Add Dijkstra algorithm.

alib2graph_algo/src/shortest_path/Dijkstra.cpp

+// Dijkstra.cpp
+//
+//     Created on: 18. 12. 2017
+//         Author: Jan Uhlik
+//    Modified by:
+//
+// Copyright (c) 2017 Czech Technical University in Prague | Faculty of Information Technology. All rights reserved.
+// Git repository: https://gitlab.fit.cvut.cz/algorithms-library-toolkit/automata-library
+
+#include "Dijkstra.hpp"
+
+#include <registration/AlgoRegistration.hpp>
+
+namespace shortest_path {
+class DijkstraBidirectional {};
+}
+
+namespace {
+
+// ---------------------------------------------------------------------------------------------------------------------
+// uni-directional
+
+auto Dijkstra1 = registration::AbstractRegister<shortest_path::Dijkstra,
+                                                ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+                                                const graph::WeightedUndirectedGraph<> &,
+                                                const DefaultNodeType &,
+                                                const DefaultNodeType &>(shortest_path::Dijkstra::findPathRegistration);
+
+auto Dijkstra2 = registration::AbstractRegister<shortest_path::Dijkstra,
+                                                ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+                                                const graph::WeightedUndirectedMultiGraph<> &,
+                                                const DefaultNodeType &,
+                                                const DefaultNodeType &>(shortest_path::Dijkstra::findPathRegistration);
+
+auto Dijkstra3 = registration::AbstractRegister<shortest_path::Dijkstra,
+                                                ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+                                                const graph::WeightedDirectedGraph<> &,
+                                                const DefaultNodeType &,
+                                                const DefaultNodeType &>(shortest_path::Dijkstra::findPathRegistration);
+
+auto Dijkstra4 = registration::AbstractRegister<shortest_path::Dijkstra,
+                                                ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+                                                const graph::WeightedDirectedMultiGraph<> &,
+                                                const DefaultNodeType &,
+                                                const DefaultNodeType &>(shortest_path::Dijkstra::findPathRegistration);
+
+auto Dijkstra5 = registration::AbstractRegister<shortest_path::Dijkstra,
+                                                ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+                                                const graph::WeightedMixedGraph<> &,
+                                                const DefaultNodeType &,
+                                                const DefaultNodeType &>(shortest_path::Dijkstra::findPathRegistration);
+
+auto Dijkstra6 = registration::AbstractRegister<shortest_path::Dijkstra,
+                                                ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+                                                const graph::WeightedMixedMultiGraph<> &,
+                                                const DefaultNodeType &,
+                                                const DefaultNodeType &>(shortest_path::Dijkstra::findPathRegistration);
+
+auto DijkstraGrid1 = registration::AbstractRegister<shortest_path::Dijkstra,
+                                                    ext::pair<ext::vector<DefaultSquareGridNodeType>,
+                                                              DefaultWeightType>,
+                                                    const grid::WeightedSquareGrid4<> &,
+                                                    const DefaultSquareGridNodeType &,
+                                                    const DefaultSquareGridNodeType &>(shortest_path::Dijkstra::findPathRegistration);
+
+auto DijkstraGrid2 = registration::AbstractRegister<shortest_path::Dijkstra,
+                                                    ext::pair<ext::vector<DefaultSquareGridNodeType>,
+                                                              DefaultWeightType>,
+                                                    const grid::WeightedSquareGrid8<> &,
+                                                    const DefaultSquareGridNodeType &,
+                                                    const DefaultSquareGridNodeType &>(shortest_path::Dijkstra::findPathRegistration);
+
+// ---------------------------------------------------------------------------------------------------------------------
+// bidirectional
+
+
+auto DijkstraBidirectional1 = registration::AbstractRegister<shortest_path::DijkstraBidirectional,
+                                                             ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+                                                             const graph::WeightedUndirectedGraph<> &,
+                                                             const DefaultNodeType &,
+                                                             const DefaultNodeType &>(shortest_path::Dijkstra::findPathBidirectionalRegistration);
+
