From bc4f44e844742561661484491b8c763def5a5296 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jan=20Uhl=C3=ADk?= <jan@uhlik.me>
Date: Thu, 29 Mar 2018 21:01:03 +0200
Subject: [PATCH] Add A* algorithm.
---
alib2graph_algo/src/shortest_path/AStar.cpp | 174 +++++++++
alib2graph_algo/src/shortest_path/AStar.hpp | 400 ++++++++++++++++++++
2 files changed, 574 insertions(+)
create mode 100644 alib2graph_algo/src/shortest_path/AStar.cpp
create mode 100644 alib2graph_algo/src/shortest_path/AStar.hpp
diff --git a/alib2graph_algo/src/shortest_path/AStar.cpp b/alib2graph_algo/src/shortest_path/AStar.cpp
new file mode 100644
index 0000000000..5751bc1c59
--- /dev/null
+++ b/alib2graph_algo/src/shortest_path/AStar.cpp
@@ -0,0 +1,174 @@
+// Astar.cpp
+//
+// Created on: 29. 01. 2018
+// 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 "AStar.hpp"
+
+#include <registration/AlgoRegistration.hpp>
+
+namespace shortest_path {
+class AStarBidirectional {};
+}
+
+namespace {
+
+// ---------------------------------------------------------------------------------------------------------------------
+// uni-directional
+
+auto AStar1 = registration::AbstractRegister<shortest_path::AStar,
+ ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+ const graph::WeightedUndirectedGraph<> &,
+ const DefaultNodeType &,
+ const DefaultNodeType &,
+ std::function<DefaultWeightType(const DefaultNodeType &,
+ const DefaultNodeType &)> >(
+ shortest_path::AStar::findPathRegistration);
+
+auto AStar2 = registration::AbstractRegister<shortest_path::AStar,
+ ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+ const graph::WeightedUndirectedMultiGraph<> &,
+ const DefaultNodeType &,
+ const DefaultNodeType &,
+ std::function<DefaultWeightType(const DefaultNodeType &,
+ const DefaultNodeType &)> >(
+ shortest_path::AStar::findPathRegistration);
+
+auto AStar3 = registration::AbstractRegister<shortest_path::AStar,
+ ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+ const graph::WeightedDirectedGraph<> &,
+ const DefaultNodeType &,
+ const DefaultNodeType &,
+ std::function<DefaultWeightType(const DefaultNodeType &,
+ const DefaultNodeType &)> >(
+ shortest_path::AStar::findPathRegistration);
+
+auto AStar4 = registration::AbstractRegister<shortest_path::AStar,
+ ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+ const graph::WeightedDirectedMultiGraph<> &,
+ const DefaultNodeType &,
+ const DefaultNodeType &,
+ std::function<DefaultWeightType(const DefaultNodeType &,
+ const DefaultNodeType &)> >(
+ shortest_path::AStar::findPathRegistration);
+
+auto AStar5 = registration::AbstractRegister<shortest_path::AStar,
+ ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+ const graph::WeightedMixedGraph<> &,
+ const DefaultNodeType &,
+ const DefaultNodeType &,
+ std::function<DefaultWeightType(const DefaultNodeType &,
+ const DefaultNodeType &)> >(
+ shortest_path::AStar::findPathRegistration);
+
+auto AStar6 = registration::AbstractRegister<shortest_path::AStar,
+ ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+ const graph::WeightedMixedMultiGraph<> &,
+ const DefaultNodeType &,
+ const DefaultNodeType &,
+ std::function<DefaultWeightType(const DefaultNodeType &,
+ const DefaultNodeType &)> >(
+ shortest_path::AStar::findPathRegistration);
+
+auto AStarGrid1 = registration::AbstractRegister<shortest_path::AStar,
+ ext::pair<ext::vector<DefaultSquareGridNodeType>, DefaultWeightType>,
+ const grid::WeightedSquareGrid4<> &,
+ const DefaultSquareGridNodeType &,
+ const DefaultSquareGridNodeType &,
+ std::function<DefaultWeightType(const DefaultSquareGridNodeType &,
+ const DefaultSquareGridNodeType &)> >(
+ shortest_path::AStar::findPathRegistration);
+
+auto AStarGrid2 = registration::AbstractRegister<shortest_path::AStar,
+ ext::pair<ext::vector<DefaultSquareGridNodeType>, DefaultWeightType>,
+ const grid::WeightedSquareGrid8<> &,
+ const DefaultSquareGridNodeType &,
+ const DefaultSquareGridNodeType &,
+ std::function<DefaultWeightType(const DefaultSquareGridNodeType &,
+ const DefaultSquareGridNodeType &)> >(
+ shortest_path::AStar::findPathRegistration);
+
+// ---------------------------------------------------------------------------------------------------------------------
+// bidirectional
+
