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/* * Copyright (c) 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/> */ //! Dijkstra's shortest path algorithm. //! //! Dijkstra's algorithm computes the shortest path from some start node $s \in //! V$ to all other nodes in (directed or undirected) graph. Each edge is //! assigned a non-negative weight (or length) $w \colon E \to \mathbb{R}_+$. //! //! Dijkstra's algorithm is essentially an [A*-search][crate::search::astar] //! using the zero potential (heuristic) for all nodes. //! //! # Example //! //! ``` //! use rs_graph::{LinkedListGraph, Builder, EdgeVec, traits::*}; //! use rs_graph::adjacencies::Neighbors; //! use rs_graph::shortestpath::dijkstra; //! use rs_graph::string::from_ascii; //! //! let data = from_ascii::<LinkedListGraph>(r" //! a-----9-----b //! / \ \ //! | 2 6 //! | \ \ //! 14 c-----8-----d //! | / \ / //! | 9 10 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']; //! //! let mut preds: Vec<_> = dijkstra::start(&Neighbors(&g), e, |e| weights[e.index()]) //! .map(|(u, e, d)| { //! let uv = g.enodes(e); //! if uv.0 == u { (uv.1, u, d) } else { (uv.0, u, d) } //! }) //! .collect(); //! //! assert_eq!(preds, vec![(e,f,7), (e,c,9), (c,a,11), (c,d,17), (a,b,20)]); //! //! let (path, dist) = dijkstra::find_undirected_path(&g, e, b, |e| weights[e.index()]).unwrap(); //! //! assert_eq!(dist, 20); //! //! let path = path //! .into_iter() //! .map(|e| g.enodes(e)) //! .map(|(u,v)| if g.node_id(u) < g.node_id(v) { (u,v) } else { (v,u) }) //! .collect::<Vec<_>>(); //! assert_eq!(path, vec![(c,e), (a,c), (a,b)]); //! ``` use crate::adjacencies::{Adjacencies, Neighbors, OutEdges}; use crate::collections::{ItemMap, ItemPriQueue}; use crate::search::astar::{ self, AStar, AStarHeuristic, Accumulator, Data, DefaultMap, DefaultPriQueue, SumAccumulator, }; use crate::traits::{Digraph, Graph}; use crate::num::traits::Zero; use std::hash::Hash; use std::ops::{Add, Neg, Sub}; /// Internal type used when no heuristic is required. /// /// Used for standard Dijkstra. #[derive(Clone, Copy, Default)] pub struct NoHeur; impl<N> AStarHeuristic<N> for NoHeur { type Result = NoHeur; fn call(&self, _u: N) -> NoHeur { NoHeur } } impl<T> Add<T> for NoHeur { type Output = T; fn add(self, x: T) -> T { x } } impl Neg for NoHeur { type Output = NoHeur; fn neg(self) -> Self { self } } /// Dijkstra search iterator. pub type Dijkstra<'a, A, D, W, M, P, Accum> = AStar<'a, A, D, W, M, P, NoHeur, Accum>; /// The Dijkstra-iterator with default types. pub type DijkstraDefault<'a, A, D, W> = Dijkstra<'a, A, D, W, DefaultMap<'a, A, D, NoHeur>, DefaultPriQueue<'a, A, D, NoHeur>, SumAccumulator>; /// Start and return an Dijkstra-iterator using default data structures. /// /// This is a convenience wrapper around [`start_with_data`] using the default /// data structures returned by [`default_data`][crate::search::astar::default_data]. /// /// # Parameters /// /// - `adj`: adjacency information for the graph /// - `src`: the source node at which the search should start. /// - `weights`: the weight function for each edge pub fn start<'a, A, D, W>(adj: A, src: A::Node, weights: W) -> DijkstraDefault<'a, A, D, W> where A: Adjacencies<'a>, A::Node: Hash, D: Copy + PartialOrd + Zero, W: Fn(A::Edge) -> D, { start_with_data(adj, src, weights, astar::default_data()) } /// Start and return an Dijkstra-iterator with custom data structures. /// /// The returned iterator traverses the edges in the order of an Dijkstra-search. The /// iterator returns the next node, its incoming edge and the distance to the /// start node. /// /// Note that the start node is *not* returned by the