dijkstra.h

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/* +------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)            |
   |                          http://www.mrpt.org/                          |
   |                                                                        |
   | Copyright (c) 2005-2018, Individual contributors, see AUTHORS file     |
   | See: http://www.mrpt.org/Authors - All rights reserved.                |
   | Released under BSD License. See details in http://www.mrpt.org/License |
   +------------------------------------------------------------------------+ */
#ifndef MRPT_DIJKSTRA_H
#define MRPT_DIJKSTRA_H
 
#include <mrpt/graphs/CDirectedGraph.h>
#include <mrpt/graphs/CDirectedTree.h>
#include <mrpt/containers/traits_map.h>
#include <mrpt/math/utils.h>
 
#include <limits>
#include <iostream>  // TODO - remove me
#include <vector>
#include <utility>
#include <exception>
#include <functional>
 
namespace mrpt::graphs
{
namespace detail
{
/**\brief Custom exception class that passes information in case an
 * unconnected graph is passed to a Dijkstra instance
 */
class NotConnectedGraph : public std::exception
{
   public:
    explicit NotConnectedGraph(
        const std::set<mrpt::graphs::TNodeID>& unconnected_nodeIDs,
        std::string err)
        : m_unconnected_nodeIDs(unconnected_nodeIDs), m_err(err + "\n\n")
    {
    }
 
    using std::exception::what;  // supress clang warning
    const char* what() { return m_err.c_str(); }
    ~NotConnectedGraph() throw() {}
    /**\brief Fill set with the nodeIDs Dijkstra algorithm could not reach
     * starting from the root node.
     */
    void getUnconnectedNodeIDs(
        std::set<mrpt::graphs::TNodeID>* set_nodeIDs) const
    {
        ASSERTMSG_(set_nodeIDs, "\nSet of nodes pointer is invalid\n");
 
        // fil the given set
        set_nodeIDs->clear();
        for (std::set<mrpt::graphs::TNodeID>::iterator it =
                 m_unconnected_nodeIDs.begin();
             it != m_unconnected_nodeIDs.end(); ++it)
        {
            set_nodeIDs->insert(*it);
        }
    }
 
   private:
    std::set<mrpt::graphs::TNodeID> m_unconnected_nodeIDs;
    std::string m_err;
};
}  // namespace detail
 
/** The Dijkstra algorithm for finding the shortest path between a given
 * source node in a (weighted) directed graph and all other nodes in the
 * form of a tree.
 *
 *  The constructor takes as input the graph (the set of directed edges)
 *  computes all the needed data, then successive calls to \a
 *  getShortestPathTo return the paths efficiently from the root.
 *
 *  The entire generated tree can be also retrieved with \a getTreeGraph.
 *
 *  Input graphs are represented by instances of (or classes derived from)
 *  mrpt::graphs::CDirectedGraph, and node's IDs are uint64_t values,
 *  although the type mrpt::graphs::TNodeID is also provided for clarity in
 *  the code.
 *
 *  The second template argument MAPS_IMPLEMENTATION allows choosing
 *  between a sparse std::map<> representation (using *
 *  mrpt::containers::map_traits_stdmap) for several intermediary and final
 *  results, and an alternative (using
 *  mrpt::containers::map_traits_map_as_vector as argument) dense
 *  implementation which is much faster, but can be only used if the
 *  TNodeID's start in 0 or a low value.
 *
 * See <a
 * href="http://www.mrpt.org/Example:Dijkstra_optimal_path_search_in_graphs"
 * > this page </a> for a complete example.
 *
 * \ingroup mrpt_graphs_grp
 */
template <
    class TYPE_GRAPH,
    class MAPS_IMPLEMENTATION = mrpt::containers::map_traits_stdmap>
class CDijkstra
{
   protected:
    /** Auxiliary struct for topological distances from root node */
    struct TDistance
    {
        double dist;
        inline TDistance() : dist(std::numeric_limits<double>::max()) {}
        inline TDistance(const double D) : dist(D) {}
        inline const TDistance& operator=(const double D)
        {
            dist = D;
            return *this;
        }
    };
 
    /** Auxiliary struct for backward paths */
    struct TPrevious
    {
        inline TPrevious() : id(INVALID_NODEID) {}
        TNodeID id;
    };
 
    // Cached input data:
    const TYPE_GRAPH& m_cached_graph;
    const TNodeID m_source_node_ID;
 