+auto AStarBidirectional1 = registration::AbstractRegister<shortest_path::AStarBidirectional,
+ ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+ const graph::WeightedUndirectedGraph<> &,
+ const DefaultNodeType &,
+ const DefaultNodeType &,
+ std::function<DefaultWeightType(const DefaultNodeType &,
+ const DefaultNodeType &)> >(
+ shortest_path::AStar::findPathBidirectionalRegistration);
+
+auto AStarBidirectional2 = registration::AbstractRegister<shortest_path::AStarBidirectional,
+ ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+ const graph::WeightedUndirectedMultiGraph<> &,
+ const DefaultNodeType &,
+ const DefaultNodeType &,
+ std::function<DefaultWeightType(const DefaultNodeType &,
+ const DefaultNodeType &)> >(
+ shortest_path::AStar::findPathBidirectionalRegistration);
+
+auto AStarBidirectional3 = registration::AbstractRegister<shortest_path::AStarBidirectional,
+ ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+ const graph::WeightedDirectedGraph<> &,
+ const DefaultNodeType &,
+ const DefaultNodeType &,
+ std::function<DefaultWeightType(const DefaultNodeType &,
+ const DefaultNodeType &)> >(
+ shortest_path::AStar::findPathBidirectionalRegistration);
+
+auto AStarBidirectional4 = registration::AbstractRegister<shortest_path::AStarBidirectional,
+ ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+ const graph::WeightedDirectedMultiGraph<> &,
+ const DefaultNodeType &,
+ const DefaultNodeType &,
+ std::function<DefaultWeightType(const DefaultNodeType &,
+ const DefaultNodeType &)> >(
+ shortest_path::AStar::findPathBidirectionalRegistration);
+
+auto AStarBidirectional5 = registration::AbstractRegister<shortest_path::AStarBidirectional,
+ ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+ const graph::WeightedMixedGraph<> &,
+ const DefaultNodeType &,
+ const DefaultNodeType &,
+ std::function<DefaultWeightType(const DefaultNodeType &,
+ const DefaultNodeType &)> >(
+ shortest_path::AStar::findPathBidirectionalRegistration);
+
+auto AStarBidirectional6 = registration::AbstractRegister<shortest_path::AStarBidirectional,
+ ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+ const graph::WeightedMixedMultiGraph<> &,
+ const DefaultNodeType &,
+ const DefaultNodeType &,
+ std::function<DefaultWeightType(const DefaultNodeType &,
+ const DefaultNodeType &)> >(
+ shortest_path::AStar::findPathBidirectionalRegistration);
+
+auto AStarGridBidirectional1 = registration::AbstractRegister<shortest_path::AStarBidirectional,
+ ext::pair<ext::vector<DefaultSquareGridNodeType>,
+ DefaultWeightType>,
+ const grid::WeightedSquareGrid4<> &,
+ const DefaultSquareGridNodeType &,
+ const DefaultSquareGridNodeType &,
+ std::function<DefaultWeightType(const DefaultSquareGridNodeType &,
+ const DefaultSquareGridNodeType &)> >(
+ shortest_path::AStar::findPathBidirectionalRegistration);
+
+auto AStarGridBidirectional2 = registration::AbstractRegister<shortest_path::AStarBidirectional,
+ ext::pair<ext::vector<DefaultSquareGridNodeType>,
+ DefaultWeightType>,
+ const grid::WeightedSquareGrid8<> &,
+ const DefaultSquareGridNodeType &,
+ const DefaultSquareGridNodeType &,
+ std::function<DefaultWeightType(const DefaultSquareGridNodeType &,
+ const DefaultSquareGridNodeType &)> >(
+ shortest_path::AStar::findPathBidirectionalRegistration);
+
+// ---------------------------------------------------------------------------------------------------------------------
+}
+
diff --git a/alib2graph_algo/src/shortest_path/AStar.hpp b/alib2graph_algo/src/shortest_path/AStar.hpp
new file mode 100644
index 0000000000..331fb5ee04
--- /dev/null
+++ b/alib2graph_algo/src/shortest_path/AStar.hpp
@@ -0,0 +1,400 @@
+// AStar.hpp
+//
+// Created on: 29. 1. 2018
+// 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_ASTAR_HPP
+#define ALIB2_ASTAR_HPP
+
+#include <alib/list>
+#include <alib/set>
+#include <queue>
+#include <alib/map>
+#include <alib/vector>
+#include <stdexcept>
+#include <functional>
+
+#include <common/ReconstructPath.hpp>
+#include <common/SupportFunction.hpp>
+
+namespace shortest_path {
+
+class AStar {
+// ---------------------------------------------------------------------------------------------------------------------
+
+ public:
+
+ /// Find the shortest path using AStar 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).
