Dijkstra’s algorithm is a graph traversal algorithm that finds the shortest path between the source vertex and all other vertices in the graph. data structure Vertex: a struct that holds the vertex id. Edge: a struct that holds the vertex id of the start and end points, and the cost of the edge which must be a positive integer. Graph: a struct that holds the vertices and edges. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 use std::cmp::Ordering; #[derive(Debug, PartialEq, Eq, Clone, Hash)] pub struct Vertex { // `id`: A unique identifier for the vertex, represented as a String. id: String, } #[derive(Debug, PartialEq, Eq, Clone)] pub struct Edge { // `from`: The ID of the starting vertex of the edge. from: String, // `to`: The ID of the ending vertex of the edge. to: String, // `cost`: The weight or cost associated with traversing the edge. cost: u32, } #[derive(Debug, PartialEq, Eq)] pub struct Graph { // `vertices`: A vector of `Vertex` structs, representing all vertices in the graph. vertices: Vec<Vertex>, // `edges`: A vector of `Edge` structs, representing all edges in the graph. edges: Vec<Edge>, } #[derive(Clone, Eq, PartialEq)] struct Node { // `cost`: The current shortest distance from the source vertex to this vertex. cost: u32, // `vertex_id`: The ID of the vertex represented by this node. vertex_id: String, } // Implement `Ord` trait for `Node` to make it usable in `BinaryHeap`. impl Ord for Node { fn cmp(&self, other: &Self) -> Ordering { // Reverse the ordering of `cost` to make `BinaryHeap` behave as a min-heap. // `BinaryHeap` in Rust is a max-heap by default, so flipping the comparison results // in a min-heap behavior. other.cost.cmp(&self.cost) } } // Implement `PartialOrd` trait for `Node`. impl PartialOrd for Node { fn partial_cmp(&self, other: &Self) -> Option<Ordering> { Some(self.cmp(other)) } } Dijkstra algorithm lowest cost Initialize the distance from the source vertex to itself as 0. Push the source vertex into the priority queue with cost 0. Loop until the priority queue is empty. Pop the vertex with the smallest distance from the priority queue. If the current vertex is the destination, break the loop. If a shorter path to the current vertex has already been found, skip it. Iterate over all edges starting from the current vertex. Calculate the cost to the neighbor vertex through the current vertex. If a shorter path to the neighbor vertex is found, update the distance, and push it into the priority queue. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 use std::collections::{BinaryHeap, HashMap}; impl Graph { // Computes the lowest cost from src to dest using Dijkstra's algorithm. pub fn dijkstra_cost(&self, src: &str, dest: &str) -> Option<u32> { // `distances`: A `HashMap` to store the shortest distances from the source vertex to each vertex. let mut distances: HashMap<String, u32> = HashMap::new(); // `pq`: A `BinaryHeap` (priority queue) to efficiently select the vertex with the smallest distance. let mut pq: BinaryHeap<Node> = BinaryHeap::new(); // Initialize the distance from the source vertex to itself as 0. distances.insert(src.to_string(), 0); // Push the source vertex into the priority queue with cost 0. pq.push(Node { cost: 0, vertex_id: src.to_string(), }); // Loop until the priority queue is empty. while let Some(Node { cost, vertex_id }) = pq.pop() { // If the current vertex is the destination, return the cost. if vertex_id == dest { return Some(cost); } // If a shorter path to the current vertex has already been found, skip it. if cost > *distances.get(&vertex_id).unwrap_or(&u32::MAX) { continue; } // Iterate over all edges starting from the current vertex. for edge in self.edges.iter().filter(|e| e.from == vertex_id) { // Calculate the cost to the neighbor vertex through the current vertex. let next_cost = cost + edge.cost; // If a shorter path to the neighbor vertex is found, update the distance and push it into the priority queue. if next_cost < *distances.get(&edge.to).unwrap_or(&u32::MAX) { distances.insert(edge.to.clone(), next_cost); pq.push(Node { cost: next_cost, vertex_id: edge.to.clone(), }); } } } // If no path is found, return None. None } } shortest path Much the same as the lowest cost, but keep a previous HashMap to store the previous vertex in the shortest path to each vertex. ...
