src/main.rs

@@ -1,3 +1,6 @@
+use std::cmp::Ordering;
+use std::collections::BinaryHeap;
+
 #[derive(Copy, Clone, PartialEq, Eq, Debug)]
 struct Vertex(usize);
 
@@ -74,6 +77,70 @@ impl Graph {
     }
 }
 
+#[derive(PartialEq, Eq)]
+struct DistanceOrderedVertex {
+    distance: u32,
+    vertex: Vertex,
+}
+
+impl PartialOrd for DistanceOrderedVertex {
+    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+        Some(self.distance.cmp(&other.distance))
+    }
+}
+
+impl Ord for DistanceOrderedVertex {
+    fn cmp(&self, other: &Self) -> Ordering {
+        other.distance.cmp(&self.distance)
+    }
+}
+
+// TODO: Maybe introduce a return struct type for Dijkstra's algorithm?
+fn dijkstra(graph: &Graph, source: Vertex) -> (Vec<Option<u32>>, Vec<Option<Vertex>>) {
+    let mut distances = vec![None; graph.vertex_count()];
+    let mut predecessors = vec![None; graph.vertex_count()];
+    let mut heap = BinaryHeap::new();
+
+    distances[source.0] = Some(0);
+    heap.push(DistanceOrderedVertex {
+        vertex: source,
+        distance: 0,
+    });
+    while let Some(v) = heap.pop() {
+        // TODO: Simplify with a neighbor iterator.
+        // Finds the first neighbor of v.
+        let Some(mut incidence) = graph.incidence_headers[v.vertex.0].first_incidence else {
+            break;
+        };
+        loop {
+            // Processes one neighbor of v.
+            let neighbor = graph.incidence_vertices[incidence.0];
+            // TODO: Add a way to provide custom edge weights for Dijkstra's algorithm.
+            let edge_weight = 1;
+            let new_distance = distances[v.vertex.0].unwrap() + edge_weight;
+            if match distances[neighbor.0] {
+                None => true,
+                Some(old_distance) if old_distance > new_distance => true,
+                _ => false,
+            } {
+                distances[neighbor.0] = Some(new_distance);
+                predecessors[neighbor.0] = Some(v.vertex);
+                heap.push(DistanceOrderedVertex {
+                    vertex: neighbor,
+                    distance: new_distance,
+                });
+            }
+
+            // Finds next neighbor of v.
+            let Some(next) = graph.next_incidences[incidence.0] else {
+                break;
+            };
+            incidence = next;
+        }
+    }
+    (distances, predecessors)
+}
+
 fn main() {
     // TODO: Move this graph example into one or more tests.
     let mut graph = Graph {
@@ -154,6 +221,52 @@ fn main() {
         );
     }
 
-    // TODO: test Dijkstra's algorithm starting at 0 and at another vertex.
-    let expected_distances_to_v0 = [0, 1, 2, 2, 2, 3, 3, 3, 3, 4];
+    let (distances, predecessors) = dijkstra(&graph, vertices[0]);
+    let expected_distances_from_v0 = [
+        Some(0),
+        Some(1),
+        Some(2),
+        Some(2),
+        Some(2),
+        Some(3),
+        Some(3),
+        Some(3),
+        Some(3),
+        Some(4),
+    ];
+    let expected_predecessors_from_v0 = [
+        vec![None],
+        vec![Some(vertices[0])],
+        vec![Some(vertices[1])],
+        vec![Some(vertices[1])],
+        vec![Some(vertices[1])],
+        vec![Some(vertices[2])],
+        vec![Some(vertices[2]), Some(vertices[3])],
+        vec![Some(vertices[4])],
+        vec![Some(vertices[4])],
+        vec![Some(vertices[5]), Some(vertices[6]), Some(vertices[7])],
+    ];
+    assert_eq!(
+        distances.len(),
+        graph.vertex_count(),
+        "distances count from Dijkstra's algorithm must equal vertex count"
+    );
+    assert_eq!(
+        predecessors.len(),
+        graph.vertex_count(),
+        "predecessors count from Dijkstra's algorithm must equal vertex count"
+    );
+    for i in 0..graph.vertex_count() {
+        assert_eq!(
+            distances[i], expected_distances_from_v0[i],
+            "unexpected distance from {:?} to {:?} from Dijkstra's algorithm",
+            vertices[0], vertices[i]
+        );
+        assert!(
+            expected_predecessors_from_v0[i].contains(&predecessors[i]),
+            "unexpected predecessor {:?} of {:?} from Dijkstra's algorithm",
+            predecessors[i],
+            vertices[i]
+        );
+    }
 }