+auto DijkstraBidirectional2 = registration::AbstractRegister<shortest_path::DijkstraBidirectional,
+                                                             ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+                                                             const graph::WeightedUndirectedMultiGraph<> &,
+                                                             const DefaultNodeType &,
+                                                             const DefaultNodeType &>(shortest_path::Dijkstra::findPathBidirectionalRegistration);
+
+auto DijkstraBidirectional3 = registration::AbstractRegister<shortest_path::DijkstraBidirectional,
+                                                             ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+                                                             const graph::WeightedDirectedGraph<> &,
+                                                             const DefaultNodeType &,
+                                                             const DefaultNodeType &>(shortest_path::Dijkstra::findPathBidirectionalRegistration);
+
+auto DijkstraBidirectional4 = registration::AbstractRegister<shortest_path::DijkstraBidirectional,
+                                                             ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+                                                             const graph::WeightedDirectedMultiGraph<> &,
+                                                             const DefaultNodeType &,
+                                                             const DefaultNodeType &>(shortest_path::Dijkstra::findPathBidirectionalRegistration);
+
+auto DijkstraBidirectional5 = registration::AbstractRegister<shortest_path::DijkstraBidirectional,
+                                                             ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+                                                             const graph::WeightedMixedGraph<> &,
+                                                             const DefaultNodeType &,
+                                                             const DefaultNodeType &>(shortest_path::Dijkstra::findPathBidirectionalRegistration);
+
+auto DijkstraBidirectional6 = registration::AbstractRegister<shortest_path::DijkstraBidirectional,
+                                                             ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+                                                             const graph::WeightedMixedMultiGraph<> &,
+                                                             const DefaultNodeType &,
+                                                             const DefaultNodeType &>(shortest_path::Dijkstra::findPathBidirectionalRegistration);
+
+auto DijkstraGridBidirectional1 = registration::AbstractRegister<shortest_path::DijkstraBidirectional,
+                                                                 ext::pair<ext::vector<DefaultSquareGridNodeType>,
+                                                                           DefaultWeightType>,
+                                                                 const grid::WeightedSquareGrid4<> &,
+                                                                 const DefaultSquareGridNodeType &,
+                                                                 const DefaultSquareGridNodeType &>(shortest_path::Dijkstra::findPathBidirectionalRegistration);
+
+auto DijkstraGridbidirectional2 = registration::AbstractRegister<shortest_path::DijkstraBidirectional,
+                                                                 ext::pair<ext::vector<DefaultSquareGridNodeType>,
+                                                                           DefaultWeightType>,
+                                                                 const grid::WeightedSquareGrid8<> &,
+                                                                 const DefaultSquareGridNodeType &,
+                                                                 const DefaultSquareGridNodeType &>(shortest_path::Dijkstra::findPathBidirectionalRegistration);
+
+// ---------------------------------------------------------------------------------------------------------------------
+}

alib2graph_algo/src/shortest_path/Dijkstra.hpp

+// Dijkstra.hpp
+//
+//     Created on: 18. 12. 2017
+//         Author: Jan Uhlik
+//    Modified by:
+//
+// Copyright (c) 2017 Czech Technical University in Prague | Faculty of Information Technology. All rights reserved.
+// Git repository: https://gitlab.fit.cvut.cz/algorithms-library-toolkit/automata-library
+
+#ifndef ALIB2_DIJKSTRA_HPP
+#define ALIB2_DIJKSTRA_HPP
+
+#include <list>
+#include <alib/set>
+#include <alib/map>
+#include <queue>
+#include <stdexcept>
+#include <functional>
+
+#include <common/ReconstructPath.hpp>
+#include <common/SupportFunction.hpp>
+
+namespace shortest_path {
+
+class Dijkstra {
+// ---------------------------------------------------------------------------------------------------------------------
+
+ public:
+
+  /// Run Dijkstra algorithm from the \p start node in the \p graph.
+  ///
+  /// Whenever node is opened, \p f_user is called with two parameters (the opened node and value of currently shortest path).
+  /// If return of \p f_user is true, then the algorithm is stopped.
+  ///
+  /// \param graph to explore.
