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#![deny( missing_docs, // missing_doc_code_examples, missing_debug_implementations, missing_copy_implementations, trivial_casts, trivial_numeric_casts, unsafe_code, unstable_features, unused_import_braces, unused_qualifications )] //! A crate to quickly approximate Paths on a Grid. //! //! ## Introduction //! //! Finding Paths on a Grid is an expensive Operation. Consider the following Setup: //! //! ![The Setup](https://github.com/mich101mich/hierarchical_pathfinding/blob/master/img/problem.png?raw=true) //! //! In order to calculate a Path from Start to End using regular A*, it is necessary to check a //! lot of Tiles: //! //! ![A*](https://github.com/mich101mich/hierarchical_pathfinding/blob/master/img/a_star.png?raw=true) //! //! (This is simply a small example, longer Paths require a quadratic increase in Tile checks, //! and unreachable Goals require the check of _**every single**_ Tile) //! //! The Solution that Hierarchical Pathfinding provides is to divide the Grid into Chunks and //! cache the Paths between Chunk entrances as a Graph of Nodes: //! //! ![The Graph](https://github.com/mich101mich/hierarchical_pathfinding/blob/master/img/hpa.png?raw=true) //! //! This allows Paths to be generated by connecting the Start and End to the Nodes within the //! Chunk and using the Graph for the rest: //! //! ![The Solution](https://github.com/mich101mich/hierarchical_pathfinding/blob/master/img/hpa_solution.png?raw=true) //! //! Since the Graph is not an exact representation of the Grid, **the resulting Paths will //! be slightly worse than the actual best Path** (unless [`config.perfect_paths`](PathCacheConfig::perfect_paths) //! is set to `true`). This is usually not a problem, since the purpose of Hierarchical Pathfinding //! is to quickly find the next direction to go in or a Heuristic for the Cost and existence //! of a Path. //! //! The only time where the actual best Path would noticeably differ is in the case of short Paths. //! That is why this crate calls the regular A* search after HPA* confirmed the length and //! existence. (This behavior can be turned of using the Config). //! //! This crate provides an implementation of a Hierarchical Pathfinding Algorithm for any generic Grid. //! Paths can be searched using either A* for a Path to a single Tile, or Dijkstra for searching //! multiple Targets. It handles solid walls in the Grid and actually finding a Path to a wall. //! //! ## Examples //! Creating the Cache: //! ``` //! use hierarchical_pathfinding::{prelude::*, Point}; //! //! // create and initialize Grid //! // 0 = empty, 1 = swamp, 2 = wall //! let mut grid = [ //! [0, 2, 0, 0, 0], //! [0, 2, 2, 2, 0], //! [0, 1, 0, 0, 0], //! [0, 1, 0, 2, 0], //! [0, 0, 0, 2, 0], //! ]; //! let (width, height) = (grid.len(), grid[0].len()); //! //! let cost_map = [ //! 1, // empty //! 10, // swamp //! -1, // wall = solid //! ]; //! //! let mut pathfinding = PathCache::new( //! (width, height), // the size of the Grid //! |(x, y)| cost_map[grid[y][x]], // get the cost for walking over a Tile //! ManhattanNeighborhood::new(width, height), // the Neighborhood //! PathCacheConfig { chunk_size: 3, ..Default::default() }, // config //! ); //! ``` //! Note that the PathCache never actually asks for the Grid itself. This allows the user to //! store the Grid in any format they want (Array, Vec, HashMap, kd-tree, ...), //! as long as they are somehow able to access a specific (x, y) on the Grid when