//! Generators for common graphs.

use crate::models::AppendGraph;
use crate::traits::{GraphTopology, GraphTopologyAddition, GraphTopologyConversion};

/// Builds a graph of type `G` by running a generator on a temporary graph.
///
/// `generate_as` fills a temporary [`AppendGraph`] and converts it to `G`. It returns the handles
/// of the elements it created as handles of the resulting graph. This makes it possible to obtain
/// graph types directly that do not implement [`GraphTopologyAddition`], such as [`FrozenGraph`].
///
/// # Examples
///
/// ```
/// use grapherity::prelude::*;
/// use grapherity::generators;
/// use grapherity::models::FrozenGraph;
///
/// // Generates a parameterless Petersen graph as a FrozenGraph model.
/// let (graph, vertices, edges) = generators::generate_as::<FrozenGraph>(generators::petersen);
/// assert_eq!(graph.vertex_count(), 10);
/// assert!(graph.vertices().all(|v| graph.degree(v) == 3));
///
/// // Generates a parameterized complete graph as a FrozenGraph model.
/// let (graph, vertices, edges) = generators::generate_as::<FrozenGraph>(|g| generators::complete(g, 5));
/// assert_eq!(graph.vertex_count(), 5);
/// assert!(graph.vertices().all(|v| graph.degree(v) == 4));
/// ```
///
/// [`FrozenGraph`]: crate::models::FrozenGraph
pub fn generate_as<G>(
    generator: impl FnOnce(
        &mut AppendGraph,
    ) -> (
        Vec<<AppendGraph as GraphTopology>::Vertex>,
        Vec<<AppendGraph as GraphTopology>::Edge>,
    ),
) -> (G, Vec<G::Vertex>, Vec<G::Edge>)
where
    G: GraphTopologyConversion,
{
    let mut builder = AppendGraph::new();
    let (vertices, edges) = generator(&mut builder);
    let (graph, iso) = G::convert(&builder);
    (
        graph,
        vertices.into_iter().map(|v| iso.vertex(v)).collect(),
        edges.into_iter().map(|e| iso.edge(e)).collect(),
    )
}

/// Generates a path graph.
///
/// Generates a [path graph] *P(n)* with `n` vertices and `n - 1` edges in `graph` as a new
/// connected component and returns the new vertices *v0, v1, ..., v(n - 1)* and edges
/// *e0, e1, ..., e(n - 2)* in order, i.e. *e0 = (v0, v1)*, *e1 = (v1, v2)*, etc. and *v0* and
/// *v(n-1)* being the two terminal vertices
///
/// For `n == 0`, nothing is added. For `n == 1`, only a single vertex and no edges are added.
///
/// [Path graph]: https://en.wikipedia.org/wiki/Path_graph
pub fn path<G: GraphTopologyAddition>(graph: &mut G, n: usize) -> (Vec<G::Vertex>, Vec<G::Edge>) {
    let edge_capacity = n.saturating_sub(1);
    graph.reserve_vertices(n);
    graph.reserve_edges(edge_capacity);
    let vertices: Vec<_> = (0..n).map(|_| graph.add_vertex()).collect();
    let edges = (0..edge_capacity)
        .map(|i| graph.add_edge(vertices[i], vertices[i + 1]))
        .collect();
    (vertices, edges)
}

/// Generates a cycle graph.
///
/// Generates a [cycle graph] *C(n)* with `n` vertices and `n` edges in `graph` as a new connected
/// component and returns the new vertices *v0, v1, ..., v(n - 1)* and edges *e0, e1, ..., e(n - 1)*
/// in order, i.e. *e0 = (v0, v1), e1 = (v1, v2), ..., e(n - 1) = (v(n - 1), v0)*.
///
/// For `n == 0`, nothing is added. For `n == 1`, a single vertex with a loop is added. For
/// `n == 2`, two vertices and two edges between them (multi-edge) are added.
///
/// [Cycle graph]: https://en.wikipedia.org/wiki/Cycle_graph
pub fn cycle<G: GraphTopologyAddition>(graph: &mut G, n: usize) -> (Vec<G::Vertex>, Vec<G::Edge>) {
    graph.reserve_vertices(n);
    graph.reserve_edges(n);
    let vertices: Vec<_> = (0..n).map(|_| graph.add_vertex()).collect();
    let edges = (0..n)
        .map(|i| graph.add_edge(vertices[i], vertices[if i < n - 1 { i + 1 } else { 0 }]))
        .collect();
    (vertices, edges)
}

