Add remaining docs for algorithms module

src/algorithms.rs

@@ -14,7 +14,7 @@
 //! [Breadth-first search] traverses a graph topology, exploring all neighboring vertices first
 //! before descending further into their neighborhoods.
 //!
-//! Variants: [`bfs`], [`bfs_distances`], [`bfs_find`], [`bfs_find_where`]
+//! Variants: [`bfs`], [`bfs_distances`], [`bfs_find`], [`bfs_find_where`].
 //!
 //! # Depth-first search
 //!
@@ -22,7 +22,7 @@
 //! first before backtracking and exploring other branches.
 //!
 //! Variants: [`dfs`], [`dfs_visited`], [`dfs_find`], [`dfs_find_where`], [`dfs_find_path`],
-//! [`dfs_find_path_where`]
+//! [`dfs_find_path_where`].
 //!
 //! [Breadth-first search]: https://en.wikipedia.org/wiki/Breadth-first_search
 //! [Depth-first search]: https://en.wikipedia.org/wiki/Depth-first_search
@@ -52,17 +52,21 @@ impl<V: Eq> Ord for DistanceOrderedVertex<V> {
     }
 }
 
-/// Return data type for [`dijkstra`] and [`dijkstra unweighted`].
+/// Return data type for [`dijkstra`] and [`dijkstra_unweighted`].
 pub struct DijkstraResult<V: Copy> {
     /// Vertex map of minimum distances from a given `source` vertex.
     pub distances: VertexMap<V, Option<u32>>,
-
     /// Vertex map of predecessors on some shortest path from a given `source` vertex.
     pub predecessors: VertexMap<V, Option<V>>,
 }
 
 // TODO: Generalize the return type of the weight function.
-/// Dijkstra's algorithm with custom edge weights, returns minimum distances and predecessors.
+/// [Dijkstra's algorithm] with custom edge weights, returns minimum distances and predecessors.
+///
+/// Calculates the shortest paths from `source` to all vertices in `graph` with edge weights given
+/// by `weight` function. Returns the distances from `source` to each vertex, and the predecessors
+/// of each vertex on some shortest path from `source` to that vertex. Returns `None` for any vertex
+/// not connected to `source`.
 ///
 /// # Panics
 ///
@@ -85,6 +89,8 @@ pub struct DijkstraResult<V: Copy> {
 /// assert_eq!(result.distances[target], Some(5));
 /// assert_eq!(result.predecessors[target], Some(source));
 /// ```
+///
+/// [Dijkstra's algorithm]: https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
 pub fn dijkstra<G, W>(graph: &G, source: G::Vertex, weight: W) -> DijkstraResult<G::Vertex>
 where
     G: GraphTopology,
@@ -100,7 +106,11 @@ where
     }
 }
 
-/// Dijkstra's algorithm with custom edge weights, returns minimum distances.
+/// [Dijkstra's algorithm] with custom edge weights, returns minimum distances.
+///
+/// Calculates the shortest paths from `source` to all vertices in `graph` with edge weights given
+/// by `weight` function. Returns the distances from `source` to each vertex. Returns `None` for any
+/// vertex not connected to `source`.
 ///
 /// # Panics
 ///
@@ -110,7 +120,7 @@ where
 ///
 /// ```
 /// # use grapherity::prelude::*;
-/// # use grapherity::algorithms::{dijkstra, dijkstra_distances};
+/// # use grapherity::algorithms::dijkstra_distances;
 /// # use grapherity::models::Graph;
 /// let mut graph = Graph::new();
 /// let source = graph.add_vertex();
@@ -122,6 +132,8 @@ where
 /// let distances = dijkstra_distances(&graph, source, |e| weights[e]);
 /// assert_eq!(distances[target], Some(5));
 /// ```
+///
+/// [Dijkstra's algorithm]: https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
 pub fn dijkstra_distances<G, W>(
     graph: &G,
     source: G::Vertex,
@@ -134,8 +146,13 @@ where
     dijkstra_impl(graph, source, weight, |_, _| {})
 }
 