asked. //! //! The provided function takes a Position on the Grid as parameter and returns, how "expensive" //! it is to walk across the Tile at that Position. This Cost is what will be used for calculating //! the Cost of a Path to find the most optimal one. A negative Cost implies that the Tile cannot //! be walked across. //! //! Unfortunately, it is necessary to provide this function to every method of PathCache, since //! storing it would make the Grid immutable. See also [Updating the PathCache](#updating-the-pathcache). //! //! **Note**: If copying the Cost function everywhere would create too much Code / less readable //! code, [currying](https://en.wikipedia.org/wiki/Currying) may be used: //! ``` //! # use hierarchical_pathfinding::{prelude::*, Point}; //! # //! # // create and initialize Grid //! # // 0 = empty, 1 = swamp, 2 = wall //! # let mut grid = [ //! # [0, 2, 0, 0, 0], //! # [0, 2, 2, 2, 0], //! # [0, 1, 0, 0, 0], //! # [0, 1, 0, 2, 0], //! # [0, 0, 0, 2, 0], //! # ]; //! # let (width, height) = (grid.len(), grid[0].len()); //! # //! const COST_MAP: [isize; 3] = [1, 10, -1]; //! //! // only references the Grid when called //! fn cost_fn<'a>(grid: &'a [[usize; 5]; 5]) -> impl 'a + FnMut(Point) -> isize { //! move |(x, y)| COST_MAP[grid[y][x]] //! } //! //! let mut pathfinding = PathCache::new( //! (width, height), // the size of the Grid //! //! // simply call the creator function to take a reference of the Grid //! cost_fn(&grid), //! //! // ... //! # ManhattanNeighborhood::new(width, height), // the Neighborhood //! # PathCacheConfig { chunk_size: 3, ..Default::default() }, // config //! ); //! //! # let start = (0, 0); //! # let goal = (4, 4); //! // ... //! //! let path = pathfinding.find_path( //! start, goal, //! //! // function can be reused at any time //! cost_fn(&grid), //! //! ); //! ``` //! //! ### Pathfinding //! Finding the Path to a single Goal: //! ``` //! # use hierarchical_pathfinding::{prelude::*, Point}; //! # //! # // create and initialize Grid //! # // 0 = empty, 1 = swamp, 2 = wall //! # let mut grid = [ //! # [0, 2, 0, 0, 0], //! # [0, 2, 2, 2, 2], //! # [0, 1, 0, 0, 0], //! # [0, 1, 0, 2, 0], //! # [0, 0, 0, 2, 0], //! # ]; //! # let (width, height) = (grid.len(), grid[0].len()); //! # //! # const COST_MAP: [isize; 3] = [1, 10, -1]; //! # //! # fn cost_fn<'a>(grid: &'a [[usize; 5]; 5]) -> impl 'a + FnMut(Point) -> isize { //! # move |(x, y)| COST_MAP[grid[y][x]] //! # } //! # //! # let mut pathfinding = PathCache::new( //! # (width, height), //! # cost_fn(&grid), //! # ManhattanNeighborhood::new(width, height), //! # PathCacheConfig { chunk_size: 3, ..Default::default() }, //! # ); //! # //! let start = (0, 0); //! let goal = (4, 4); //! //! // find_path returns Some(Path) on success //! let path = pathfinding.find_path( //! start, //! goal, //! cost_fn(&grid), //! ); //! //! assert!(path.is_some()); //! let mut path = path.unwrap(); //! //! assert_eq!(path.cost(), 12); //! ``` //! For more information, see [`find_path`](PathCache::find_path). //! //! Finding multiple Goals: //! ``` //! # use hierarchical_pathfinding::{prelude::*, Point}; //! # //! # // create and initialize Grid //! # // 0 = empty, 1 = swamp, 2 = wall //! # let mut grid = [ //! # [0, 2, 0, 0, 0], //! # [0, 2, 2, 2, 2], //! # [0, 1, 0, 0, 0], //! # [0, 1, 0, 2, 0], //! # [0, 0, 0, 2, 0], //! # ]; //! # let (width, height) = (grid.len(), grid[0].len()); //! # //! # const COST_MAP: [isize; 3] = [1, 10, -1]; //! # //! # fn cost_fn<'a>(grid: &'a [[usize; 5]; 5]) -> impl 'a + FnMut(Point) -> isize { //! # move |(x, y)| COST_MAP[grid[y][x]] //! # } //! # //! # let mut pathfinding = PathCache::new( //! # (width, height), //! # cost_fn(&grid), //! # ManhattanNeighborhood::new(width, height), //! # PathCacheConfig { chunk_size: 3, ..Default::default() }, //! # ); //! # //! let start = (0, 0); //! let goals = [(4, 4), (2, 0)]; //! //! // find_paths returns a HashMap<goal, Path> for all successes //! let paths = pathfinding.find_paths( //! start, //! &goals, //! cost_fn(&grid), //! ); //! //! // (4, 4) is reachable //! assert!(paths.contains_key(&goals[0])); //! //! // (2, 0) is not reachable //! assert!(!paths.contains_key(&goals[1])); //! ``` //! For more information, see [`find_paths`](PathCache::find_paths). //! //! ### Using a Path //! The easiest information obtainable from a Path is its existence. Despite being an //! approximation of an optimal Path, HPA* is 100% correct when it comes to the existence //! of a Path. Meaning that if HPA* cannot find a Path, no one can, and if HPA* returns a Path, //! it is valid, given correct Neighborhood and Cost functions. //! //! The next step is to obtain information about the Path itself. The part that is always //! available is the total Cost of the Path. Once again, it is just an approximation. However, //! it gives a pretty good estimate of the actual Cost, with only minimal deviations. //! //! As for following the Path, HPA* was designed to allow Units to immediately start moving //! and minimize lost time when the surroundings change in a way that alters the Path. //! That is why it does not calculate the full Path immediately. It does, however, generate //! the first steps of the Path without too much overhead. That is why it is advised to //! mostly use the `next()` method of the returned Path for a few steps. //! //! ``` //! # use hierarchical_pathfinding::{prelude::*, Point}; //! # //! # // create and initialize Grid //! # // 0 = empty, 1 = swamp, 2 = wall //! # let mut grid = [ //! # [0, 2, 0, 0, 0], //! # [0, 2, 2, 2, 2], //! # [0, 1, 0, 0, 0], //! # [0, 1, 0, 2, 0], //! # [0, 0, 0, 2, 0], //! # ]; //! # let (width, height) = (grid.len(), grid[0].len()); //! # //! # const COST_MAP: [isize; 3] = [1, 10, -1]; //! # //! # fn cost_fn<'a>(grid: &'a [[usize; 5]; 5]) -> impl 'a + FnMut(Point) -> isize { //! # move |(x, y)| COST_MAP[grid[y][x]] //! # } //! # //! # let mut pathfinding = PathCache::new( //! # (width, height), //! # cost_fn(&grid), //! # ManhattanNeighborhood::new(width, height), //! # PathCacheConfig { chunk_size: 3, ..Default::default() }, //! # ); //! # struct Player{ pos: (usize, usize) } //! # impl Player { //! # pub fn move_to(&mut self, pos: (usize, usize)) { //! # self.pos = pos; //! # } //! # } //! # //! let mut player = Player { //! pos: (0, 0), //! //... //! }; //! let goal = (4, 4); //! //! let mut path = pathfinding.find_path( //! player.pos, //! goal, //! cost_fn(&grid), //! ).unwrap(); //! //! player.move_to(path.next().unwrap()); //! assert_eq!(player.pos, (0, 1)); //! //! // wait for next turn or whatever //! //! player.move_to(path.next().unwrap()); //! assert_eq!