/// Generates a complete graph.
///
/// Generates a [complete graph] *K(n)* with `n` vertices and `n * (n - 1) / 2` edges in `graph` as
/// a new connected component and returns the new vertices and edges.
///
/// For `n == 0`, nothing is added. For `n == 1`, only a single vertex is added.
///
/// [Complete graph]: https://en.wikipedia.org/wiki/Complete_graph
pub fn complete<G: GraphTopologyAddition>(
    graph: &mut G,
    n: usize,
) -> (Vec<G::Vertex>, Vec<G::Edge>) {
    let edge_capacity = n * n.saturating_sub(1) / 2;
    graph.reserve_vertices(n);
    graph.reserve_edges(edge_capacity);
    let vertices: Vec<_> = (0..n).map(|_| graph.add_vertex()).collect();
    let mut edges = Vec::with_capacity(edge_capacity);
    for (i, &u) in vertices.iter().enumerate() {
        for &v in &vertices[i + 1..] {
            edges.push(graph.add_edge(u, v));
        }
    }
    (vertices, edges)
}

/// Generates a Petersen graph.
///
/// Generates a [Petersen graph] in `graph` as a new connected component and returns the new
/// vertices and edges. This graph is also the Kneser graph *KG(5, 2)*.
///
/// [Petersen graph]: https://en.wikipedia.org/wiki/Petersen_graph
pub fn petersen<G: GraphTopologyAddition>(graph: &mut G) -> (Vec<G::Vertex>, Vec<G::Edge>) {
    const N: usize = 5;
    const K: usize = 2;

    graph.reserve_vertices(10);
    graph.reserve_edges(15);
    let vertices: Vec<_> = (0..10).map(|_| graph.add_vertex()).collect();
    let edges = (0..15)
        .map(|j| {
            let i = j / 3;
            match j % 3 {
                0 => {
                    let outer = if i < N - 1 { i + 1 } else { 0 };
                    graph.add_edge(vertices[i], vertices[outer])
                }
                1 => {
                    let inner = if i < N - K { i + N + K } else { i + K };
                    graph.add_edge(vertices[i + N], vertices[inner])
                }
                _ => graph.add_edge(vertices[i], vertices[i + N]),
            }
        })
        .collect();
    (vertices, edges)
}

#[cfg(test)]
mod tests {
    use std::fmt::Debug;

    use super::*;
    use crate::testing::fixtures::MakeTestGraph;

    #[derive(Debug, Clone, Copy)]
    enum Spec {
        Path(usize),
        Cycle(usize),
        Complete(usize),
        Petersen,
    }

    impl Spec {
        fn generate<G: GraphTopologyAddition>(
            &self,
            graph: &mut G,
        ) -> (Vec<G::Vertex>, Vec<G::Edge>) {
            match *self {
                Spec::Path(n) => path(graph, n),
                Spec::Cycle(n) => cycle(graph, n),
                Spec::Complete(n) => complete(graph, n),
                Spec::Petersen => petersen(graph),
            }
        }

        fn assert<G: GraphTopology>(&self, built: &Built<G>)
        where
            G::Vertex: Debug,
            G::Edge: Debug,
        {
            match *self {
                Spec::Path(n) => assert_path(built, n),
                Spec::Cycle(n) => assert_cycle(built, n),
                Spec::Complete(n) => assert_complete(built, n),
                Spec::Petersen => assert_petersen(built),
            }
        }
    }

    struct Built<G: GraphTopology> {
        graph: G,
        vertices: Vec<G::Vertex>,
        edges: Vec<G::Edge>,
        initial_vertex_count: usize,
        initial_edge_count: usize,
    }