-/// Dijkstra's algorithm with constant weights of *1* for all edges, returns minimum distances and
+/// [Dijkstra's algorithm] with unit edge weights, returns minimum distances and predecessors.
-/// predecessors.
+///
+/// Calculates the shortest paths from `source` to all vertices in an unweighted `graph`. Returns
+/// the distances from `source` to each vertex, and the predecessors of each vertex on some shortest
+/// path from `source` to that vertex. Returns `None` for any vertex not connected to `source`.
+///
+/// Prefer [`bfs`] for unweighted graphs, it has better time and space complexity.
 ///
 /// # Panics
 ///
@@ -145,7 +162,7 @@ where
 ///
 /// ```
 /// # use grapherity::prelude::*;
-/// # use grapherity::algorithms::{dijkstra, dijkstra_unweighted};
+/// # use grapherity::algorithms::dijkstra_unweighted;
 /// # use grapherity::models::Graph;
 /// let mut graph = Graph::new();
 /// let source = graph.add_vertex();
@@ -156,6 +173,8 @@ where
 /// assert_eq!(result.distances[target], Some(1));
 /// assert_eq!(result.predecessors[target], Some(source));
 /// ```
+///
+/// [Dijkstra's algorithm]: https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
 pub fn dijkstra_unweighted<G>(graph: &G, source: G::Vertex) -> DijkstraResult<G::Vertex>
 where
     G: GraphTopology,
@@ -163,7 +182,13 @@ where
     dijkstra(graph, source, |_| 1)
 }
 
-/// Dijkstra's algorithm with constant weights of *1* for all edges, returns minimum distances.
+/// [Dijkstra's algorithm] with unit edge weights, returns minimum distances.
+///
+/// Calculates the shortest paths from `source` to all vertices in an unweighted `graph`. Returns
+/// the distances from `source` to each vertex. Returns `None` for any vertex not connected to
+/// `source`.
+///
+/// Prefer [`bfs_distances`] for unweighted graphs, it has better time and space complexity.
 ///
 /// # Panics
 ///
@@ -173,7 +198,7 @@ where
 ///
 /// ```
 /// # use grapherity::prelude::*;
-/// # use grapherity::algorithms::{dijkstra, dijkstra_distances_unweighted};
+/// # use grapherity::algorithms::dijkstra_distances_unweighted;
 /// # use grapherity::models::Graph;
 /// let mut graph = Graph::new();
 /// let source = graph.add_vertex();
@@ -183,6 +208,8 @@ where
 /// let distances = dijkstra_distances_unweighted(&graph, source);
 /// assert_eq!(distances[target], Some(1));
 /// ```
+///
+/// [Dijkstra's algorithm]: https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
 pub fn dijkstra_distances_unweighted<G>(
     graph: &G,
     source: G::Vertex,
@@ -233,11 +260,44 @@ where
     distances
 }
 
+/// Return data type for [`bfs`].
 pub struct BfsResult<V: Copy> {
+    /// Vertex map of minimum distances from a given `source` vertex.
     pub distances: VertexMap<V, Option<u32>>,
+    /// Vertex map of predecessors on some shortest path from a given `source` vertex.
     pub predecessors: VertexMap<V, Option<V>>,
 }
 
+/// [Breadth-first search] traversal from `source`, returns distances and predecessors.
+///
+/// Traverses vertices in `graph` starting from `source`, exploring all neighbors before descending
+/// further. Returns the distances from `source` to each vertex, and the predecessors of each vertex
+/// on some shortest path from `source` to that vertex. Returns `None` for any vertex not connected
+/// to `source`.
+///
+/// Time complexity is *O(|V| + |E|)*, space complexity is *O(|V|)*.
+///
+/// # Panics
+///
+/// Panics if `source` is not a valid vertex of `graph`.
+///
+/// # Examples
+///
+/// ```
+/// # use grapherity::prelude::*;
+/// # use grapherity::algorithms::bfs;
+/// # use grapherity::models::Graph;
+/// let mut graph = Graph::new();
+/// let source = graph.add_vertex();
+/// let target = graph.add_vertex();
+/// graph.add_edge(source, target);
+///
+/// let result = bfs(&graph, source);
+/// assert_eq!(result.distances[target], Some(1));
+/// assert_eq!(result.predecessors[target], Some(source));
+/// ```
+///
+/// [Breadth-first search]: https://en.wikipedia.org/wiki/Breadth-first_search
 pub fn bfs<G>(graph: &G, source: G::Vertex) -> BfsResult<G::Vertex>
 where
     G: GraphTopology,
@@ -253,6 +313,34 @@ where
     }
 }
 
