Add Dijkstra's algorithm implementation and tests

Cargo.toml

@@ -37,3 +37,7 @@ path = "adventofcode/2019/d8/d8.rs"
 [[bin]]
 name = "aoc-2019-d24"
 path = "adventofcode/2019/d24/d24.rs"
+
+[[bin]]
+name = "dijkstra"
+path = "graph/dijkstra.rs"

graph/dijkstra.rs

@@ -0,0 +1,151 @@
+use std::collections::{BinaryHeap, HashMap};
+use std::cmp::Ordering;
+
+// Define the Graph structure
+struct Graph {
+    edges: HashMap<usize, Vec<(usize, usize)>>,
+}
+
+// Define the Node structure for the priority queue
+#[derive(Copy, Clone, Eq, PartialEq)]
+struct Node {
+    cost: usize,
+    vertex: usize,
+}
+
+// Implement Ord and PartialOrd for Node to use in BinaryHeap
+impl Ord for Node {
+    fn cmp(&self, other: &Self) -> Ordering {
+        other.cost.cmp(&self.cost)
+    }
+}
+
+impl PartialOrd for Node {
+    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+        Some(self.cmp(other))
+    }
+}
+
+impl Graph {
+    // Constructor for Graph
+    fn new() -> Self {
+        Graph {
+            edges: HashMap::new(),
+        }
+    }
+
+    // Method to add an edge to the graph
+    fn add_edge(&mut self, from: usize, to: usize, cost: usize) {
+        self.edges.entry(from).or_insert(Vec::new()).push((to, cost));
+        self.edges.entry(to).or_insert(Vec::new()); // Ensure all vertices are in the map
+    }
+
+    // Dijkstra's algorithm to find the shortest path
+    fn dijkstra(&self, start: usize, end: usize) -> Option<(Vec<usize>, usize)> {
+        let mut distances: HashMap<usize, usize> = HashMap::new();
+        let mut heap = BinaryHeap::new();
+        let mut predecessors: HashMap<usize, usize> = HashMap::new();
+
+        // Initialize distances
+        for &vertex in self.edges.keys() {
+            distances.insert(vertex, std::usize::MAX);
+        }
+        distances.insert(start, 0);
+        heap.push(Node { cost: 0, vertex: start });
+
+        while let Some(Node { cost, vertex }) = heap.pop() {
+            if vertex == end {
+                let mut path = vec![end];
+                let mut current = end;
+                while let Some(&pred) = predecessors.get(&current) {
+                    path.push(pred);
+                    current = pred;
+                }
+                path.reverse();
+                return Some((path, cost));
+            }
+
+            if cost > distances[&vertex] {
+                continue;
+            }
+
+            if let Some(neighbors) = self.edges.get(&vertex) {
+                for &(neighbor, edge_cost) in neighbors {
+                    let new_cost = cost + edge_cost;
+                    if new_cost < distances[&neighbor] {
+                        distances.insert(neighbor, new_cost);
+                        predecessors.insert(neighbor, vertex);
+                        heap.push(Node { cost: new_cost, vertex: neighbor });
+                    }
+                }
+            }
+        }
+
+        None // No path found
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_simple_path() {
+        let mut graph = Graph::new();
+        graph.add_edge(0, 1, 4);
+        graph.add_edge(1, 2, 3);
+        graph.add_edge(2, 3, 2);
+
+        let result = graph.dijkstra(0, 3);
+        assert_eq!(result, Some((vec![0, 1, 2, 3], 9)));
+    }
+
+    #[test]
+    fn test_multiple_paths() {
+        let mut graph = Graph::new();
+        graph.add_edge(0, 1, 4);
+        graph.add_edge(0, 2, 1);
+        graph.add_edge(1, 3, 1);
+        graph.add_edge(2, 1, 2);
+        graph.add_edge(2, 3, 5);
+
+        let result = graph.dijkstra(0, 3);
+        assert_eq!(result, Some((vec![0, 2, 1, 3], 4)));
+    }
+
+    #[test]
+    fn test_no_path() {
+        let mut graph = Graph::new();
+        graph.add_edge(0, 1, 4);
+        graph.add_edge(1, 2, 3);
+        graph.add_edge(3, 4, 2);
+
+        let result = graph.dijkstra(0, 4);
+        assert_eq!(result, None);
+    }
+
+    #[test]
+    fn test_graph_with_cycle() {
+        let mut graph = Graph::new();
+        graph.add_edge(0, 1, 1);
+        graph.add_edge(1, 2, 2);
+        graph.add_edge(2, 3, 3);
+        graph.add_edge(3, 1, 1);
+        graph.add_edge(3, 4, 4);
+
+        let result = graph.dijkstra(0, 4);
+        assert_eq!(result, Some((vec![0, 1, 2, 3, 4], 10)));
+    }
+
+    #[test]
+    fn test_large_graph() {
+        let mut graph = Graph::new();
+        for i in 0..1000 {
+            graph.add_edge(i, i + 1, 1);
+        }
+        graph.add_edge(0, 1000, 999);
+
+        let result = graph.dijkstra(0, 1000);
+        assert_eq!(result, Some((vec![0, 1000], 999)));
+    }
+}