+  /// \param start initial node.
+  /// \param f_user function which is called for every opened node with value of currently shortest path.
+  ///
+  /// \note TEdge of \p graph must follow graph::edge::WeightedEdge interface.
+  /// \sa graph::edge_type::WeightedEdge.
+  ///
+  /// \throws std::out_of_range if \p graph contains an edge with a negative weight.
+  ///
+  template<
+      typename TGraph,
+      typename TNode,
+      typename F = std::function<bool(const TNode &,
+                                      const typename TGraph::edge_type::weight_type &)>>
+  static
+  void
+  run(const TGraph &graph,
+      const TNode &start,
+      F f_user = [](const TNode &,
+                    const typename TGraph::edge_type::weight_type &) -> bool { return false; });
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+  /// Find the shortest path using Dijkstra algorithm from the \p start node to the \p goal node in the \p graph.
+  ///
+  /// Whenever node is opened, \p f_user is called with two parameters (the opened node and value of currently shortest path).
+  ///
+  /// \param graph to explore.
+  /// \param start initial node.
+  /// \param goal final node.
+  /// \param f_user function which is called for every open node with value of currently shortest path.
+  ///
+  /// \returns pair where first := shortest path := distance of path, if there is no such path vector is empty and distance std::numeric_limits<edge_type:weight_type>::max().
+  ///
+  /// \note TEdge of \p graph must follow graph::edge::WeightedEdge interface.
+  /// \sa graph::edge_type::WeightedEdge.
+  ///
+  /// \throws std::out_of_range if \p graph contains an edge with a negative weight.
+  ///
+  template<
+      typename TGraph,
+      typename TNode,
+      typename F = std::function<void(const TNode &,
+                                      const typename TGraph::edge_type::weight_type &)>>
+  static
+  ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+  findPath(const TGraph &graph,
+           const TNode &start,
+           const TNode &goal,
+           F f_user = [](const TNode &,
+                         const typename TGraph::edge_type::weight_type &) {});
+
+  template<typename TGraph, typename TNode>
+  static
+  ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+  findPathRegistration(const TGraph &graph,
+                       const TNode &start,
+                       const TNode &goal) {
+    return findPath(graph, start, goal);
+  }
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+  /// Find the shortest path using Dijkstra algorithm from the \p start node to the \p goal node in the \p graph.
+  /// This algorithm is run in both direction, from \p start and also from \p goal.
+  ///
+  /// Whenever node is opened, \p f_user is called with two parameters (the opened node and value of currently shortest path).
+  ///
+  /// \param graph to explore.
+  /// \param start initial node.
+  /// \param goal final node.
+  /// \param f_user function which is called for every open node with value of currently shortest path.
+  ///
+  /// \returns pair where first := shortest path := distance of path, if there is no such path vector is empty and distance std::numeric_limits<edge_type:weight_type>::max().
+  ///
+  /// \note TEdge of \p graph must follow graph::edge::WeightedEdge interface.
+  /// \sa graph::edge_type::WeightedEdge.
+  ///
+  /// \throws std::out_of_range if \p graph contains an edge with a negative weight.