    // Private typedefs:
    /** A std::map (or a similar container according to MAPS_IMPLEMENTATION)
     * with all the neighbors of every node. */
    using list_all_neighbors_t =
        typename MAPS_IMPLEMENTATION::template map<TNodeID, std::set<TNodeID>>;
    using id2pairIDs_map_t =
        typename MAPS_IMPLEMENTATION::template map<TNodeID, TPairNodeIDs>;
    using id2dist_map_t =
        typename MAPS_IMPLEMENTATION::template map<TNodeID, TDistance>;
    using id2id_map_t =
        typename MAPS_IMPLEMENTATION::template map<TNodeID, TPrevious>;
 
    // Intermediary and final results:
    /** All the distances */
    id2dist_map_t m_distances;
    std::map<TNodeID, TDistance>
        m_distances_non_visited;  // Use a std::map here in all cases.
    id2id_map_t m_prev_node;
    id2pairIDs_map_t m_prev_arc;
    std::set<TNodeID> m_lstNode_IDs;
    list_all_neighbors_t m_allNeighbors;
 
   public:
    /** @name Useful typedefs
        @{ */
 
    /** The type of the graph, typically a mrpt::graphs::CDirectedGraph<> or any
     * other derived class */
    using graph_t = TYPE_GRAPH;
    /** The type of edge data in graph_t */
    using edge_t = typename graph_t::edge_t;
    /** A list of edges used to describe a path on the graph */
    using edge_list_t = std::list<TPairNodeIDs>;
 
    using functor_edge_weight_t = std::function<double(
        const graph_t& graph, const TNodeID id_from, const TNodeID id_to,
        const edge_t& edge)>;
 
    using functor_on_progress_t =
        std::function<void(const graph_t& graph, size_t visitedCount)>;
 
    /** @} */
 
    /** Constructor which takes the input graph and executes the entire
     * Dijkstra algorithm from the given root node ID.
     *
     *  The graph is given by the set of directed edges, stored in a
     *  mrpt::graphs::CDirectedGraph class.
     *
     *  If a function \a functor_edge_weight is provided, it will be used to
     *  compute the weight of edges.  Otherwise, all edges weight the unity.
     *
     *  After construction, call \a getShortestPathTo to get the shortest
     *  path to a node or \a getTreeGraph for the tree representation.
     *
     * \sa getShortestPathTo, getTreeGraph
     *
     * \exception std::exception If the source nodeID is not found in the
     * graph
     */
    CDijkstra(
        const graph_t& graph, const TNodeID source_node_ID,
        functor_edge_weight_t functor_edge_weight = functor_edge_weight_t(),
        functor_on_progress_t functor_on_progress = functor_on_progress_t())
        : m_cached_graph(graph), m_source_node_ID(source_node_ID)
    {
        /*
        1  function Dijkstra(G, w, s)
        2     for each vertex v in V[G]                        //
        Initializations
        3           m_distances[v] := infinity
        4           m_prev_node[v] := undefined
        5     m_distances[s] := 0
        6     S := empty set
        7     Q := V[G]
        8     while Q is not an empty set                      // The algorithm
        itself
        9           u := Extract_Min(Q)
        10           S := S union {u}
        11           for each edge (u,v) outgoing from u
        12                  if m_distances[u] + w(u,v) < m_distances[v]
        // Relax (u,v)
        13                        m_distances[v] := m_distances[u] + w(u,v)
        14                        m_prev_node[v] := u
        */
 
        // Make a list of all the nodes in the graph:
        graph.getAllNodes(m_lstNode_IDs);
        const size_t nNodes = m_lstNode_IDs.size();
 
        if (m_lstNode_IDs.find(source_node_ID) == m_lstNode_IDs.end())
        {
            THROW_EXCEPTION_FMT(
                "Cannot find the source node_ID=%lu in the graph",
                static_cast<unsigned long>(source_node_ID));
        }
 
        // Init:
        // m_distances: already initialized to infinity by default.
        // m_prev_node: idem
        // m_prev_arc: idem
        // m_visited: idem
        size_t visitedCount = 0;
        m_distances[source_node_ID] = 0;
        m_distances_non_visited[source_node_ID] = 0;
 
        // Precompute all neighbors of all the nodes in the given graph:
        graph.getAdjacencyMatrix(m_allNeighbors);
 
        using namespace std;
 
        TNodeID u;
        // as long as there are nodes not yet visited.
        do
        {  // The algorithm:
            // Find the nodeID with the minimum known distance so far
            // considered:
            double min_d = std::numeric_limits<double>::max();
            u = INVALID_NODEID;
 
