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
150
151
152
153

use arboretum_td::graph::{BaseGraph, HashMapGraph};
use std::collections::HashSet;

pub fn is_independent_set(graph: &HashMapGraph, sol: &HashSet<usize>) -> bool {
    let sol: Vec<usize> = sol.iter().copied().collect();

    for i in 0..sol.len() {
        let u = sol[i];

        if !graph.has_vertex(u) {
            continue;
        }

        #[allow(clippy::needless_range_loop)]
        for j in i + 1..sol.len() {
            let v = sol[j];

            if !graph.has_vertex(v) {
                continue;
            }

            if graph.has_edge(u, v) {
                return false;
            }
        }
    }

    true
}

pub fn brute_force_max_independent_set(graph: &HashMapGraph) -> HashSet<usize> {
    let n = graph.order();

    for i in 0..n + 1 {
        let mut sol = HashSet::new();
        if brute_force_max_independent_set_rec(graph, &mut sol, n - i, 0) {
            return sol;
        }
    }

    panic!("should never happen")
}

fn brute_force_max_independent_set_rec(
    graph: &HashMapGraph,
    sol: &mut HashSet<usize>,
    mio_size: usize,
    current_vertex: usize,
) -> bool {
    if current_vertex == graph.order() {
        if sol.len() != mio_size {
            return false;
        }

        return is_independent_set(graph, sol);
    }

    sol.insert(current_vertex);
    if brute_force_max_independent_set_rec(graph, sol, mio_size, current_vertex + 1) {
        return true;
    }

    sol.remove(&current_vertex);
    if brute_force_max_independent_set_rec(graph, sol, mio_size, current_vertex + 1) {
        return true;
    }

    false
}

#[cfg(test)]
mod tests {
    use crate::{
        generation::erdos_renyi::generate_hash_map_graph,
        utils::max_independent_set::{brute_force_max_independent_set, is_independent_set},
    };
    use arboretum_td::graph::{HashMapGraph, MutableGraph};
    use std::collections::HashSet;

    #[test]
    fn empty_set() {
        let sol = HashSet::new();

        for n in 1..10 {
            let graph = generate_hash_map_graph(n, 0.3, Some(n as u64));

            assert!(is_independent_set(&graph, &sol));
            assert!(is_independent_set(
                &graph,
                &brute_force_max_independent_set(&graph)
            ))
        }
    }

    #[test]
    fn isolated() {
        let mut sol = HashSet::new();

        for n in 1..10 {
            let graph = generate_hash_map_graph(n, 0., Some(n as u64));
            sol.insert(n - 1);

            assert!(is_independent_set(&graph, &sol));
            assert!(is_independent_set(
                &graph,
                &brute_force_max_independent_set(&graph)
            ))
        }
    }

    #[test]
    fn single_edge() {
        let mut graph = HashMapGraph::new();
        graph.add_vertex(0);
        graph.add_vertex(1);
        graph.add_edge(0, 1);

        let mut sol = HashSet::new();
        sol.insert(0);
        assert!(is_independent_set(&graph, &sol));

        sol.insert(1);
        assert!(!is_independent_set(&graph, &sol));

        assert!(is_independent_set(
            &graph,
            &brute_force_max_independent_set(&graph)
        ))
    }

    #[test]
    fn clique() {
        let mut sol = HashSet::new();
        sol.insert(0);

        for n in 2..15 {
            let graph = generate_hash_map_graph(n, 1., Some(n as u64));

            let v = n - 1;

            sol.insert(v);
            assert!(!is_independent_set(&graph, &sol));

            sol.remove(&v);
            assert!(is_independent_set(&graph, &sol));

            assert!(is_independent_set(
                &graph,
                &brute_force_max_independent_set(&graph)
            ))
        }
    }
}