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Dijkstra's algorithm
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| object Dijkstra { | |
| case class Edge[T](node: T, cost: Double) | |
| case class Path[T](nodes: List[T], cost: Double) | |
| type Graph[T] = Map[T, List[Edge[T]]] | |
| def dijkstra[T](graph: Graph[T], paths: List[Path[T]], dest: T, visited: Set[T]): Option[Path[T]] = { | |
| def unvisitedPaths(node: T, path: Path[T]): List[Path[T]] = | |
| graph(node).filterNot(edge => visited.contains(edge.node)) | |
| .map(edge => Path(edge.node +: path.nodes, path.cost + edge.cost)) | |
| for { | |
| path <- paths.headOption | |
| node <- path.nodes.headOption | |
| result <- if (node == dest) | |
| Some(Path(path.nodes.reverse, path.cost)) | |
| else | |
| dijkstra(graph, (unvisitedPaths(node, path) ++ paths.tail).sortBy(_.cost), dest, visited + node) | |
| } yield result | |
| } | |
| def main(args: Array[String]): Unit = { | |
| val graph: Graph[String] = Map( | |
| "a" -> List(Edge("b", 7.0), Edge("c", 9.0), Edge("f", 14.0)), | |
| "b" -> List(Edge("c", 10.0), Edge("d", 15.0)), | |
| "c" -> List(Edge("d", 11.0), Edge("f", 2.0)), | |
| "d" -> List(Edge("e", 6.0)), | |
| "e" -> List(Edge("f", 9.0)), | |
| "f" -> List.empty | |
| ) | |
| val start = Path(List("a"), 0d) | |
| val result1 = dijkstra(graph, List(start), "e", Set.empty) | |
| println(result1) // Some(Path(List(a, c, d, e),26.0)) | |
| val result2 = dijkstra(graph, List(start), "z", Set.empty) | |
| println(result2) // None | |
| } | |
| } |
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