+/// [Breadth-first search] traversal from `source`, returns distances.
+///
+/// Traverses vertices in `graph` starting from `source`, exploring all neighbors before descending
+/// further. Returns the distances from `source` to each vertex. Returns `None` for any vertex not
+/// connected to `source`.
+///
+/// Time complexity is *O(|V| + |E|)*, space complexity is *O(|V|)*.
+///
+/// # Panics
+///
+/// Panics if `source` is not a valid vertex of `graph`.
+///
+/// # Examples
+///
+/// ```
+/// # use grapherity::prelude::*;
+/// # use grapherity::algorithms::bfs_distances;
+/// # use grapherity::models::Graph;
+/// let mut graph = Graph::new();
+/// let source = graph.add_vertex();
+/// let target = graph.add_vertex();
+/// graph.add_edge(source, target);
+///
+/// let distances = bfs_distances(&graph, source);
+/// assert_eq!(distances[target], Some(1));
+/// ```
+///
+/// [Breadth-first search]: https://en.wikipedia.org/wiki/Breadth-first_search
 pub fn bfs_distances<G>(graph: &G, source: G::Vertex) -> VertexMap<G::Vertex, Option<u32>>
 where
     G: GraphTopology,
@@ -260,6 +348,33 @@ where
     bfs_impl(graph, source, |_, _| true).distances
 }
 
+/// [Breadth-first search] from `source` for `target`, returns the distance.
+///
+/// Traverses vertices in `graph` starting from `source` until `target` is found, exploring all
+/// neighbors before descending further. Returns the minimum distance from `source` to `target` if
+/// `target` is a valid vertex of `graph` connected to `source`, or `None` otherwise.
+///
+/// Time complexity is *O(|V| + |E|)*, space complexity is *O(|V|)*.
+///
+/// # Panics
+///
+/// Panics if `source` is not a valid vertex of `graph`.
+///
+/// # Examples
+///
+/// ```
+/// # use grapherity::prelude::*;
+/// # use grapherity::algorithms::bfs_find;
+/// # use grapherity::models::Graph;
+/// let mut graph = Graph::new();
+/// let source = graph.add_vertex();
+/// let target = graph.add_vertex();
+/// graph.add_edge(source, target);
+///
+/// assert_eq!(bfs_find(&graph, source, target), Some(1));
+/// ```
+///
+/// [Breadth-first search]: https://en.wikipedia.org/wiki/Breadth-first_search
 pub fn bfs_find<G>(graph: &G, source: G::Vertex, target: G::Vertex) -> Option<u32>
 where
     G: GraphTopology,
@@ -267,6 +382,35 @@ where
     bfs_find_where(graph, source, |v| v == target).map(|(_, distance)| distance)
 }
 
+/// [Breadth-first search] from `source` for a vertex matching `predicate`, returns the vertex and
+/// its distance.
+///
+/// Traverses vertices in `graph` starting from `source` until a vertex satisfying `predicate` is
+/// found, exploring all neighbors before descending further. Returns the first vertex satisfying
+/// `predicate` and its minimum distance from `source`, or `None` if no such vertex is connected to
+/// `source`.
+///
+/// Time complexity is *O(|V| + |E|)*, space complexity is *O(|V|)*.
+///
+/// # Panics
+///
+/// Panics if `source` is not a valid vertex of `graph`.
+///
+/// # Examples
+///
+/// ```
+/// # use grapherity::prelude::*;
+/// # use grapherity::algorithms::bfs_find_where;
+/// # use grapherity::models::Graph;
+/// let mut graph = Graph::new();
+/// let source = graph.add_vertex();
+/// let target = graph.add_vertex();
+/// graph.add_edge(source, target);
+///
+/// assert_eq!(bfs_find_where(&graph, source, |v| v == target), Some((target, 1)));
+/// ```
+///
+/// [Breadth-first search]: https://en.wikipedia.org/wiki/Breadth-first_search
 pub fn bfs_find_where<G, P>(graph: &G, source: G::Vertex, predicate: P) -> Option<(G::Vertex, u32)>
 where
     G: GraphTopology,
@@ -315,11 +459,44 @@ where
     }
 }
 