+ ///
+ /// The heuristic function must be admissible and monotone.
+ ///
+ /// \param graph to explore.
+ /// \param start initial node.
+ /// \param goal final node.
+ /// \param f_heuristic heuristic function which accept node and return edge_type::weight_type.
+ /// \param f_user function which is called for every opened 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 F1 = std::function<typename TGraph::edge_type::weight_type(const TNode &)>,
+ typename F2 = 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,
+ F1 f_heuristic,
+ F2 f_user = [](const TNode &,
+ const typename TGraph::edge_type::weight_type &) {});
+
+ template<
+ typename TGraph,
+ typename TNode,
+ typename F1 = std::function<typename TGraph::edge_type::weight_type(const TNode &, const TNode &)>
+ >
+ static
+ ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+ findPathRegistration(const TGraph &graph,
+ const TNode &start,
+ const TNode &goal,
+ F1 f_heuristic) {
+ return findPath(graph, start, goal, [&](const TNode &n) { return f_heuristic(goal, n); });
+ }
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+ /// Find the shortest path using AStar 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).
+ ///
+ /// The heuristic function must be admissible and monotone.
+ ///
+ /// \param graph to explore.
+ /// \param start initial node.
+ /// \param goal final node.
+ /// \param f_heuristic_forward front-to-end (node->goal) heuristic function which accept node and return edge_type::weight_type.
+ /// \param f_heuristic_backward front-to-end (node->start) heuristic function which accept node and return edge_type::weight_type.
+ /// \param f_user function which is called for every opened 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 F1 = std::function<typename TGraph::edge_type::weight_type(const TNode &)>,
+ typename F2 = std::function<typename TGraph::edge_type::weight_type(const TNode &)>,
+ typename F3 = 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,
+ F1 f_heuristic_forward,
+ F2 f_heuristic_backward,
+ F3 f_user = [](const TNode &,
+ const typename TGraph::edge_type::weight_type &) {});
+
+ template<
+ typename TGraph,
+ typename TNode,
+ typename F1 = std::function<typename TGraph::edge_type::weight_type(const TNode &, const TNode &)>
+ >
+ static
+ ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+ findPathBidirectionalRegistration(const TGraph &graph,
+ const TNode &start,
+ const TNode &goal,
+ F1 f_heuristic) {
+ return findPathBidirectional(graph, start, goal,
+ [&](const TNode &n) { return f_heuristic(goal, n); },
+ [&](const TNode &n) { return f_heuristic(start, n); });
+ }
+
+
+// =====================================================================================================================
+
+ private:
+
+ template<typename TNode, typename TWeight>
+ struct Data {
+ ext::set<ext::pair<TWeight, TNode>> queue; // priority queue
+ ext::map<TNode, TWeight> g; // G score
+ ext::map<TNode, TWeight> f; // F score
+ ext::map<TNode, TNode> p; // parents
+ };
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+ template<typename TGraph, typename TNode, typename F1, typename F2, typename F3>
+ static
+ ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+ impl(const TGraph &graph,
+ const TNode &start,
+ const TNode &goal,
+ F1 f_heuristic,
+ F2 f_user,
+ F3 f_stop);
+
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+ template<typename FSuccEdge, typename TNode, typename TWeight, typename F1, typename F2, typename F3, typename F4>
+ static bool relaxation(FSuccEdge successor_edges,
+ Data<TNode, TWeight> &data,
+ F1 f_heuristic,
+ F2 f_user,
+ F3 f_stop,
+ F4 f_update);
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+ template<typename TGraph, typename TNode, typename F1, typename F2, typename F3, typename F4>
+ static
+ ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+ implBidirectional(const TGraph &graph,
+ const TNode &start,
+ const TNode &goal,
+ F1 f_heuristic_forward,
+ F2 f_heuristic_backward,
+ F3 f_user,
+ F4 f_stop);
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+ template<typename TNode, typename TWeight, typename F>
+ inline static void init(AStar::Data<TNode, TWeight> &data, const TNode &start, F f_heuristic);
+
+// ---------------------------------------------------------------------------------------------------------------------
+};
+
+// =====================================================================================================================
+
+template<typename TGraph, typename TNode, typename F1, typename F2>
+ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+AStar::findPath(const TGraph &graph,