            // No need to check if the min. distance node is not visited yet,
            // since we
            // keep two lists: m_distances_non_visited & m_distances
            for (typename std::map<TNodeID, TDistance>::const_iterator itDist =
                     m_distances_non_visited.begin();
                 itDist != m_distances_non_visited.end(); ++itDist)
            {
                // TODO - remove these
                // cout << "Current min distance: " << min_d << endl;
                // cout << "itDist->first: " << itDist->first << endl;
                // cout << "itDist->second (distance to this node): " <<
                // itDist->second.dist << endl;
 
                if (itDist->second.dist < min_d)
                {
                    u = itDist->first;
                    min_d = itDist->second.dist;
                    // cout << "updating u, min_d... " << endl;
                }
                // cout << "finished for." << endl;
            }
 
            // make sure we have found the next nodeID from the available
            // non-visited distances
            if (u == INVALID_NODEID)
            {
                std::set<TNodeID> nodeIDs_unconnected;
 
                // for all the nodes in the graph
                for (typename TYPE_GRAPH::global_poses_t::const_iterator n_it =
                         graph.nodes.begin();
                     n_it != graph.nodes.end(); ++n_it)
                {
                    // have I already visited this node in Dijkstra?
                    bool have_traversed = false;
                    for (typename id2dist_map_t::const_iterator d_it =
                             m_distances.begin();
                         d_it != m_distances.end(); ++d_it)
                    {
                        if (n_it->first == d_it->first)
                        {
                            have_traversed = true;
                            break;
                        }
                    }
 
                    if (!have_traversed)
                    {
                        nodeIDs_unconnected.insert(n_it->first);
                    }
                }
 
                std::string err_str =
                    mrpt::format("Graph is not fully connected!");
                throw mrpt::graphs::detail::NotConnectedGraph(
                    nodeIDs_unconnected, err_str);
            }
 
            // Update distance (for possible future reference...) and remove
            // this node from "non-visited":
            m_distances[u] = m_distances_non_visited[u];
            m_distances_non_visited.erase(u);
 
            visitedCount++;
 
            // Let the user know about our progress...
            if (functor_on_progress) functor_on_progress(graph, visitedCount);
 
            // For each arc from "u":
            const std::set<TNodeID>& neighborsOfU =
                m_allNeighbors[u];  // graph.getNeighborsOf(u,neighborsOfU);
            for (std::set<TNodeID>::const_iterator itNei = neighborsOfU.begin();
                 itNei != neighborsOfU.end(); ++itNei)
            {
                const TNodeID i = *itNei;
                if (i == u) continue;  // ignore self-loops...
 
                // the "edge_ui" may be searched here or a bit later, so the
                // "bool" var will tell us.
                typename graph_t::const_iterator edge_ui;
                bool edge_ui_reverse = false;
                bool edge_ui_found = false;
 
                // Get weight of edge u<->i
                double edge_ui_weight;
                if (!functor_edge_weight)
                    edge_ui_weight = 1.;
                else
                {  // edge may be i->u or u->i:
                    edge_ui = graph.edges.find(std::make_pair(u, i));
                    if (edge_ui == graph.edges.end())
                    {
                        edge_ui = graph.edges.find(std::make_pair(i, u));
                        edge_ui_reverse = true;
                    }
                    ASSERT_(edge_ui != graph.edges.end());
                    edge_ui_weight = functor_edge_weight(
                        graph, edge_ui->first.first, edge_ui->first.second,
                        edge_ui->second);
                    edge_ui_found = true;
                }
 
                if ((min_d + edge_ui_weight) < m_distances[i].dist)
                {  // the [] creates the entry if needed
                    // update m_distances, m_distances_non_visited
                    m_distances_non_visited[i].dist = min_d + edge_ui_weight;
                    m_distances[i].dist = min_d + edge_ui_weight;
 
                    m_prev_node[i].id = u;
                    // If still not done above, detect the direction of the arc
                    // now:
                    if (!edge_ui_found)
                    {
                        edge_ui = graph.edges.find(std::make_pair(u, i));
                        if (edge_ui == graph.edges.end())
                        {
                            edge_ui = graph.edges.find(std::make_pair(i, u));
                            edge_ui_reverse = true;
                        }
                        ASSERT_(edge_ui != graph.edges.end());
                    }
 
                    if (!edge_ui_reverse)
                        m_prev_arc[i] = std::make_pair(u, i);  // *u -> *i
                    else
                        m_prev_arc[i] = std::make_pair(i, u);  // *i -> *u
                }
            }
        } while (visitedCount < nNodes);
 
