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// Copyright (c) 2016, 2017, 2018 Frank Fischer <frank-fischer@shadow-soft.de> // // This program is free software: you can redistribute it and/or // modify it under the terms of the GNU General Public License as // published by the Free Software Foundation, either version 3 of the // License, or (at your option) any later version. // // This program is distributed in the hope that it will be useful, but // WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU // General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see <http://www.gnu.org/licenses/> // #![allow(clippy::type_complexity)] //! Dijkstra's bidirectional shortest path algorithm. //! //! The bidirectional Dijkstra algorithm starts the search at the start and the //! end node simultaneously. The shortest path is found if the two searches //! meet. //! //! This is actually a [bidirectional A*-search][crate::search::biastar] with //! the all zero node potential. //! //! # Example //! //! ``` //! use rs_graph::{LinkedListGraph, Builder, EdgeVec, traits::*}; //! use rs_graph::adjacencies::Neighbors; //! use rs_graph::shortestpath::bidijkstra; //! use rs_graph::string::from_ascii; //! //! let data = from_ascii::<LinkedListGraph>(r" //! a-----9-----b //! / \ \ //! | 2 6 //! | \ \ //! 14 c-----8-----d //! | / \ / //! | 10 12 15 //! \ / \ / //! e----7--f---- //! ").unwrap(); //! let g = data.graph; //! let weights = data.weights; //! let nodes = data.nodes; //! let a = nodes[&'a']; //! let b = nodes[&'b']; //! let c = nodes[&'c']; //! let d = nodes[&'d']; //! let e = nodes[&'e']; //! let f = nodes[&'f']; //! //! // ensure that the nodes are visited in the correct order //! let visited = bidijkstra::start(&Neighbors(&g), &Neighbors(&g), e, b, |e| weights[e.index()]) //! .map(|(u, _ , d)| (u, d)) //! .collect::<Vec<_>>(); //! assert_eq!(visited, vec![(d, 6), (f, 7), (a, 9), (c, 10), (a, 12)]); //! //! // obtain the shortest path directly. //! let (path, dist) = bidijkstra::find_undirected_path(&g, e, b, |e| weights[e.index()]).unwrap(); //! //! assert_eq!(dist, 21); //! //! let path = path.into_iter() //! .map(|e| g.enodes(e)) //! .map(|(u,v)| if g.node_id(u) > g.node_id(v) { (v,u) } else { (u,v) }) //! .collect::<Vec<_>>(); //! assert_eq!(path, vec![(c,e), (a,c), (a,b)]); //! ``` use crate::adjacencies::{Adjacencies, InEdges, Neighbors, OutEdges}; use crate::collections::{ItemMap, ItemPriQueue}; use crate::search::biastar::{self, BiAStar, BiData, DefaultMap, DefaultPriQueue, Direction}; pub use crate::shortestpath::dijkstra::NoHeur; use crate::traits::{Digraph, Graph}; use either::Either; use num_traits::Zero; use std::hash::Hash; use std::ops::{Add, Sub}; /// Bi-Dijkstra search iterator. pub type BiDijkstra<'a, Aout, Ain, D, W, M, P> = BiAStar<'a, Aout, Ain, D, W, M, P, NoHeur>; /// Bi-Dijkstra search iterator with default data structures. pub type BiDijkstraDefault<'a, Aout, Ain, D, W> = BiDijkstra<'a, Aout, Ain, D, W, DefaultMap<'a, Aout, D, NoHeur>, DefaultPriQueue<'a, Aout, D, NoHeur>>; /// Compute a shortest path with bidirectional Dijkstra algorithm using default data structures. /// /// This is a convenience wrapper around [`start_with_data`] using the default /// data structures returned by /// [`default_data`][crate::search::biastar::default_data]. /// /// # Parameters /// - `adjout`: adjacency information for the forward search (i.e outgoing edges) /// - `adjin`: adjacency information for the backward search (i.e incoming edges) /// - `src`: the source node at which the path should start. /// - `snk`: the snk node at which the path should end. /// - `weights`: the (non-negative) weight function for each edge pub fn start<'a, Aout, Ain, D, W>( adjout: Aout, adjin: Ain, src: Aout::Node, snk: Aout::Node, weights: W, ) -> BiDijkstraDefault<'a, Aout, Ain, D, W> where Aout: Adjacencies<'a>, Aout::Node: Hash, Ain: Adjacencies<'a, Node = Aout::Node, Edge = Aout::Edge>, D: Copy + PartialOrd + Zero, W: Fn(Aout::Edge) -> D, { start_with_data(adjout, adjin, src, snk, weights, biastar::default_data()) } /// Run bidirectional Dijkstra on a generic graph with custom data structures. /// /// The returned iterator traverses the edges in the order of a bidirectional /// Dijkstra-search. The iterator returns the next node, its incoming edge with /// direction information and the distance to the start node or end node /// depending on the direction. /// /// Note that the start and end nodes are *not* returned by the iterator. /// /// The algorithm requires a pair `(M, P)` with `M` implementing /// [`ItemMap<Direction<Node>, Item>`][crate::collections::ItemMap], and `P` /// implementing [`ItemPriQueue<Direction<Node>, /// D>`][crate::collections::ItemStack] as internal data structures. The map is /// used to store information about the last edge on a shortest path for each /// reachable node. The priority queue is used the handle the nodes in the /// correct order. The data structures can be reused for multiple searches. /// /// # Parameters /// - `adjout`: adjacency information for the forward search (i.e outgoing edges) /// - `adjin`: adjacency information for the backward search (i.e incoming edges) /// - `src`: the source node at which the path should start. /// - `snk`: the snk node at which the path should end. /// - `weights`: the (non-negative) weight function for each edge /// - `heur`: the heuristic used in the search /// - `data`: the data structures pub fn start_with_data<'a, Aout, Ain, D, W, M, P>( adjout: Aout, adjin: Ain, src: Aout::Node, snk: Aout::Node, weights: W, data: (M, P), ) -> BiDijkstra<'a, Aout, Ain, D, W, M, P> where Aout: Adjacencies<'a>, Ain: Adjacencies<'a, Node = Aout::Node, Edge = Aout::Edge>, D: Copy + PartialOrd + Zero, W: Fn(Aout::Edge) -> D, M: ItemMap<Direction<Aout::Node>, Either<P::Item, D>>, P: ItemPriQueue<Direction<Aout::Node>, BiData<Aout::Edge, D, NoHeur>>, { biastar::start_with_data(adjout, adjin, src, snk, weights, NoHeur, data) } /// Start a bidirectional Dijkstra-search on an undirected graph. /// /// Each edge can be traversed in both directions with the same weight. /// /// This is a convenience wrapper to start the search on an undirected graph /// with the default data structures. /// /// # Parameters /// /// - `g`: the undirected graph /// - `src`: the source node at which the path should start. /// - `snk`: the snk node at which the path should end. /// - `weights`: the weight function for each edge pub fn start_undirected<'a, G, D, W>( g: &'a G, src: G::Node, snk: G::Node, weights: W, ) -> BiDijkstraDefault<'a, Neighbors<'a, G>, Neighbors<'a, G>, D, W> where G: Graph<'a>, G::Node: Hash, D: Copy + PartialOrd + Zero, W: Fn(G::Edge) -> D, { start(Neighbors(g), Neighbors(g), src, snk, weights) } /// Run a bidirectional Dijkstra-search on an undirected graph and return the path. /// /// Each edge can be traversed in both directions with the same weight. /// /// This is a convenience wrapper to run the search on an undirected graph /// with the default data structures and obtain the shortest path. /// /// # Parameters /// /// - `g`: the undirected graph /// - `src`: the source node at which the path should start. /// - `snk`: the snk node at which the path should end. /// - `weights`: the weight function for each edge /// /// The function returns the edges on the path and its length. pub fn find_undirected_path<'a, G, D, W>(g: &'a G, src: G::Node, snk: G::Node, weights: W) -> Option<(Vec<G::Edge>, D)> where G: Graph<'a>, G::Node: Hash, D: Copy + PartialOrd + Zero + Add<D, Output = D> + Sub<D, Output = D>, W: Fn(G::Edge) -> D, { biastar::find_undirected_path(g, src, snk, weights, NoHeur) } /// Start a bidirectional Dijkstra-search on a directed graph. /// /// This is a convenience wrapper to start the search on an directed graph /// with the default data structures. /// /// # Parameters /// /// - `g`: the directed graph /// - `src`: the source node at which the path should start. /// - `snk`: the snk node at which the path should end. /// - `weights`: the weight function for each edge /// - `heur`: the heuristic used in the search pub fn start_directed<'a, G, D, W>( g: &'a G, src: G::Node, snk: G::Node, weights: W, ) -> BiDijkstraDefault<'a, OutEdges<'a, G>, InEdges<'a, G>, D, W> where G: Digraph<'a>, G::Node: Hash, D: Copy + PartialOrd + Zero, W: Fn(G::Edge) -> D, { start(OutEdges(g), InEdges(g), src, snk, weights) } /// Run a bidirectional Dijkstra-search on an directed graph and return the path. /// /// This is a convenience wrapper to run the search on an directed graph /// with the default data structures and obtain the shortest path. /// /// # Parameters /// /// - `g`: the directed graph /// - `src`: the source node at which the path should start. /// - `snk`: the snk node at which the path should end. /// - `weights`: the weight function for each edge /// /// The function returns the edges on the path and its length. pub fn find_directed_path<'a, G, D, W>(g: &'a G, src: G::Node, snk: G::Node, weights: W) -> Option<(Vec<G::Edge>, D)> where G: Digraph<'a>, G::Node: Hash, D: Copy + PartialOrd + Zero + Add<D, Output = D> + Sub<D, Output = D>, W: Fn(G::Edge) -> D, { biastar::find_directed_path(g, src, snk, weights, NoHeur) }