+/// Return data type for [`dfs`].
 pub struct DfsResult<V: Copy> {
+    /// Vertex map indicating which vertices were visited during the search.
     pub visited: VertexMap<V, bool>,
+    /// Vertex map of predecessors on the DFS tree path from a given `source` vertex.
     pub predecessors: VertexMap<V, Option<V>>,
 }
 
+/// [Depth-first search] traversal from `source`, returns visited vertices and predecessors.
+///
+/// Traverses vertices in `graph` starting from `source`, exploring each branch as far as possible
+/// before backtracking. Returns for each vertex whether it was visited, and the predecessors of
+/// each vertex on the DFS tree path from `source` to that vertex. Any vertex not connected to
+/// `source` is marked unvisited and has no predecessor.
+///
+/// Time complexity is *O(|V| + |E|)*, space complexity is *O(|V|)*.
+///
+/// # Panics
+///
+/// Panics if `source` is not a valid vertex of `graph`.
+///
+/// # Examples
+///
+/// ```
+/// # use grapherity::prelude::*;
+/// # use grapherity::algorithms::dfs;
+/// # use grapherity::models::Graph;
+/// let mut graph = Graph::new();
+/// let source = graph.add_vertex();
+/// let target = graph.add_vertex();
+/// graph.add_edge(source, target);
+///
+/// let result = dfs(&graph, source);
+/// assert!(result.visited[target]);
+/// assert_eq!(result.predecessors[target], Some(source));
+/// ```
+///
+/// [Depth-first search]: https://en.wikipedia.org/wiki/Depth-first_search
 pub fn dfs<G>(graph: &G, source: G::Vertex) -> DfsResult<G::Vertex>
 where
     G: GraphTopology,
@@ -335,6 +512,34 @@ where
     }
 }
 
+/// [Depth-first search] traversal from `source`, returns visited vertices.
+///
+/// Traverses vertices in `graph` starting from `source`, exploring each branch as far as possible
+/// before backtracking. Returns a map indicating which vertices were visited, i.e. which vertices
+/// are connected to `source`.
+///
+/// Time complexity is *O(|V| + |E|)*, space complexity is *O(|V|)*.
+///
+/// # Panics
+///
+/// Panics if `source` is not a valid vertex of `graph`.
+///
+/// # Examples
+///
+/// ```
+/// # use grapherity::prelude::*;
+/// # use grapherity::algorithms::dfs_visited;
+/// # use grapherity::models::Graph;
+/// let mut graph = Graph::new();
+/// let source = graph.add_vertex();
+/// let target = graph.add_vertex();
+/// graph.add_edge(source, target);
+///
+/// let visited = dfs_visited(&graph, source);
+/// assert!(visited[target]);
+/// ```
+///
+/// [Depth-first search]: https://en.wikipedia.org/wiki/Depth-first_search
 pub fn dfs_visited<G>(graph: &G, source: G::Vertex) -> VertexMap<G::Vertex, bool>
 where
     G: GraphTopology,
@@ -342,6 +547,33 @@ where
     dfs_impl(graph, source, |_, _| true).visited
 }
 
+/// [Depth-first search] from `source` for `target`, returns whether it was found.
+///
+/// Traverses vertices in `graph` starting from `source` until `target` is found, exploring each
+/// branch as far as possible before backtracking. Returns `true` if `target` is a valid vertex of
+/// `graph` connected to `source`, or `false` otherwise.
+///
+/// Time complexity is *O(|V| + |E|)*, space complexity is *O(|V|)*.
+///
+/// # Panics
+///
+/// Panics if `source` is not a valid vertex of `graph`.
+///
+/// # Examples
+///
+/// ```
+/// # use grapherity::prelude::*;
+/// # use grapherity::algorithms::dfs_find;
+/// # use grapherity::models::Graph;
+/// let mut graph = Graph::new();
+/// let source = graph.add_vertex();
+/// let target = graph.add_vertex();
+/// graph.add_edge(source, target);
+///
+/// assert!(dfs_find(&graph, source, target));
+/// ```
+///
+/// [Depth-first search]: https://en.wikipedia.org/wiki/Depth-first_search
 pub fn dfs_find<G>(graph: &G, source: G::Vertex, target: G::Vertex) -> bool
 where
     G: GraphTopology,
@@ -349,6 +581,33 @@ where
     dfs_find_where(graph, source, |v| v == target).is_some()
 }
 
