graphalgs 0.2.0

//! Algorithms that simplify work with such type of graphs as a
//! [tournament](https://en.wikipedia.org/wiki/Tournament_(graph_theory)).

use rand::Rng;
use std::collections::HashSet;
use std::hash::Hash;

use crate::traits::EdgeCount;
use petgraph::visit::{EdgeRef, IntoEdgeReferences, IntoNodeIdentifiers, NodeCount};

/// Is the graph a [tournament](https://en.wikipedia.org/wiki/Tournament_(graph_theory))?
///
/// This function checks if the given graph is a tournament and returns the corresponding boolean value.
///
/// # Examples
///
/// ```
/// use graphalgs::tournament::is_tournament;
/// use petgraph::Graph;
///
/// let graph = Graph::<(), ()>::from_edges(&[
///     (0, 2), (1, 0), (1, 2),
///     (3, 0), (3, 1), (3, 2),
/// ]);
///
/// assert!(is_tournament(&graph));
///
/// let graph = Graph::<(), ()>::from_edges(&[
///     (0, 2), (1, 0), (1, 2),
///     (3, 0), (3, 1), (1, 3),
/// ]);
///
/// // The graph is not a tournament, because it contains a pair of opposite edges.
/// assert!(!is_tournament(&graph));
/// ```
pub fn is_tournament<G>(graph: G) -> bool
where
    G: IntoEdgeReferences + NodeCount + EdgeCount,
    G::NodeId: Eq + Hash,
{
    // Tournament has |V|*(|V|-1)/2 edges.
    if 2 * graph.number_of_edges() != graph.node_count() * (graph.node_count() - 1) {
        return false;
    }

    let mut edges: HashSet<(G::NodeId, G::NodeId)> = HashSet::new();

    for edge in graph.edge_references() {
        let source = edge.source();
        let target = edge.target();

        if source == target
            || edges.contains(&(target, source))
            || edges.contains(&(source, target))
        {
            return false;
        }

        edges.insert((source, target));
    }

    true
}

/// Random tournament on n vertices.
///
/// Returns a vector of edges `Vec<(usize, usize)>`.
///
/// # Examples
///
/// ```
/// use graphalgs::tournament::{ random_tournament, is_tournament };
/// use petgraph::{ Graph, Directed };
///
/// let graph: Graph::<(), (), Directed, usize> = Graph::from_edges(random_tournament(4));
/// assert!(is_tournament(&graph));
/// ```
pub fn random_tournament(n: usize) -> Vec<(usize, usize)> {
    if n == 0 {
        return vec![];
    }

    let mut rng = rand::thread_rng();
    let mut edges = Vec::with_capacity(n * (n - 1) / 2);

    for i in 0..n - 1 {
        for j in i + 1..n {
            if rng.gen::<bool>() {
                edges.push((i, j));
            } else {
                edges.push((j, i));
            }
        }
    }

    edges
}

/// Is the tournament transitive?
///
/// Check if the tournament is transitive and return the corresponding boolean value.
///
/// # Examples
///
/// ```
/// use graphalgs::tournament::is_tournament_transitive;
/// use petgraph::Graph;
///
/// let graph = Graph::<(), ()>::from_edges(&[
///     (0, 1), (0, 2), (0, 3),
///     (1, 2), (1, 3), (2, 3),
/// ]);
/// assert!(is_tournament_transitive(&graph));
///
/// let graph = Graph::<(), ()>::from_edges(&[
///     (0, 2), (1, 0), (1, 2),
///     (3, 0), (3, 1), (2, 3),
/// ]);
/// assert!(!is_tournament_transitive(&graph));
/// ```
pub fn is_tournament_transitive<G>(graph: G) -> bool
where
    G: IntoEdgeReferences + NodeCount + EdgeCount + IntoNodeIdentifiers,
    G::NodeId: Eq + Hash,
{
    let mut edges: HashSet<(G::NodeId, G::NodeId)> =
        HashSet::with_capacity(graph.number_of_edges());
    edges.extend(
        graph
            .edge_references()
            .map(|edge| (edge.source(), edge.target())),
    );

    for x in graph.node_identifiers() {
        for y in graph.node_identifiers() {
            if x != y {
                for z in graph.node_identifiers() {
                    if z != y
                        && z != x
                        && edges.contains(&(x, y))
                        && edges.contains(&(y, z))
                        && edges.contains(&(z, x))
                    {
                        return false;
                    }
                }
            }
        }
    }

    true
}

#[cfg(test)]
mod tests {
    use super::*;
    use petgraph::csr::Csr;
    use petgraph::graphmap::GraphMap;
    use petgraph::matrix_graph::MatrixGraph;
    use petgraph::matrix_graph::UnMatrix;
    use petgraph::stable_graph::StableGraph;
    use petgraph::Directed;
    use petgraph::Graph;

