prepona 0.1.0

A graph crate with simplicity in mind
Documentation 
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use anyhow::Result;
use magnitude::Magnitude;
use num_traits::Zero;
use std::collections::HashMap;
use std::{any::Any, collections::HashSet};

use crate::algo::Error;
use crate::provide::{Edges, Graph, Vertices};
use crate::{
    graph::{subgraph::ShortestPathSubgraph, Edge, EdgeDir},
    prelude::Neighbors,
};

/// Finds shortest path from a single source to all other vertices using bellman-ford algorithm.
///
/// # Examples
/// ```
/// use prepona::prelude::*;
/// use prepona::storage::DiMat;
/// use prepona::graph::MatGraph;
/// use prepona::algo::BellmanFord;
///
/// // Given: Graph
/// //          6       1
/// //      a  -->  b  <--  c ---
/// //    1 |       |           |
/// //      |  2 /`````\ 2      |
/// //      |````       ````|   |
/// //      v               v   | 1
/// //      d  ---------->  e --'
/// //              1
/// let mut graph = MatGraph::init(DiMat::<usize>::init());
/// let a = graph.add_vertex(); // 0
/// let b = graph.add_vertex(); // 1
/// let c = graph.add_vertex(); // 2
/// let d = graph.add_vertex(); // 3
/// let e = graph.add_vertex(); // 4
///
/// graph.add_edge_unchecked(a, b, 6.into());
/// let ad = graph.add_edge_unchecked(a, d, 1.into());
/// graph.add_edge_unchecked(b, d, 2.into());
/// graph.add_edge_unchecked(b, e, 2.into());
/// let cb = graph.add_edge_unchecked(c, b, 1.into());
/// let ec = graph.add_edge_unchecked(e, c, 1.into());
/// let de = graph.add_edge_unchecked(d, e, 1.into());
///
/// // When: Performing BellmanFord algorithm.
/// let sp_subgraph = BellmanFord::init(&graph).execute(&graph, a).unwrap();
///
/// // Then:
/// assert_eq!(sp_subgraph.vertex_count(), 5);
/// assert_eq!(sp_subgraph.edges_count(), 4);
/// assert!(vec![a, b, c, d, e]
///     .iter()
///     .all(|vertex_id| sp_subgraph.vertices().contains(vertex_id)));
/// assert!(vec![ad, cb, ec, de]
///     .into_iter()
///     .all(|edge_id| sp_subgraph.edge(edge_id).is_ok()));
/// assert_eq!(sp_subgraph.distance_to(a).unwrap(), 0.into());
/// assert_eq!(sp_subgraph.distance_to(b).unwrap(), 4.into());
/// assert_eq!(sp_subgraph.distance_to(c).unwrap(), 3.into());
/// assert_eq!(sp_subgraph.distance_to(d).unwrap(), 1.into());
/// assert_eq!(sp_subgraph.distance_to(e).unwrap(), 2.into());
/// ```
pub struct BellmanFord<W> {
    distance: Vec<Magnitude<W>>,
    prev: Vec<Magnitude<usize>>,
}

impl<W: Copy + Any + Zero + Ord> BellmanFord<W> {
    pub fn init<E, Ty, G>(graph: &G) -> Self
    where
        E: Edge<W>,
        Ty: EdgeDir,
        G: Vertices + Edges<W, E> + Graph<W, E, Ty>,
    {
        let vertex_count = graph.vertex_count();

        BellmanFord {
            distance: vec![Magnitude::PosInfinite; vertex_count],
            prev: vec![Magnitude::PosInfinite; vertex_count],
        }
    }

    /// Finds shortest path from a single source to all other vertices.
    ///
    /// # Arguments
    /// * `graph`: Graph to search for the shortest paths in.
    /// * `src_id`: Id of the source vertex(Shortest path will be calculated from this vertex to all other vertices)
    ///
    /// # Returns
    /// * `Ok`: The shortest path as a subgraph of the original graph.
    /// You can query shortest path from source to each destination using api provided by `ShortestPathSubgraph`.
    /// * `Err`: If graph contains negative cycle.
    pub fn execute<E, Ty, G>(
        mut self,
        graph: &G,
        src_id: usize,
    ) -> Result<ShortestPathSubgraph<W, E, Ty, G>>
    where
        E: Edge<W>,
        Ty: EdgeDir,
        G: Vertices + Edges<W, E> + Neighbors + Graph<W, E, Ty>,
    {
        let mut sp_edges = vec![];

        let vertex_count = graph.vertex_count();

        let id_map = graph.continuos_id_map();

        let src_virt_id = id_map.virt_id_of(src_id);

        self.distance[src_virt_id] = W::zero().into();

        let edges = graph.as_directed_edges();