+  ///
+  template<typename TGraph,
+      typename TNode,
+      typename F = std::function<void(const TNode &,
+                                      const typename TGraph::edge_type::weight_type &)>>
+  static
+  ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+  findPathBidirectional(const TGraph &graph,
+                        const TNode &start,
+                        const TNode &goal,
+                        F f_user = [](const TNode &,
+                                      const typename TGraph::edge_type::weight_type &) {});
+
+  template<typename TGraph, typename TNode>
+  static
+  ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+  findPathBidirectionalRegistration(const TGraph &graph,
+                                    const TNode &start,
+                                    const TNode &goal) {
+    return findPathBidirectional(graph, start, goal);
+  }
+
+
+// =====================================================================================================================
+
+ private:
+
+  template<typename TNode, typename TWeight>
+  struct Data {
+    ext::set<ext::pair<TWeight, TNode>> queue; // priority queue
+    ext::map<TNode, TWeight> g; // distances (aka G score)
+    ext::map<TNode, TNode> p; // parents
+  };
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+  template<typename TGraph, typename TNode, typename F1, typename F2>
+  static
+  ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+  impl(const TGraph &graph,
+       const TNode &start,
+       const TNode &goal,
+       F1 f_user,
+       F2 f_stop);
+
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+  template<typename FEdges, typename TNode, typename TWeight, typename F1, typename F2, typename F3>
+  static bool relaxation(FEdges successor_edges,
+                         Data<TNode, TWeight> &data,
+                         F1 f_user,
+                         F2 f_stop,
+                         F3 f_update);
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+  template<typename TGraph, typename TNode, typename F1, typename F2>
+  static
+  ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+  implBidirectional(const TGraph &graph,
+                    const TNode &start,
+                    const TNode &goal,
+                    F1 f_user,
+                    F2 f_stop);
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+  template<typename TNode, typename TWeight>
+  inline static void init(Dijkstra::Data<TNode, TWeight> &data, const TNode &start);
+
+
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+};
+
+// =====================================================================================================================
+
+template<typename TGraph, typename TNode, typename F>
+void Dijkstra::run(const TGraph &graph, const TNode &start, F f_user) {
+  // goal -> start: in order to avoid call constructor
+  impl(graph, start, start, f_user, [](const TNode &) -> bool { return false; });
+}
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+template<typename TGraph, typename TNode, typename F>
+ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+Dijkstra::findPath(const TGraph &graph,
+                   const TNode &start,
+                   const TNode &goal,
+                   F f_user) {
+  // We need to change user function to return false for every node in order to have only one relaxation function
+  return impl(graph, start, goal,
+              [&](const TNode &n, const typename TGraph::edge_type::weight_type &w) -> bool {
+                f_user(n, w);
+                return false;
+              }, [&goal](const TNode &n) -> bool { return goal == n; });
+}
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+template<typename TGraph, typename TNode, typename F>
+ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+Dijkstra::findPathBidirectional(const TGraph &graph,
+                                const TNode &start,
+                                const TNode &goal,
+                                F f_user) {
+  // We need to change user function to return false for every node in order to have only one relaxation function
+  return implBidirectional(graph, start, goal,
+                           [&](const TNode &n, const typename TGraph::edge_type::weight_type &w) -> bool {
+                             f_user(n, w);
+                             return false;
+                           },
+                           [](const TNode &) -> bool { return false; });
+}
+
+// =====================================================================================================================
+
+template<typename TGraph, typename TNode, typename F1, typename F2>
+ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+Dijkstra::impl(const TGraph &graph,
+               const TNode &start,
+               const TNode &goal,
+               F1 f_user,
+               F2 f_stop) {
+  using weight_type = typename TGraph::edge_type::weight_type;
+
+  Data<TNode, weight_type> data;
+
+  // Init search
+  init(data, start);
+
+  while (!data.queue.empty()) {
+    bool stop = relaxation([&](const auto &node) -> auto { return graph.successorEdges(node); },
+                           data,
+                           f_user,
+                           f_stop,
+                           [](const TNode &) -> void {});
