1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139

//! Weighted Union Find
use std::collections::{HashMap, HashSet};
#[derive(Debug, Clone)]
enum Node {
    Root(usize),
    Child((usize, i64)),
}
///UnionFind
#[derive(Clone, Debug)]
pub struct WeightedDisjointSetUnion {
    uf: Vec<Node>,
}

impl WeightedDisjointSetUnion {
    pub fn new(n: usize) -> WeightedDisjointSetUnion {
        WeightedDisjointSetUnion {
            uf: vec![Node::Root(1); n],
        }
    }

    pub fn root(&mut self, target: usize) -> (usize, i64) {
        match self.uf[target] {
            Node::Root(_) => (target, 0),
            Node::Child((par, w)) => {
                let (root, root_w) = self.root(par);
                self.uf[target] = Node::Child((root, root_w + w));
                (root, root_w + w)
            }
        }
    }
    pub fn unite(&mut self, x: usize, y: usize, weight: i64) -> bool {
        let rx = self.root(x);
        let ry = self.root(y);
        if rx.0 == ry.0 {
            return false;
        }
        let size_x = self.size(x);
        let size_y = self.size(y);
        let w = weight + ry.1 - rx.1;

        let (rx, ry, w) = if size_x > size_y {
            (rx, ry, -w)
        } else {
            (ry, rx, w)
        };

        self.uf[rx.0] = Node::Root(size_x + size_y);
        self.uf[ry.0] = Node::Child((rx.0, w));

        true
    }
    pub fn is_same(&mut self, x: usize, y: usize) -> bool {
        self.root(x).0 == self.root(y).0
    }
    pub fn size(&mut self, x: usize) -> usize {
        let (root, _) = self.root(x);
        match self.uf[root] {
            Node::Root(size) => size,
            Node::Child(_) => 0,
        }
    }
    pub fn get_diff(&mut self, x: usize, y: usize) -> i64 {
        let rx = self.root(x);
        let ry = self.root(y);
        assert_eq!(rx.0, ry.0);
        rx.1 - ry.1
    }
    pub fn get_same_group(&mut self, x: usize) -> HashSet<usize> {
        let root = self.root(x);
        let mut g = HashSet::new();
        for i in 0..self.uf.len() {
            if root.0 == self.root(i).0 {
                g.insert(i);
            }
        }
        g
    }
    pub fn get_all_groups(&mut self) -> HashMap<usize, HashSet<(usize, i64)>> {
        let mut map = HashMap::new();
        for i in 0..self.uf.len() {
            let (root, w) = self.root(i);

            map.entry(root).or_insert_with(HashSet::new).insert((i, w));
        }
        map
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_dsu() {
        let mut d = WeightedDisjointSetUnion::new(5);
        d.unite(0, 1, 1);
        assert!(d.is_same(0, 1));
        d.unite(1, 2, 1);
        assert!(d.is_same(0, 2));
        assert_eq!(d.size(0), 3);
        assert!(!d.is_same(0, 3));

        d.unite(0, 3, 3);
        d.unite(1, 4, 3);

        for i in 0..5 {
            assert_eq!(d.get_diff(0, i), i as i64);
        }
    }
    #[test]
    fn test_dsu_w2() {
        let mut dsu = WeightedDisjointSetUnion::new(16);
        dsu.unite(0, 1, 2);
        dsu.unite(2, 3, 4);
        dsu.unite(4, 5, 5);
        dsu.unite(6, 7, 5);
        dsu.unite(8, 9, 8);
        dsu.unite(10, 11, 5);
        dsu.unite(12, 13, 8);
        dsu.unite(14, 15, 7);

        dsu.unite(15, 13, -16);
        dsu.unite(11, 9, -9);
        dsu.unite(7, 5, -53);
        dsu.unite(3, 1, -9);

        dsu.unite(0, 15, 973);
        dsu.unite(4, 11, 81);

        dsu.unite(3, 4, 853);

        let ans = vec![
            0, 2, 7, 11, 864, 869, 917, 922, 928, 936, 940, 945, 949, 957, 966, 973,
        ];
        for (i, &v) in ans.iter().enumerate() {
            assert_eq!(dsu.get_diff(0, i), v);
        }
    }
}