    fn graph1() -> Graph<(), ()> {
        let mut graph = Graph::new();
        let n0 = graph.add_node(());
        let n1 = graph.add_node(());
        graph.add_node(());
        graph.add_edge(n0, n1, ());
        graph
    }

    fn graph2() -> Graph<(), ()> {
        let mut graph = Graph::new();
        let n0 = graph.add_node(());
        let n1 = graph.add_node(());
        let n2 = graph.add_node(());
        graph.add_edge(n0, n1, ());
        graph.add_edge(n1, n2, ());
        graph.add_edge(n2, n0, ());
        graph.add_edge(n2, n1, ());
        graph
    }

    fn graph3() -> Graph<(), ()> {
        Graph::<(), ()>::from_edges([(0, 2), (1, 0), (1, 2), (3, 0), (3, 1), (1, 2)])
    }

    fn graph4() -> Graph<(), ()> {
        Graph::<(), ()>::from_edges([(0, 2), (1, 0), (1, 2), (3, 0), (3, 1), (1, 1)])
    }

    fn graph_tour() -> Graph<(), i32> {
        let mut graph = Graph::new();
        let n0 = graph.add_node(());
        let n1 = graph.add_node(());
        let n2 = graph.add_node(());
        graph.add_edge(n0, n1, 0);
        graph.add_edge(n1, n2, 1);
        graph.add_edge(n2, n0, 2);
        graph
    }

    fn stable_graph_tour() -> StableGraph<(), i32> {
        let mut graph = StableGraph::new();
        let n0 = graph.add_node(());
        let n1 = graph.add_node(());
        let n2 = graph.add_node(());
        graph.add_edge(n0, n1, 0);
        graph.add_edge(n1, n2, 1);
        graph.add_edge(n2, n0, 2);
        graph
    }

    fn graphmap_tour() -> GraphMap<i8, i32, Directed> {
        let mut graph = GraphMap::new();
        let n0 = graph.add_node(0);
        let n1 = graph.add_node(1);
        let n2 = graph.add_node(2);
        graph.add_edge(n0, n1, 1);
        graph.add_edge(n1, n2, 3);
        graph.add_edge(n0, n2, 2);
        graph
    }

    fn matrix_graph_tour() -> UnMatrix<(), i32> {
        let mut graph = MatrixGraph::new_undirected();
        let n0 = graph.add_node(());
        let n1 = graph.add_node(());
        let n2 = graph.add_node(());
        graph.add_edge(n0, n1, 0);
        graph.add_edge(n1, n2, 1);
        graph.add_edge(n0, n2, 2);
        graph
    }

    fn csr_tour() -> Csr<(), i32> {
        let mut graph = Csr::new();
        let n0 = graph.add_node(());
        let n1 = graph.add_node(());
        let n2 = graph.add_node(());
        let n3 = graph.add_node(());
        graph.add_edge(n0, n1, 0);
        graph.add_edge(n0, n2, 2);
        graph.add_edge(n0, n3, 3);
        graph.add_edge(n1, n2, 3);
        graph.add_edge(n1, n3, 4);
        graph.add_edge(n2, n3, 5);
        graph
    }

    #[test]
    fn test_is_tournament() {
        // At the same time testing EdgeCount trait.
        assert!(!is_tournament(&graph1()));
        assert!(!is_tournament(&graph2()));
        assert!(!is_tournament(&graph3()));
        assert!(!is_tournament(&graph4()));
        assert!(is_tournament(&graph_tour()));
        assert!(is_tournament(&stable_graph_tour()));
        assert!(is_tournament(&graphmap_tour()));
        assert!(is_tournament(&matrix_graph_tour()));
        assert!(is_tournament(&csr_tour()));
    }

    #[test]
    fn test_random_tournament() {
        assert_eq!(random_tournament(0), vec![]);
        assert_eq!(random_tournament(1), vec![]);
        for i in 2..100 {
            assert!(is_tournament(
                &Graph::<(), (), Directed, usize>::from_edges(random_tournament(i))
            ));
        }
    }

    #[test]
    fn test_is_tournament_transitive() {
        assert!(!is_tournament_transitive(&graph_tour()));
        assert!(!is_tournament_transitive(&stable_graph_tour()));
        assert!(is_tournament_transitive(&graphmap_tour()));
        assert!(is_tournament_transitive(&matrix_graph_tour()));
        assert!(is_tournament_transitive(&csr_tour()));
        assert!(is_tournament_transitive(
            &Graph::<(), (), Directed, usize>::from_edges(random_tournament(2))
        ));

        let mut graph = Graph::<(), ()>::new();
        assert!(is_tournament_transitive(&graph));
        graph.add_node(());
        assert!(is_tournament_transitive(&graph));
    }
}