    }  // end Dijkstra
 
    /** @name Query Dijkstra results
      @{ */
 
    /** Return the distance from the root node to any other node using the
     * Dijkstra-generated tree
     *
     * \exception std::exception On unknown node ID
     */
    inline double getNodeDistanceToRoot(const TNodeID id) const
    {
        typename id2dist_map_t::const_iterator it = m_distances.find(id);
        if (it == m_distances.end())
            THROW_EXCEPTION(
                "Node was not found in the graph when running Dijkstra");
        return it->second.dist;
    }
 
    /** Return the set of all known node IDs (actually, a const ref to the
     * internal set object). */
    inline const std::set<TNodeID>& getListOfAllNodes() const
    {
        return m_lstNode_IDs;
    }
 
    /** Return the node ID of the tree root, as passed in the constructor */
    inline TNodeID getRootNodeID() const { return m_source_node_ID; }
    /** Return the adjacency matrix of the input graph, which is cached at
     * construction so if needed later just use this copy to avoid
     * recomputing it
     *
     * \sa  mrpt::graphs::CDirectedGraph::getAdjacencyMatrix
     * */
    inline const list_all_neighbors_t& getCachedAdjacencyMatrix() const
    {
        return m_allNeighbors;
    }
 
    /** Returns the shortest path between the source node passed in the
     * constructor and the given target node. The reconstructed path
     * contains a list of arcs (all of them exist in the graph with the given
     * direction), such as the the first edge starts at the origin passed in
     * the constructor, and the last one contains the given target.
     *
     * \note An empty list of edges is returned when target equals the source
     * node.
     *
     * \sa getTreeGraph
     */
    void getShortestPathTo(
        const TNodeID target_node_ID, edge_list_t& out_path) const
    {
        out_path.clear();
        if (target_node_ID == m_source_node_ID) return;
 
        TNodeID nod = target_node_ID;
        do
        {
            typename id2pairIDs_map_t::const_iterator it = m_prev_arc.find(nod);
            ASSERT_(it != m_prev_arc.end());
            out_path.push_front(it->second);
            nod = m_prev_node.find(nod)->second.id;
        } while (nod != m_source_node_ID);
 
    }  // end of getShortestPathTo
 
    /** Type for graph returned by \a getTreeGraph: a graph like the original
     * input graph, but with edge data being pointers to the original data
     * (to save copy time & memory)
     */
    using tree_graph_t = CDirectedTree<const edge_t*>;
 
    /** Returns a tree representation of the graph, as determined by the
     * Dijkstra shortest paths from the root node.
     * Note that the annotations on each edge in the tree are "const pointers"
     * to the original graph edge data, so
     * it's mandatory for the original input graph not to be deleted as long as
     * this tree is used.
     * \sa getShortestPathTo
     */
    void getTreeGraph(tree_graph_t& out_tree) const
    {
        using TreeEdgeInfo = typename tree_graph_t::TEdgeInfo;
 
        out_tree.clear();
        out_tree.root = m_source_node_ID;
        // For each saved arc in "m_prev_arc", recover the original data in the
        // input graph and save it to the output tree structure.
        for (typename id2pairIDs_map_t::const_iterator itArcs =
                 m_prev_arc.begin();
             itArcs != m_prev_arc.end(); ++itArcs)
        {
            const TNodeID id = itArcs->first;
            const TNodeID id_from = itArcs->second.first;
            const TNodeID id_to = itArcs->second.second;
 
            std::list<TreeEdgeInfo>& edges =
                out_tree.edges_to_children[id == id_from ? id_to : id_from];
            TreeEdgeInfo newEdge(id);
            newEdge.reverse = (id == id_from);  // true: root towards leafs.
            typename graph_t::edges_map_t::const_iterator itEdgeData =
                m_cached_graph.edges.find(std::make_pair(id_from, id_to));
            ASSERTMSG_(
                itEdgeData != m_cached_graph.edges.end(),
                format(
                    "Edge %u->%u is in Dijkstra paths but not in original "
                    "graph!",
                    static_cast<unsigned int>(id_from),
                    static_cast<unsigned int>(id_to)));
            newEdge.data = &itEdgeData->second;
            edges.push_back(newEdge);
        }
 
    }  // end getTreeGraph
 
    /** @} */
 
};  // end class
 
}
#endif