(player.pos, (0, 2)); //! ``` //! //! ### Updating the PathCache //! The PathCache does not contain a copy or reference of the Grid for mutability and Ownership reasons. //! This means however, that the user is responsible for storing and maintaining both the Grid and the PathCache. //! It is also necessary to update the PathCache when the Grid has changed to keep it consistent: //! ``` //! # use hierarchical_pathfinding::{prelude::*, Point}; //! # //! # // create and initialize Grid //! # // 0 = empty, 1 = swamp, 2 = wall //! # let mut grid = [ //! # [0, 2, 0, 0, 0], //! # [0, 2, 2, 2, 2], //! # [0, 1, 0, 0, 0], //! # [0, 1, 0, 2, 0], //! # [0, 0, 0, 2, 0], //! # ]; //! # let (width, height) = (grid.len(), grid[0].len()); //! # //! # const COST_MAP: [isize; 3] = [1, 10, -1]; //! # //! # fn cost_fn<'a>(grid: &'a [[usize; 5]; 5]) -> impl 'a + FnMut(Point) -> isize { //! # move |(x, y)| COST_MAP[grid[y][x]] //! # } //! # //! # let mut pathfinding = PathCache::new( //! # (width, height), //! # cost_fn(&grid), //! # ManhattanNeighborhood::new(width, height), //! # PathCacheConfig { chunk_size: 3, ..Default::default() }, //! # ); //! # //! let (start, goal) = ((0, 0), (2, 0)); //! //! let path = pathfinding.find_path(start, goal, cost_fn(&grid)); //! assert!(path.is_none()); //! //! grid[0][1] = 0; //! grid[4][4] = 2; //! //! assert_eq!(grid, [ //! [0, 0, 0, 0, 0], //! [0, 2, 2, 2, 2], //! [0, 1, 0, 0, 0], //! [0, 1, 0, 2, 0], //! [0, 0, 0, 2, 2], //! ]); //! //! pathfinding.tiles_changed( //! &[(1, 0), (4, 4)], //! cost_fn(&grid), //! ); //! //! let path = pathfinding.find_path(start, goal, cost_fn(&grid)); //! assert!(path.is_some()); //! ``` //! //! ### Configuration //! The last parameter for PathCache::new is a [`PathCacheConfig`] object with different options to have more control over the generated PathCache. //! These options are mostly used to adjust the balance between Performance and Memory Usage, with the default values aiming more at Performance. //! The PathCacheConfig struct also provides defaults for low Memory Usage [`PathCacheConfig::LOW_MEM`] //! or best Performance [`PathCacheConfig::HIGH_PERFORMANCE`] //! ``` //! # use hierarchical_pathfinding::{prelude::*, Point}; //! # //! # // create and initialize Grid //! # // 0 = empty, 1 = swamp, 2 = wall //! # let mut grid = [ //! # [0, 2, 0, 0, 0], //! # [0, 2, 2, 2, 2], //! # [0, 1, 0, 0, 0], //! # [0, 1, 0, 2, 0], //! # [0, 0, 0, 2, 0], //! # ]; //! # let (width, height) = (grid.len(), grid[0].len()); //! # //! # const COST_MAP: [isize; 3] = [1, 10, -1]; //! # //! # fn cost_fn<'a>(grid: &'a [[usize; 5]; 5]) -> impl 'a + FnMut(Point) -> isize { //! # move |(x, y)| COST_MAP[grid[y][x]] //! # } //! //! let mut pathfinding = PathCache::new( //! (width, height), // the size of the Grid //! cost_fn(&grid), // get the cost for walking over a Tile //! ManhattanNeighborhood::new(width, height), // the Neighborhood //! PathCacheConfig { //! chunk_size: 3, //! ..PathCacheConfig::LOW_MEM //! } //! ); //! //! assert_eq!(pathfinding.config().chunk_size, 3); //! ``` /// The Type used to reference a Node in the abstracted Graph pub type NodeID = u32; /// A shorthand for Points on the grid pub type Point = (usize, usize); type PointMap<V> = fnv::FnvHashMap<Point, V>; type PointSet = fnv::FnvHashSet<Point>; mod path_cache; pub use self::path_cache::{AbstractPath, PathCache, PathCacheConfig}; pub mod neighbors; pub mod generics; pub mod node_id; /// The prelude for this crate. /// /// Note: Even though most examples use the internal type-definition [`Point`] /// (aka `(usize, usize)`), it is not included in the prelude since most users probably have /// another implementation with the same name in scope. pub mod prelude { pub use crate::{ neighbors::{ManhattanNeighborhood, MooreNeighborhood, Neighborhood}, AbstractPath, PathCache, PathCacheConfig, }; }