        for _ in 0..vertex_count - 1 {
            for (u_real_id, v_real_id, edge) in &edges {
                let u_virt_id = id_map.virt_id_of(*u_real_id);
                let v_virt_id = id_map.virt_id_of(*v_real_id);

                let alt = self.distance[u_virt_id] + *edge.get_weight();
                if alt < self.distance[v_virt_id] {
                    self.distance[v_virt_id] = alt;
                    self.prev[v_virt_id] = u_virt_id.into();

                    sp_edges.retain(|(_, dst_id, _)| dst_id != v_real_id); // remove edge to neighbor
                    sp_edges.push((*u_real_id, *v_real_id, edge.get_id())); // add new edge
                }
            }
        }

        for (u_real_id, v_real_id, edge) in &edges {
            let u_virt_id = id_map.real_id_of(*u_real_id);
            let v_virt_id = id_map.real_id_of(*v_real_id);

            let alt = self.distance[u_virt_id] + *edge.get_weight();
            if alt < self.distance[v_virt_id] {
                Err(Error::new_ncd())?
            }
        }

        let mut distance_map = HashMap::new();
        for virt_id in 0..graph.vertex_count() {
            let real_id = id_map.real_id_of(virt_id);
            distance_map.insert(real_id, self.distance[virt_id]);
        }

        let vertices = edges
            .iter()
            .flat_map(|(src_id, dst_id, _)| vec![*src_id, *dst_id])
            .chain(std::iter::once(src_id))
            .collect::<HashSet<usize>>();

        Ok(ShortestPathSubgraph::init(
            graph,
            sp_edges,
            vertices,
            distance_map,
        ))
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::graph::MatGraph;
    use crate::storage::{DiMat, Mat};

    #[test]
    fn one_vertex_undirected_graph() {
        // Given: Graph
        //
        //      a
        //
        let mut graph = MatGraph::init(Mat::<usize>::init());
        let a = graph.add_vertex();

        let sp_subgraph = BellmanFord::init(&graph).execute(&graph, a);

        assert!(sp_subgraph.is_ok());
        let sp_subgraph = sp_subgraph.unwrap();
        assert_eq!(sp_subgraph.distance_to(a).unwrap(), 0.into());
        assert_eq!(sp_subgraph.vertex_count(), 1);
        assert_eq!(sp_subgraph.vertices()[0], a);
        assert_eq!(sp_subgraph.edges_count(), 0);
    }

    #[test]
    fn one_vertex_directed_graph() {
        // Given: Graph
        //
        //      a
        //
        let mut graph = MatGraph::init(DiMat::<usize>::init());
        let a = graph.add_vertex();

        let sp_subgraph = BellmanFord::init(&graph).execute(&graph, a);

        // Then
        assert!(sp_subgraph.is_ok());
        let sp_subgraph = sp_subgraph.unwrap();
        assert_eq!(sp_subgraph.distance_to(a).unwrap(), 0.into());
        assert_eq!(sp_subgraph.vertex_count(), 1);
        assert_eq!(sp_subgraph.vertices()[0], a);
        assert_eq!(sp_subgraph.edges_count(), 0);
    }

    #[test]
    fn trivial_undirected_graph() {
        // Given: Graph
        //          6       5
        //      a  ---  b  ---  c
        //    1 |       |       | 5
        //      |  2 /`````\ 2  |
        //      |````       ````|
        //      d  -----------  e
        //              1
        let mut graph = MatGraph::init(Mat::<usize>::init());
        let a = graph.add_vertex();
        let b = graph.add_vertex();
        let c = graph.add_vertex();
        let d = graph.add_vertex();
        let e = graph.add_vertex();

        graph.add_edge_unchecked(a, b, 6.into());
        let ad = graph.add_edge_unchecked(a, d, 1.into());
        let bd = graph.add_edge_unchecked(b, d, 2.into());
        graph.add_edge_unchecked(b, c, 5.into());
        graph.add_edge_unchecked(b, e, 2.into());
        let ce = graph.add_edge_unchecked(c, e, 5.into());
        let de = graph.add_edge_unchecked(d, e, 1.into());

        // When: Performing BellmanFord algorithm.
        let sp_subgraph = BellmanFord::init(&graph).execute(&graph, a);