+/// [Depth-first search] from `source` for a vertex matching `predicate`, returns the vertex.
+///
+/// Traverses vertices in `graph` starting from `source` until a vertex satisfying `predicate` is
+/// found, exploring each branch as far as possible before backtracking. Returns the first vertex
+/// satisfying `predicate`, or `None` if no such vertex is connected to `source`.
+///
+/// Time complexity is *O(|V| + |E|)*, space complexity is *O(|V|)*.
+///
+/// # Panics
+///
+/// Panics if `source` is not a valid vertex of `graph`.
+///
+/// # Examples
+///
+/// ```
+/// # use grapherity::prelude::*;
+/// # use grapherity::algorithms::dfs_find_where;
+/// # use grapherity::models::Graph;
+/// let mut graph = Graph::new();
+/// let source = graph.add_vertex();
+/// let target = graph.add_vertex();
+/// graph.add_edge(source, target);
+///
+/// assert_eq!(dfs_find_where(&graph, source, |v| v == target), Some(target));
+/// ```
+///
+/// [Depth-first search]: https://en.wikipedia.org/wiki/Depth-first_search
 pub fn dfs_find_where<G, P>(graph: &G, source: G::Vertex, predicate: P) -> Option<G::Vertex>
 where
     G: GraphTopology,
@@ -396,6 +655,35 @@ where
     }
 }
 
+/// [Depth-first search] from `source` for `target`, returns the path as a sequence of edges.
+///
+/// Traverses vertices in `graph` starting from `source` until `target` is found, exploring each
+/// branch as far as possible before backtracking. Returns some path from `source` to `target` as a
+/// sequence of edges in traversal order if `target` is a valid vertex of `graph` connected to
+/// `source`, or `None` otherwise. The returned path is empty if and only if `source` equals
+/// `target`.
+///
+/// Time complexity is *O(|V| + |E|)*, space complexity is *O(|V|)*.
+///
+/// # Panics
+///
+/// Panics if `source` is not a valid vertex of `graph`.
+///
+/// # Examples
+///
+/// ```
+/// # use grapherity::prelude::*;
+/// # use grapherity::algorithms::dfs_find_path;
+/// # use grapherity::models::Graph;
+/// let mut graph = Graph::new();
+/// let source = graph.add_vertex();
+/// let target = graph.add_vertex();
+/// let e = graph.add_edge(source, target);
+///
+/// assert_eq!(dfs_find_path(&graph, source, target), Some(vec![e]));
+/// ```
+///
+/// [Depth-first search]: https://en.wikipedia.org/wiki/Depth-first_search
 pub fn dfs_find_path<G>(graph: &G, source: G::Vertex, target: G::Vertex) -> Option<Vec<G::Edge>>
 where
     G: GraphTopology,
@@ -403,6 +691,36 @@ where
     dfs_find_path_where(graph, source, |v| v == target)
 }
 
+/// [Depth-first search] from `source` for a vertex matching `predicate`, returns the path as a
+/// sequence of edges.
+///
+/// Traverses vertices in `graph` starting from `source` until a vertex satisfying `predicate` is
+/// found, exploring each branch as far as possible before backtracking. Returns some path from
+/// `source` to the first vertex satisfying `predicate` as a sequence of edges in traversal order,
+/// or `None` if no such vertex is connected to `source`. The returned path is empty if and only if
+/// `source` satisfies `predicate`.
+///
+/// Time complexity is *O(|V| + |E|)*, space complexity is *O(|V|)*.
+///
+/// # Panics
+///
+/// Panics if `source` is not a valid vertex of `graph`.
+///
+/// # Examples
+///
+/// ```
+/// # use grapherity::prelude::*;
+/// # use grapherity::algorithms::dfs_find_path_where;
+/// # use grapherity::models::Graph;
+/// let mut graph = Graph::new();
+/// let source = graph.add_vertex();
+/// let target = graph.add_vertex();
+/// let e = graph.add_edge(source, target);
+///
+/// assert_eq!(dfs_find_path_where(&graph, source, |v| v == target), Some(vec![e]));
+/// ```
+///
+/// [Depth-first search]: https://en.wikipedia.org/wiki/Depth-first_search
 pub fn dfs_find_path_where<G, P>(graph: &G, source: G::Vertex, predicate: P) -> Option<Vec<G::Edge>>
 where
     G: GraphTopology,