+ const TNode &start,
+ const TNode &goal,
+ F1 f_heuristic,
+ F2 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,
+ f_heuristic,
+ f_user,
+ [&goal](const TNode &n) -> bool { return goal == n; });
+}
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+template<typename TGraph, typename TNode, typename F1, typename F2, typename F3>
+ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+AStar::findPathBidirectional(const TGraph &graph,
+ const TNode &start,
+ const TNode &goal,
+ F1 f_heuristic_forward,
+ F2 f_heuristic_backward,
+ F3 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,
+ f_heuristic_forward,
+ f_heuristic_backward,
+ f_user,
+ [](const TNode &) -> bool { return false; });
+}
+
+// =====================================================================================================================
+
+template<typename TGraph, typename TNode, typename F1, typename F2, typename F3>
+ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+AStar::impl(const TGraph &graph,
+ const TNode &start,
+ const TNode &goal,
+ F1 f_heuristic,
+ F2 f_user,
+ F3 f_stop) {
+ using weight_type = typename TGraph::edge_type::weight_type;
+
+ Data<TNode, weight_type> data;
+
+ // Init search
+ init(data, start, f_heuristic);
+
+ while (!data.queue.empty()) {
+ bool stop = relaxation([&](const auto &node) -> auto { return graph.successorEdges(node); },
+ data,
+ f_heuristic,
+ f_user,
+ f_stop,
+ [](const TNode &) -> void {});
+
+ if (stop) {
+ break;
+ }
+ }
+
+ return common::ReconstructPath::reconstructWeightedPath(data.p, data.g, start, goal);
+}
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+template<typename FSuccEdge, typename TNode, typename TWeight, typename F1, typename F2, typename F3, typename F4>
+bool AStar::relaxation(FSuccEdge successor_edges,
+ Data<TNode, TWeight> &data,
+ F1 f_heuristic,
+ F2 f_user,
+ F3 f_stop,
+ F4 f_update) {
+ TNode n = data.queue.begin()->second;
+ data.queue.erase(data.queue.begin());
+
+ // Run user's function
+ f_user(n, data.g[n]);
+
+ // 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("AStar: 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_g = data.g.find(s);
+
+ // If not or the G score can be improve do relaxation
+ if (search_g == data.g.end() || data.g.at(s) > gscore) {
+ // Search if the node s is in OPEN
+ auto search_q = data.queue.find(ext::make_pair(data.f[s], s));
+ if (search_q != data.queue.end()) {
+ // Erase node from priority queue
+ data.queue.erase(search_q);
+ }
+
+ data.g[s] = gscore;
+ data.f[s] = gscore + f_heuristic(s);
+ data.p.insert_or_assign(s, n);
+ data.queue.insert(ext::make_pair(data.f[s], s));
+
+ f_update(s); // Update currently best path
+ }
+ }
+
+ return false;
+}
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+template<typename TGraph, typename TNode, typename F1, typename F2, typename F3, typename F4>
+ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+AStar::implBidirectional(const TGraph &graph,
+ const TNode &start,
+ const TNode &goal,
+ F1 f_heuristic_forward,
+ F2 f_heuristic_backward,
+ F3 f_user,
+ F4 f_stop) {
+ using TWeight = typename TGraph::edge_type::weight_type;
+
+ TWeight p = std::numeric_limits<TWeight>::max(); // Currently best path weight
+ ext::vector<TNode> intersection_nodes; // Last one is currently best intersection node
+ Data<TNode, TWeight> forward_data, backward_data;
+
+ // Init forward search
+ init(forward_data, start, f_heuristic_forward);
+ 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, f_heuristic_backward);
+ 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 (std::max(forward_data.queue.begin()->first, backward_data.queue.begin()->first) >= 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_heuristic_forward,
+ f_user,
+ f_stop,
+ f_forward_update);
+ } else {
+ // Backward search relaxationBidirectional
+ relaxation([&](const auto &node) -> auto { return graph.predecessorEdges(node); },
+ backward_data,
+ f_heuristic_backward,
+ f_user,
+ f_stop,
+ f_backward_update);
+ }
+ }
+
+ return ext::make_pair(ext::vector<TNode>(), p);
+}
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+template<typename TNode, typename TWeight, typename F>
+void AStar::init(AStar::Data<TNode, TWeight> &data, const TNode &start, F f_heuristic) {
+ data.g[start] = 0;
+ data.f[start] = data.g[start] + f_heuristic(start);
+ data.p.insert_or_assign(start, start);
+ data.queue.insert(ext::make_pair(data.f[start], start));
+}
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+} // namespace shortest_path
+#endif //ALIB2_ASTAR_HPP
--
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