pathfinding

This crate implements several pathfinding, flow, and graph algorithms in Rust.

Algorithms

The algorithms are generic over their arguments.

Directed graphs

• A*: find the shortest path in a weighted graph using an heuristic to guide the process (⇒ Wikipedia)
• BFS: explore nearest successors first, then widen the search (⇒ Wikipedia)
• Brent: find a cycle in an infinite sequence (⇒ Wikipedia)
• DFS: explore a graph by going as far as possible, then backtrack (⇒ Wikipedia)
• Dijkstra: find the shortest path in a weighted graph (⇒ Wikipedia)
• Edmonds Karp: find the maximum flow in a weighted graph (⇒ Wikipedia)
• Floyd: find a cycle in an infinite sequence (⇒ Wikipedia)
• Fringe: find the shortest path in a weighted graph using an heuristic to guide the process (⇒ Wikipedia)
• IDA*: explore longer and longer paths in a weighted graph at the cost of multiple similar examinations (⇒ Wikipedia)
• IDDFS: explore longer and longer paths in an unweighted graph at the cost of multiple similar examinations (⇒ Wikipedia)
• strongly connected components: find strongly connected components in a directed graph (⇒ Wikipedia)
• topological sorting: find an acceptable topological order in a directed graph (⇒ Wikipedia)
• Yen: find k-shortest paths using Dijkstra (⇒ Wikipedia)

Undirected graphs

• connected components: find disjoint connected sets of vertices (⇒ Wikipedia)
• Kruskal: find a minimum-spanning-tree (⇒ Wikipedia)

Matching

• Kuhn-Munkres (Hungarian algorithm): find the maximum (or minimum) matching in a weighted bipartite graph (⇒ Wikipedia)

Miscellaneous structures

• A Grid type representing a rectangular grid in which vertices can be added or removed, with automatic creation of edges between adjacent vertices.
• A Matrix type to store data of arbitrary types, with neighbour-aware methods.

Using this crate

In your Cargo.toml, put:

[dependencies]
pathfinding = "4.8.2"

You can then pull your preferred algorithm (BFS in this example) using:

use pathfinding::prelude::bfs;

Example

We will search the shortest path on a chess board to go from (1, 1) to (4, 6) doing only knight moves.

use pathfinding::prelude::bfs;

#[derive(Clone, Debug, Eq, Hash, Ord, PartialEq, PartialOrd)]
struct Pos(i32, i32);

impl Pos {
  fn successors(&self) -> Vec<Pos> {
    let &Pos(x, y) = self;
    vec![Pos(x+1,y+2), Pos(x+1,y-2), Pos(x-1,y+2), Pos(x-1,y-2),
         Pos(x+2,y+1), Pos(x+2,y-1), Pos(x-2,y+1), Pos(x-2,y-1)]
  }
}

static GOAL: Pos = Pos(4, 6);
let result = bfs(&Pos(1, 1), |p| p.successors(), |p| *p == GOAL);
assert_eq!(result.expect("no path found").len(), 5);

Note on floating-point types

Several algorithms require that the numerical types used to describe edge weights implement Ord. If you wish to use Rust built-in floating-point types (such as f32) that implement PartialOrd in this context, you can wrap them into compliant types using the ordered-float crate.

The minimum supported Rust version (MSRV) is Rust 1.70.0.

License

This code is released under a dual Apache 2.0 / MIT free software license.

Contributing

You are welcome to contribute by opening issues or submitting pull requests. Please open an issue before implementing a new feature, in case it is a work in progress already or it is fit for this repository.

In order to pass the continuous integration tests, your code must be formatted using the latest rustfmt with the nightly rust toolchain, and pass cargo clippy and pre-commit checks. Those will run automatically when you submit a pull request. You can install pre-commit to your checked out version of the repository by running:

$ pre-commit install --hook-type commit-msg

This repository uses the conventional commits commit message style, such as:

• feat(matrix): add Matrix::transpose()
• fix(tests): remove unused imports

If a pull-request should automatically close an open issue, please include "Fix #xxx# or "Close #xxx" in the pull-request cover-letter.