+
+    if (stop) {
+      break;
+    }
+  }
+
+  return common::ReconstructPath::reconstructWeightedPath(data.p, data.g, start, goal);
+}
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+template<typename FEdges, typename TNode, typename TWeight, typename F1, typename F2, typename F3>
+bool Dijkstra::relaxation(FEdges successor_edges,
+                          Data<TNode, TWeight> &data,
+                          F1 f_user,
+                          F2 f_stop,
+                          F3 f_update) {
+  TNode n = data.queue.begin()->second;
+  data.queue.erase(data.queue.begin());
+
+  // Run user's function
+  if (f_user(n, data.g[n])) {
+    return true;
+  }
+
+  // Stop if reach the goal
+  if (f_stop(n)) {
+    return true;
+  }
+
+  for (const auto &s_edge: successor_edges(n)) {
+    const TNode &s = common::SupportFunction::other(s_edge, n); // successor
+
+    // Check for negative edge
+    if (s_edge.weight() < 0) {
+      throw std::out_of_range("Dijkstra: Detect negative weight on edge in graph.");
+    }
+
+    // Calculate new G score
+    TWeight gscore = data.g.at(n) + s_edge.weight();
+
+    // Search if the node s was already visited
+    auto search_d = data.g.find(s);
+
+    // If not or the distance can be improve do relaxation
+    if (search_d == data.g.end() || search_d->second > gscore) {
+      // Search if the node s is in OPEN
+      auto search_q = data.queue.find(ext::make_pair(search_d->second, s));
+      if (search_q != data.queue.end()) {
+        // Erase node from priority queue
+        data.queue.erase(search_q);
+      }
+
+      data.g[s] = gscore;
+      data.p.insert_or_assign(s, n);
+      data.queue.insert(ext::make_pair(data.g[s], s));
+
+      f_update(s); // Update currently best path
+    }
+  }
+
+  return false;
+}
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+template<typename TGraph, typename TNode, typename F1, typename F2>
+ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+Dijkstra::implBidirectional(const TGraph &graph,
+                            const TNode &start,
+                            const TNode &goal,
+                            F1 f_user,
+                            F2 f_stop) {
+  using weight_type = typename TGraph::edge_type::weight_type;
+
+  // Check for negative edge
+  weight_type eps = common::SupportFunction::getMinEdgeValue(graph); // Smallest value of the weight in graph
+
+  weight_type p = std::numeric_limits<weight_type>::max(); // Currently best path weight
+  ext::vector<TNode> intersection_nodes; // Last one is currently best intersection node
+  Data<TNode, weight_type> forward_data, backward_data;
+
+  // Init forward search
+  init(forward_data, start);
+  auto f_forward_update = [&](const auto &s) -> void {
+    if (backward_data.g.find(s) != backward_data.g.end()) {
+      if (forward_data.g.at(s) + backward_data.g.at(s) < p) {
+        p = forward_data.g.at(s) + backward_data.g.at(s);
+        intersection_nodes.push_back(s);
+      }
+    }
+  };
+
+  // Init backward search
+  init(backward_data, goal);
+  auto f_backward_update = [&](const auto &s) -> void {
+    if (forward_data.g.find(s) != forward_data.g.end()) {
+      if (backward_data.g.at(s) + forward_data.g.at(s) < p) {
+        p = backward_data.g.at(s) + forward_data.g.at(s);
+        intersection_nodes.push_back(s);
+      }
+    }
+  };
+
+  while (!forward_data.queue.empty() && !backward_data.queue.empty()) {
+    if (forward_data.queue.begin()->first + backward_data.queue.begin()->first + eps >= p) {
+      return common::ReconstructPath::reconstructWeightedPath(forward_data.p,
+                                                              backward_data.p,
+                                                              forward_data.g,
+                                                              backward_data.g,
+                                                              start,
+                                                              goal,
+                                                              intersection_nodes.back());
+    }
+
+    // Expand the lower value
+    if (forward_data.queue.begin()->first < backward_data.queue.begin()->first) {
+      // Forward search relaxationBidirectional
+      relaxation([&](const auto &node) -> auto { return graph.successorEdges(node); },
+                 forward_data,
+                 f_user,
+                 f_stop,
+                 f_forward_update);
+    } else {
+      // Backward search relaxationBidirectional
+      relaxation([&](const auto &node) -> auto { return graph.predecessorEdges(node); },
+                 backward_data,
+                 f_user,
+                 f_stop,
+                 f_backward_update);
+    }
+  }
+
+  return ext::make_pair(ext::vector<TNode>(), p);
+
+}
+// ---------------------------------------------------------------------------------------------------------------------
+
+template<typename TNode, typename TWeight>
+void Dijkstra::init(Dijkstra::Data<TNode, TWeight> &data, const TNode &start) {
+  data.g[start] = 0;
+  data.p.insert_or_assign(start, start);
+  data.queue.insert(ext::make_pair(data.g[start], start));
+}
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+} // namespace shortest_path
+#endif //ALIB2_DIJKSTRA_HPP