    /// Generates the test for the `append_graph` harness for the given `Spec` expression.
    macro_rules! min_harness_tests {
        ($spec:expr) => {
            #[test]
            fn append_graph() {
                run($spec, add_to_empty::<$crate::models::AppendGraph>);
            }
        };
    }

    /// Generates one test per harness for the given `Spec` expression.
    macro_rules! all_harness_tests {
        ($spec:expr) => {
            min_harness_tests!($spec);

            #[test]
            fn append_graph_non_empty() {
                run($spec, add_to_standard::<$crate::models::AppendGraph>);
            }

            #[test]
            fn graph() {
                run($spec, add_to_empty::<$crate::models::Graph>);
            }

            #[test]
            fn graph_non_empty() {
                run($spec, add_to_standard::<$crate::models::Graph>);
            }

            #[test]
            fn frozen_graph() {
                run($spec, conv_generate_as::<$crate::models::FrozenGraph>);
            }
        };
    }

    /// Generates the module tree `<group>::<case>::<harness>` for each generator case.
    ///
    /// The `all_harnesses` cases run on every harness, the `min_harnesses` cases only on a reduced
    /// set of harnesses.
    macro_rules! generator_tests {
        ($($group:ident {
            all { $($all_case:ident => $all_generator:expr),+ $(,)? }
            min { $($min_case:ident => $min_generator:expr),* $(,)? }
        })+) => {
            $(
                mod $group {
                    use super::*;

                    $(
                        mod $all_case {
                            use super::*;

                            all_harness_tests!($all_generator);
                        }
                    )+

                    $(
                        mod $min_case {
                            use super::*;

                            min_harness_tests!($min_generator);
                        }
                    )*
                }
            )+
        };
    }

    generator_tests! {
        path {
            all {
                small => Spec::Path(4),
            }
            min {
                empty => Spec::Path(0),
                single_vertex => Spec::Path(1),
                single_edge => Spec::Path(2),
                large => Spec::Path(21),
            }
        }
        cycle {
            all {
                small_even => Spec::Cycle(4),
            }
            min {
                empty => Spec::Cycle(0),
                loop_edge => Spec::Cycle(1),
                multi_edge => Spec::Cycle(2),
                large_odd => Spec::Cycle(21),
            }
        }
        complete {
            all {
                small_even => Spec::Complete(4),
            }
            min {
                empty => Spec::Complete(0),
                single_vertex => Spec::Complete(1),
                single_edge => Spec::Complete(2),
                large_odd => Spec::Complete(13),
            }
        }
    }

    mod petersen {
        use super::*;

        all_harness_tests!(Spec::Petersen);
    }

    /// Builds a graph with `harness` and asserts that it matches what `spec` should produce.
    fn run<G: GraphTopology>(spec: Spec, harness: impl FnOnce(&Spec) -> Built<G>)
    where
        G::Vertex: Debug,
        G::Edge: Debug,
    {
        let built = harness(&spec);
        spec.assert(&built);
    }

    /// Runs `spec` on an empty graph of type `G`.
    fn add_to_empty<G: GraphTopologyAddition>(spec: &Spec) -> Built<G> {
        let mut graph = G::default();
        let (vertices, edges) = spec.generate(&mut graph);
        Built {
            graph,
            vertices,
            edges,
            initial_vertex_count: 0,
            initial_edge_count: 0,
        }
    }

    /// Runs `spec` on a non-empty test graph of type `G`.
    fn add_to_standard<G: GraphTopologyAddition>(spec: &Spec) -> Built<G> {
        let (mut graph, initial_vertices, initial_edges, _) = G::standard();
        let (vertices, edges) = spec.generate(&mut graph);
        Built {
            graph,
            vertices,
            edges,
            initial_vertex_count: initial_vertices.len(),
            initial_edge_count: initial_edges.len(),
        }
    }

