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
140
141
142
143
144
145
146
147
148
149

//! Separate components of an undirected graph into disjoint sets.

use itertools::Itertools;
use std::collections::hash_map::Entry::{Occupied, Vacant};
use std::collections::{HashMap, HashSet};
use std::hash::Hash;
use std::iter::once;
use std::usize;

/// Lookup entries until we get the same value as the index, with
/// path halving. Adding a new entry to the table consists
/// into pushing the table length.
fn get_and_redirect(table: &mut [usize], mut idx: usize) -> usize {
    while idx != table[idx] {
        table[idx] = table[table[idx]];
        idx = table[idx];
    }
    idx
}

/// Separate components of an undirected graph into disjoint sets.
///
/// - `groups` is a set of group of vertices connected together. It is
///   acceptable for a group to contain only one node. Empty groups
///   receive special treatment (see below).
///
/// This function returns a pair containing:
///
/// - A mapping from every vertex to its set identifier. The set identifiers are
/// opaque and will not necessarily be compact. However, it is guaranteed that
/// they will not be greater than the number of groups.
/// - A mapping from every group to its set identifier, with the identifiers being
/// the same ones as the ones in the previous mapping. Each group corresponds to
/// the identifier at the same index, except for empty group whose identifier is
/// set to `std::usize::MAX`.
///
/// Note that if you have a raw undirected graph, you can build
/// such a structure by creating a group for every vertex containing
/// the vertex itself and its immediate neighbours.
#[must_use]
pub fn separate_components<N>(groups: &[Vec<N>]) -> (HashMap<&N, usize>, Vec<usize>)
where
    N: Hash + Eq,
{
    let mut table = (0..groups.len()).collect_vec();
    let mut indices = HashMap::new();
    for (mut group_index, group) in groups.iter().enumerate() {
        if group.is_empty() {
            table[group_index] = usize::max_value();
        }
        for element in group {
            match indices.entry(element) {
                Occupied(e) => {
                    table[group_index] = get_and_redirect(&mut table, *e.get());
                    group_index = table[group_index];
                }
                Vacant(e) => {
                    e.insert(group_index);
                }
            }
        }
    }
    for group_index in indices.values_mut() {
        *group_index = get_and_redirect(&mut table, *group_index);
    }
    for group_index in 0..groups.len() {
        if table[group_index] != usize::max_value() {
            let target = get_and_redirect(&mut table, group_index);
            // Due to path halving, this particular entry might not
            // be up-to-date yet.
            table[group_index] = target;
        }
    }
    (indices, table)
}

/// Separate components of an undirected graph into disjoint sets.
///
/// - `groups` is a set of group of vertices connected together. It is
///   acceptable for a group to contain only one node.
///
/// This function returns a list of sets of nodes forming disjoint connected
/// sets.
#[must_use]
pub fn components<N>(groups: &[Vec<N>]) -> Vec<HashSet<N>>
where
    N: Clone + Hash + Eq,
{
    let (_, gindices) = separate_components(groups);
    let gb = gindices
        .into_iter()
        .enumerate()
        .filter(|&(_, n)| n != usize::max_value())
        .sorted_by(|&(_, n1), &(_, n2)| Ord::cmp(&n1, &n2))
        .group_by(|&(_, n)| n);
    gb.into_iter()
        .map(|(_, gs)| {
            gs.flat_map(|(i, _)| groups[i].clone())
                .collect::<HashSet<_>>()
        })
        .collect()
}

/// Extract connected components from a graph.
///
/// - `starts` is a collection of vertices to be considered as start points.
/// - `neighbours` is a function returning the neighbours of a given node.
///
/// This function returns a list of sets of nodes forming disjoint connected
/// sets.
pub fn connected_components<N, FN, IN>(starts: &[N], mut neighbours: FN) -> Vec<HashSet<N>>
where
    N: Clone + Hash + Eq,
    FN: FnMut(&N) -> IN,
    IN: IntoIterator<Item = N>,
{
    components(
        &starts
            .iter()
            .map(|s| {
                neighbours(s)
                    .into_iter()
                    .chain(once(s.clone()))
                    .collect_vec()
            })
            .collect_vec(),
    )
}

/// Locate vertices amongst disjoint sets.
///
/// - `components` are disjoint vertices sets.
///
/// This function returns a map between every vertex and the index of
/// the set it belongs to in the `components` list.
#[allow(clippy::implicit_hasher)]
#[must_use]
pub fn component_index<N>(components: &[HashSet<N>]) -> HashMap<N, usize>
where
    N: Clone + Hash + Eq,
{
    let mut assoc = HashMap::with_capacity(components.len());
    for (i, c) in components.iter().enumerate() {
        for n in c {
            assoc.insert(n.clone(), i);
        }
    }
    assoc
}