Update Dijkstra's algorithm to take any weights that satisfy the new Weight trait

src/algorithms.rs

@@ -32,19 +32,46 @@ use priority_queue::PriorityQueue;
 use std::cmp::Reverse;
 use std::collections::VecDeque;
 use std::hash::Hash;
+use std::ops::Add;
 
 use crate::maps::ElementMap;
 use crate::traits::{GraphTopology, Incidence, IncidenceCursor};
 
+/// Trait that edge weights for [`dijkstra`] and its variants need to satisfy.
+///
+/// [`Default`] is used as the starting distance for `source`, so it must behave as the additive
+/// identity (typically zero) for accumulation via [`Add`] to give correct results.
+///
+/// # Examples
+///
+/// ```
+/// # use grapherity::prelude::*;
+/// # use grapherity::algorithms::dijkstra;
+/// # use grapherity::models::Graph;
+/// use std::time::Duration;
+///
+/// let mut graph = Graph::new();
+/// let source = graph.add_vertex();
+/// let target = graph.add_vertex();
+/// let e = graph.add_edge(source, target);
+/// let mut travel_time = graph.edge_map(Duration::ZERO);
+/// travel_time[e] = Duration::from_secs(5);
+///
+/// let result = dijkstra(&graph, source, |e| travel_time[e]);
+/// assert_eq!(result.distances[target], Some(Duration::from_secs(5)));
+/// ```
+pub trait Weight: Copy + Ord + Add<Output = Self> + Default {}
+
+impl<T: Copy + Ord + Add<Output = T> + Default> Weight for T {}
+
 /// Return data type for [`dijkstra`] and [`dijkstra_unweighted`].
-pub struct DijkstraResult<V: Copy> {
+pub struct DijkstraResult<V: Copy, W: Weight> {
     /// Vertex map of minimum distances from a given `source` vertex.
-    pub distances: ElementMap<V, Option<u32>>,
+    pub distances: ElementMap<V, Option<W>>,
     /// Vertex map of predecessors on some shortest path from a given `source` vertex.
     pub predecessors: ElementMap<V, Option<V>>,
 }
 
-// TODO: Generalize the return type of the weight function.
 // TODO: A Fibonacci heap would lower complexity to O(|E| + |V| log |V|) by making decrease-key O(1) amortized instead of O(log |V|). No standard Rust implementation exists; high constant factors may negate the asymptotic gain in practice.
 /// [Dijkstra's algorithm] with custom edge weights, returns minimum distances and predecessors.
 ///
@@ -78,11 +105,15 @@ pub struct DijkstraResult<V: Copy> {
 /// ```
 ///
 /// [Dijkstra's algorithm]: https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
-pub fn dijkstra<G, W>(graph: &G, source: G::Vertex, weights: W) -> DijkstraResult<G::Vertex>
+pub fn dijkstra<G, W>(
+    graph: &G,
+    source: G::Vertex,
+    weights: impl Fn(G::Edge) -> W,
+) -> DijkstraResult<G::Vertex, W>
 where
     G: GraphTopology,
     G::Vertex: Hash,
-    W: Fn(G::Edge) -> u32,
+    W: Weight,
 {
     let mut predecessors = graph.vertex_map(None);
     let distances = dijkstra_impl(graph, source, weights, |adjacent, predecessor| {
@@ -127,12 +158,12 @@ where
 pub fn dijkstra_distances<G, W>(
     graph: &G,
     source: G::Vertex,
-    weights: W,
-) -> ElementMap<G::Vertex, Option<u32>>
+    weights: impl Fn(G::Edge) -> W,
+) -> ElementMap<G::Vertex, Option<W>>
 where
     G: GraphTopology,
     G::Vertex: Hash,
-    W: Fn(G::Edge) -> u32,
+    W: Weight,
 {
     dijkstra_impl(graph, source, weights, |_, _| {})
 }
@@ -168,7 +199,7 @@ where
 /// ```
 ///
 /// [Dijkstra's algorithm]: https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
-pub fn dijkstra_unweighted<G>(graph: &G, source: G::Vertex) -> DijkstraResult<G::Vertex>
+pub fn dijkstra_unweighted<G>(graph: &G, source: G::Vertex) -> DijkstraResult<G::Vertex, u32>
 where
     G: GraphTopology,
     G::Vertex: Hash,
@@ -220,24 +251,24 @@ where
 fn dijkstra_impl<G, W, F>(
     graph: &G,
     source: G::Vertex,
-    weights: W,
+    weights: impl Fn(G::Edge) -> W,
     mut on_relax: F,
-) -> ElementMap<G::Vertex, Option<u32>>
+) -> ElementMap<G::Vertex, Option<W>>
 where
     G: GraphTopology,
     G::Vertex: Hash,
-    W: Fn(G::Edge) -> u32,
+    W: Weight,
     F: FnMut(G::Vertex, G::Vertex),
 {
     let mut distances = graph.vertex_map(None);
     let mut heap = PriorityQueue::new();
 
-    distances[source] = Some(0);
-    heap.push(source, Reverse(0u32));
+    distances[source] = Some(W::default());
+    heap.push(source, Reverse(W::default()));
 
     while let Some((v, Reverse(v_distance))) = heap.pop() {
         for Incidence { vertex: u, edge: e } in graph.incidences(v) {
-            let new_distance = v_distance + weights(e);
+            let new_distance = weights(e) + v_distance;
             if match distances[u] {
                 None => true,
                 Some(old_distance) if old_distance > new_distance => true,

tests/dijkstra.rs

@@ -173,7 +173,7 @@ where
     fixtures::assert_standard_unweighted_distances_v0(|v| distances[v], &vertices);
 }
 
-fn assert_single_vertex<G: GraphTopology>(result: &DijkstraResult<G::Vertex>, v: G::Vertex)
+fn assert_single_vertex<G: GraphTopology>(result: &DijkstraResult<G::Vertex, u32>, v: G::Vertex)
 where
     G::Vertex: Debug,
 {
@@ -195,8 +195,10 @@ fn assert_distances_single_vertex<G: GraphTopology>(
     );
 }
 
-fn assert_disconnected<G: GraphTopology>(result: &DijkstraResult<G::Vertex>, vertices: &[G::Vertex])
-where
+fn assert_disconnected<G: GraphTopology>(
+    result: &DijkstraResult<G::Vertex, u32>,
+    vertices: &[G::Vertex],
+) where
     G::Vertex: Debug,
 {
     assert_distances_disconnected::<G>(&result.distances, &vertices);