    /// Runs `spec` within `generate_as` for type `G`.
    fn conv_generate_as<G: GraphTopologyConversion>(spec: &Spec) -> Built<G> {
        let (graph, vertices, edges) = generate_as::<G>(|graph| spec.generate(graph));
        Built {
            graph,
            vertices,
            edges,
            initial_vertex_count: 0,
            initial_edge_count: 0,
        }
    }

    fn assert_path<G: GraphTopology>(built: &Built<G>, n: usize)
    where
        G::Vertex: Debug,
        G::Edge: Debug,
    {
        assert_element_counts(built, n, n.saturating_sub(1));
        assert_handles(built.graph.vertices(), &built.vertices, "vertex");
        assert_handles(built.graph.edges(), &built.edges, "edge");
        assert_no_loops(built);
        assert_no_multi_edges(built);
        match n {
            0 => {}
            1 => assert_eq!(
                built.graph.degree(built.vertices[0]),
                0,
                "path n == 1 should be an isolated vertex"
            ),
            _ => {
                for (i, &v) in built.vertices.iter().enumerate() {
                    assert_eq!(
                        built.graph.degree(v),
                        if i == 0 || i == n - 1 { 1 } else { 2 },
                        "unexpected degree of vertex {v:?} in path n == {n}"
                    );
                }
            }
        }
        assert_path_order(built);
    }

    fn assert_cycle<G: GraphTopology>(built: &Built<G>, n: usize)
    where
        G::Vertex: Debug,
        G::Edge: Debug,
    {
        assert_element_counts(built, n, n);
        assert_handles(built.graph.vertices(), &built.vertices, "vertex");
        assert_handles(built.graph.edges(), &built.edges, "edge");
        if n != 1 {
            assert_no_loops(built);
        }
        if n != 2 {
            assert_no_multi_edges(built);
        }
        assert!(
            built.vertices.iter().all(|&v| built.graph.degree(v) == 2),
            "all new vertices should have degree 2"
        );
        assert_path_order(built);
        // Asserts the closing edge e(n - 1) == (v(n - 1), v0).
        if n > 0 {
            // For n == 1, u == v and this validates the loop. For n == 2, the above asserted one of
            // the two multi-edges, and this asserts the other.
            let e = built.edges[n - 1];
            let u = built.vertices[0];
            let v = built.vertices[n - 1];
            let incident_vertices = built.graph.incident_vertices(e);
            assert!(
                incident_vertices == (u, v) || incident_vertices == (v, u),
                "edge {e:?} should have incident vertices {u:?} and {v:?}",
            );
        }
    }

    fn assert_complete<G: GraphTopology>(built: &Built<G>, n: usize)
    where
        G::Vertex: Debug,
        G::Edge: Debug,
    {
        assert_element_counts(built, n, n * n.saturating_sub(1) / 2);
        assert_handles(built.graph.vertices(), &built.vertices, "vertex");
        assert_handles(built.graph.edges(), &built.edges, "edge");
        // The predicate in `all` is only executed if `vertices` has any elements, i.e. for n > 0.
        assert!(
            built
                .vertices
                .iter()
                .all(|&v| built.graph.degree(v) == n - 1),
            "all new vertices should have degree {}",
            n - 1
        );
        // Asserts that all pairs of vertices have exactly one edge between them. This also includes
        // checks for loops and multi-edges. If there are no duplicates, then this implies that all
        // expected edges were also matched due to the validated counts from above.
        let mut seen = vec![false; n * n];
        let position = |v, e| {
            built
                .vertices
                .iter()
                .position(|&x| x == v)
                .unwrap_or_else(|| panic!("edge {e:?} has an invalid incident vertex {v:?}"))
        };
        for &e in &built.edges {
            let (u, v) = built.graph.incident_vertices(e);
            assert_ne!(u, v, "unexpected loop edge {e:?} at vertex {u:?}");
            let (i, j) = (position(u, e), position(v, e));
            let (i, j) = (i.min(j), i.max(j));
            assert!(
                !seen[i * n + j],
                "unexpected multi-edge {e:?} between vertices {u:?} and {v:?}"
            );
            seen[i * n + j] = true;
        }
    }