        // Then:
        assert!(sp_subgraph.is_ok());
        let sp_subgraph = sp_subgraph.unwrap();
        assert_eq!(sp_subgraph.vertex_count(), 5);
        assert_eq!(sp_subgraph.edges_count(), 4);
        assert!(vec![a, b, c, d, e]
            .iter()
            .all(|vertex_id| sp_subgraph.vertices().contains(vertex_id)));
        assert!(vec![ad, bd, ce, de]
            .into_iter()
            .all(|edge_id| sp_subgraph.edge(edge_id).is_ok()));
        assert_eq!(sp_subgraph.distance_to(a).unwrap(), 0.into());
        assert_eq!(sp_subgraph.distance_to(b).unwrap(), 3.into());
        assert_eq!(sp_subgraph.distance_to(c).unwrap(), 7.into());
        assert_eq!(sp_subgraph.distance_to(d).unwrap(), 1.into());
        assert_eq!(sp_subgraph.distance_to(e).unwrap(), 2.into());
    }

    #[test]
    fn trivial_directed_graph() {
        // Given: Graph
        //          6       1
        //      a  -->  b  <--  c ---
        //    1 |       |           |
        //      |  2 /`````\ 2      |
        //      |````       ````|   |
        //      v               v   | 1
        //      d  ---------->  e --'
        //              1
        let mut graph = MatGraph::init(DiMat::<usize>::init());
        let a = graph.add_vertex(); // 0
        let b = graph.add_vertex(); // 1
        let c = graph.add_vertex(); // 2
        let d = graph.add_vertex(); // 3
        let e = graph.add_vertex(); // 4

        graph.add_edge_unchecked(a, b, 6.into());
        let ad = graph.add_edge_unchecked(a, d, 1.into());
        graph.add_edge_unchecked(b, d, 2.into());
        graph.add_edge_unchecked(b, e, 2.into());
        let cb = graph.add_edge_unchecked(c, b, 1.into());
        let ec = graph.add_edge_unchecked(e, c, 1.into());
        let de = graph.add_edge_unchecked(d, e, 1.into());

        // When: Performing BellmanFord algorithm.
        let sp_subgraph = BellmanFord::init(&graph).execute(&graph, a);

        // Then:
        assert!(sp_subgraph.is_ok());
        let sp_subgraph = sp_subgraph.unwrap();
        assert_eq!(sp_subgraph.vertex_count(), 5);
        assert_eq!(sp_subgraph.edges_count(), 4);
        assert!(vec![a, b, c, d, e]
            .iter()
            .all(|vertex_id| sp_subgraph.vertices().contains(vertex_id)));
        assert!(vec![ad, cb, ec, de]
            .into_iter()
            .all(|edge_id| sp_subgraph.edge(edge_id).is_ok()));
        assert_eq!(sp_subgraph.distance_to(a).unwrap(), 0.into());
        assert_eq!(sp_subgraph.distance_to(b).unwrap(), 4.into());
        assert_eq!(sp_subgraph.distance_to(c).unwrap(), 3.into());
        assert_eq!(sp_subgraph.distance_to(d).unwrap(), 1.into());
        assert_eq!(sp_subgraph.distance_to(e).unwrap(), 2.into());
    }

    #[test]
    fn undirected_graph_with_negative_cycle() {
        // Given: Graph
        //          1
        //      a ----- b
        //      |       | 2
        //      '------ c
        //          -5
        //
        let mut graph = MatGraph::init(Mat::<isize>::init());
        let a = graph.add_vertex();
        let b = graph.add_vertex();
        let c = graph.add_vertex();
        graph.add_edge_unchecked(a, b, 1.into());
        graph.add_edge_unchecked(b, c, 2.into());
        graph.add_edge_unchecked(c, a, (-5).into());

        // When: Performing BellmanFord algorithm.
        let shortest_paths = BellmanFord::init(&graph).execute(&graph, a);

        assert!(shortest_paths.is_err());
    }

    #[test]
    fn undirected_graph_with_negative_walk() {
        // Given: Graph
        //          -1
        //      a ----- b
        //
        let mut graph = MatGraph::init(Mat::<isize>::init());
        let a = graph.add_vertex();
        let b = graph.add_vertex();
        graph.add_edge_unchecked(a, b, (-1).into());

        let shortest_paths = BellmanFord::init(&graph).execute(&graph, a);

        assert!(shortest_paths.is_err());
    }

    #[test]
    fn directed_graph_with_negative_cycle() {
        // Given: Graph
        //          1
        //      a ----> b
        //      ^       | 2
        //      |       v
        //      '------ c
        //          -5
        //
        let mut graph = MatGraph::init(DiMat::<isize>::init());
        let a = graph.add_vertex();
        let b = graph.add_vertex();
        let c = graph.add_vertex();
        graph.add_edge_unchecked(a, b, 1.into());
        graph.add_edge_unchecked(b, c, 2.into());
        graph.add_edge_unchecked(c, a, (-5).into());

        // When: Performing BellmanFord algorithm.
        let shortest_paths = BellmanFord::init(&graph).execute(&graph, a);

        assert!(shortest_paths.is_err());
    }
}