iterator. /// /// The algorithm requires a pair `(M, P)` with `M` implementing [`ItemMap<Node, /// Item>`][crate::collections::ItemMap], and `P` implementing /// [`ItemPriQueue<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 /// /// - `adj`: adjacency information for the graph /// - `src`: the source node at which the search should start. /// - `weights`: the weight function for each edge /// - `data`: the custom data structures pub fn start_with_data<'a, A, D, W, M, P>( adj: A, src: A::Node, weights: W, data: (M, P), ) -> Dijkstra<'a, A, D, W, M, P, SumAccumulator> where A: Adjacencies<'a>, D: Copy + PartialOrd + Zero, W: Fn(A::Edge) -> D, M: ItemMap<A::Node, Option<P::Item>>, P: ItemPriQueue<A::Node, Data<A::Edge, D, NoHeur>>, { start_generic(adj, src, weights, data) } /// Start and return an Dijkstra-iterator with a custom accumulator and custom /// data structures. /// /// This function differs from [`start_with_data`] in the additional type /// parameter `Accum`. The type parameter is the accumulation function for /// combining the length to the previous node with the weight of the current /// edge. It is usually just the sum ([`SumAccumulator`]). One possible use is /// the Prim's algorithm for the minimum spanning tree problem (see /// [`mst::prim`](crate::mst::prim())). pub fn start_generic<'a, A, D, W, M, P, Accum>( adj: A, src: A::Node, weights: W, data: (M, P), ) -> Dijkstra<'a, A, D, W, M, P, Accum> where A: Adjacencies<'a>, D: Copy + PartialOrd + Zero, W: Fn(A::Edge) -> D, M: ItemMap<A::Node, Option<P::Item>>, P: ItemPriQueue<A::Node, Data<A::Edge, D, NoHeur>>, Accum: Accumulator<D>, { astar::start_generic(adj, src, weights, NoHeur, data) } /// Start a Dijkstra-search on a 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. /// /// # Parameter /// - `g`: the graph /// - `weights`: the (non-negative) edge weights /// - `src`: the source node /// - `heur`: the lower bound heuristic pub fn start_undirected<'a, G, D, W>(g: &'a G, src: G::Node, weights: W) -> DijkstraDefault<'a, Neighbors<'a, G>, D, W> where G: Graph<'a>, G::Node: Hash, D: Copy + PartialOrd + Zero, W: Fn(G::Edge) -> D, { start(Neighbors(g), src, weights) } /// Run a 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 return the resulting path from `src` to /// `snk`. /// /// # Parameter /// - `g`: the graph /// - `weights`: the (non-negative) edge weights /// - `src`: the source node /// - `snk`: the sink node /// /// 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: 'a + Copy + PartialOrd + Zero + Add<D, Output = D> + Sub<D, Output = D>, W: Fn(G::Edge) -> D, { astar::find_undirected_path(g, src, snk, weights, NoHeur) } /// Start a Dijkstra-search on a directed graph. /// /// This is a convenience wrapper to start the search on an directed graph /// with the default data structures. /// /// # Parameter /// - `g`: the graph /// - `weights`: the (non-negative) edge weights /// - `src`: the source node pub fn start_directed<'a, G, D, W>(g: &'a G, src: G::Node, weights: W) -> DijkstraDefault<'a, OutEdges<'a, G>, D, W> where G: Digraph<'a>, G::Node: Hash, D: Copy + PartialOrd + Zero, W: Fn(G::Edge) -> D, { start(OutEdges(g), src, weights) } /// Run a Dijkstra-search on a 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 return the resulting path from `src` to /// `snk`. /// /// # Parameter /// - `g`: the graph /// - `weights`: the (non-negative) edge weights /// - `src`: the source node /// - `snk`: the sink node /// /// 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: 'a + Copy + PartialOrd + Zero + Add<D, Output = D> + Sub<D, Output = D>, W: Fn(G::Edge) -> D, { astar::find_directed_path(g, src, snk, weights, NoHeur) }