    fn assert_petersen<G: GraphTopology>(built: &Built<G>)
    where
        G::Vertex: Debug,
        G::Edge: Debug,
    {
        assert_element_counts(built, 10, 15);
        assert_handles(built.graph.vertices(), &built.vertices, "vertex");
        assert_handles(built.graph.edges(), &built.edges, "edge");
        assert_no_loops(built);
        assert_no_multi_edges(built);
        assert!(
            built.vertices.iter().all(|&v| built.graph.degree(v) == 3),
            "all new vertices should have degree 3"
        );
        // Checks that each pair of vertices (u, v) has no common neighbor if they are adjacent, and
        // exactly one common neighbor otherwise.
        for (i, &v) in built.vertices.iter().enumerate() {
            for &u in &built.vertices[i + 1..] {
                if built.graph.are_adjacent(v, u) {
                    assert!(
                        built.graph.common_neighbors(u, v).next().is_none(),
                        "adjacent vertices {u:?} and {v:?} should not have a common neighbor"
                    );
                } else {
                    assert_eq!(
                        built.graph.common_neighbors(u, v).count(),
                        1,
                        "non-adjacent vertices {u:?} and {v:?} should have exactly one common neighbor"
                    );
                }
            }
        }
    }

    fn assert_element_counts<G: GraphTopology>(
        built: &Built<G>,
        expected_vertex_count: usize,
        expected_edge_count: usize,
    ) {
        assert_eq!(
            built.graph.vertex_count(),
            built.initial_vertex_count + expected_vertex_count,
            "unexpected number of added vertices"
        );
        assert_eq!(
            built.vertices.len(),
            expected_vertex_count,
            "unexpected number of returned vertices"
        );
        assert_eq!(
            built.graph.edge_count(),
            built.initial_edge_count + expected_edge_count,
            "unexpected number of added edges"
        );
        assert_eq!(
            built.edges.len(),
            expected_edge_count,
            "unexpected number of returned edges"
        );
    }

    /// Asserts that every handle in `returned` is unique and in `all`.
    fn assert_handles<T: PartialEq + Debug>(
        all: impl Iterator<Item = T>,
        returned: &[T],
        kind: &str,
    ) {
        let mut remaining: Vec<T> = all.collect();
        for e in returned {
            let Some(position) = remaining.iter().position(|x| x == e) else {
                panic!("returned {kind} {e:?} is not in the graph or appears more than once");
            };
            remaining.swap_remove(position);
        }
    }

    fn assert_no_loops<G: GraphTopology>(built: &Built<G>)
    where
        G::Vertex: Debug,
        G::Edge: Debug,
    {
        for &e in &built.edges {
            let (u, v) = built.graph.incident_vertices(e);
            assert_ne!(u, v, "unexpected loop edge {e:?} at vertex {u:?}");
        }
    }

    fn assert_no_multi_edges<G: GraphTopology>(built: &Built<G>)
    where
        G::Vertex: Debug,
    {
        for &v in &built.vertices {
            let mut neighbors = Vec::new();
            let mut loop_count = 0;
            for u in built.graph.adjacent_vertices(v) {
                if u == v {
                    loop_count += 1;
                    assert!(loop_count < 3, "unexpected multi-edge loop at vertex {v:?}");
                } else {
                    assert!(
                        !neighbors.contains(&u),
                        "unexpected multi-edge between vertices {v:?} and {u:?}"
                    );
                    neighbors.push(u);
                }
            }
        }
    }

    /// Asserts that each returned edge *ei* connects the returned vertices *vi* and *v(i + 1)*.
    fn assert_path_order<G: GraphTopology>(built: &Built<G>)
    where
        G::Vertex: Debug,
        G::Edge: Debug,
    {
        for (w, &e) in built.vertices.windows(2).zip(&built.edges) {
            let incident_vertices = built.graph.incident_vertices(e);
            assert!(
                incident_vertices == (w[0], w[1]) || incident_vertices == (w[1], w[0]),
                "edge {e:?} should have incident vertices {:?} and {:?}",
                w[0],
                w[1]
            );
        }
    }
}