3, 1, 4, 4, 2, 1, 1],
};
assert_eq!(forest.trees(), vec![vec![0, 1, 2, 3], vec![4, 5, 6, 7]]);
}
#[test]
fn test_union_find_sequence() {
let mut forest = DisjointSetForest::new(6);
assert_eq!(forest.parent, vec![0, 1, 2, 3, 4, 5]);
assert_eq!(forest.num_trees(), 6);
forest.union(0, 4);
assert_eq!(forest.parent, vec![0, 1, 2, 3, 0, 5]);
assert_eq!(forest.num_trees(), 5);
forest.union(1, 3);
assert_eq!(forest.parent, vec![0, 1, 2, 1, 0, 5]);
assert_eq!(forest.num_trees(), 4);
forest.union(3, 2);
assert_eq!(forest.parent, vec![0, 1, 1, 1, 0, 5]);
assert_eq!(forest.num_trees(), 3);
forest.union(2, 4);
assert_eq!(forest.parent, vec![1, 1, 1, 1, 0, 5]);
assert_eq!(forest.num_trees(), 2);
}
#[bench]
fn bench_disjoint_set_forest(b: &mut test::Bencher) {
let num_nodes = 500;
let num_edges = 20 * num_nodes;
let mut rng: StdRng = SeedableRng::seed_from_u64(1);
let uniform = Uniform::new(0, num_nodes);
let mut forest = DisjointSetForest::new(num_nodes);
b.iter(|| {
let mut count = 0;
while count < num_edges {
let u = uniform.sample(&mut rng);
let v = uniform.sample(&mut rng);
forest.union(u, v);
count += 1;
}
test::black_box(forest.num_trees());
});
}
}