Dijkstra.hpp

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// Copyright (c) 2017 Czech Technical University in Prague | Faculty of Information Technology. All rights reserved.
 
#pragma once
 
#include <list>
#include <alib/set>
#include <alib/map>
#include <queue>
#include <stdexcept>
#include <functional>
 
#include <common/ReconstructPath.hpp>
#include <common/SupportFunction.hpp>
 
namespace graph {
 
namespace shortest_path {
 
class Dijkstra {
// ---------------------------------------------------------------------------------------------------------------------
 
 public:
 
  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; });
 
// ---------------------------------------------------------------------------------------------------------------------
 
  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);
  }
 
// ---------------------------------------------------------------------------------------------------------------------
 
  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
      if (search_d != data.g.end()) {
        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;
  Data<TNode, weight_type> 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
 
} // namespace graph