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594 lines
14 KiB
C++
594 lines
14 KiB
C++
/*
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* Graph.hpp, part of Grid
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*
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* Copyright (C) 2015 Antonin Portelli
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*
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* Grid is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* Grid is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with Grid. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef Hadrons_Graph_hpp_
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#define Hadrons_Graph_hpp_
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#include <Hadrons/Global.hpp>
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BEGIN_HADRONS_NAMESPACE
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/******************************************************************************
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* Oriented graph class *
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******************************************************************************/
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// I/O for edges
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template <typename T>
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std::ostream & operator<<(std::ostream &out, const std::pair<T, T> &e)
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{
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out << "\"" << e.first << "\" -> \"" << e.second << "\"";
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return out;
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}
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// main class
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template <typename T>
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class Graph
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{
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public:
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typedef std::pair<T, T> Edge;
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public:
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// constructor
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Graph(void) = default;
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// destructor
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virtual ~Graph(void) = default;
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// access
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void addVertex(const T &value);
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void addEdge(const Edge &e);
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void addEdge(const T &start, const T &end);
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void removeVertex(const T &value);
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void removeEdge(const Edge &e);
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void removeEdge(const T &start, const T &end);
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unsigned int size(void) const;
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// tests
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bool gotValue(const T &value) const;
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// graph topological manipulations
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std::vector<T> getAdjacentVertices(const T &value) const;
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std::vector<T> getChildren(const T &value) const;
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std::vector<T> getParents(const T &value) const;
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std::vector<T> getRoots(void) const;
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std::vector<Graph<T>> getConnectedComponents(void) const;
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std::vector<T> topoSort(void);
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std::vector<std::vector<T>> allTopoSort(void);
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// I/O
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friend std::ostream & operator<<(std::ostream &out, const Graph<T> &g)
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{
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out << "{";
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for (auto &e: g.edgeSet_)
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{
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out << e << ", ";
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}
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if (g.edgeSet_.size() != 0)
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{
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out << "\b\b";
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}
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out << "}";
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return out;
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}
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private:
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// vertex marking
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void mark(const T &value, const bool doMark = true);
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void markAll(const bool doMark = true);
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void unmark(const T &value);
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void unmarkAll(void);
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bool isMarked(const T &value) const;
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const T * getFirstMarked(const bool isMarked = true) const;
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const T * getFirstUnmarked(void) const;
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// prune marked/unmarked vertices
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void removeMarked(const bool isMarked = true);
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void removeUnmarked(void);
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// depth-first search marking
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void depthFirstSearch(void);
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void depthFirstSearch(const T &root);
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private:
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std::map<T, bool> isMarked_;
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std::set<Edge> edgeSet_;
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};
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// build depedency matrix from topological sorts
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template <typename T>
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std::map<T, std::map<T, bool>>
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makeDependencyMatrix(const std::vector<std::vector<T>> &topSort);
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/******************************************************************************
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* template implementation *
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******************************************************************************/
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// access //////////////////////////////////////////////////////////////////////
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template <typename T>
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void Graph<T>::addVertex(const T &value)
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{
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isMarked_[value] = false;
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}
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template <typename T>
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void Graph<T>::addEdge(const Edge &e)
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{
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addVertex(e.first);
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addVertex(e.second);
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edgeSet_.insert(e);
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}
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template <typename T>
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void Graph<T>::addEdge(const T &start, const T &end)
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{
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addEdge(Edge(start, end));
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}
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template <typename T>
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void Graph<T>::removeVertex(const T &value)
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{
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// remove vertex from the mark table
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auto vIt = isMarked_.find(value);
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if (vIt != isMarked_.end())
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{
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isMarked_.erase(vIt);
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}
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else
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{
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HADRON_ERROR("vertex " << value << " does not exists");
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}
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// remove all edges containing the vertex
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auto pred = [&value](const Edge &e)
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{
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return ((e.first == value) or (e.second == value));
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};
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auto eIt = find_if(edgeSet_.begin(), edgeSet_.end(), pred);
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while (eIt != edgeSet_.end())
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{
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edgeSet_.erase(eIt);
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eIt = find_if(edgeSet_.begin(), edgeSet_.end(), pred);
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}
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}
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template <typename T>
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void Graph<T>::removeEdge(const Edge &e)
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{
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auto eIt = edgeSet_.find(e);
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if (eIt != edgeSet_.end())
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{
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edgeSet_.erase(eIt);
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}
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else
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{
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HADRON_ERROR("edge " << e << " does not exists");
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}
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}
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template <typename T>
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void Graph<T>::removeEdge(const T &start, const T &end)
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{
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removeEdge(Edge(start, end));
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}
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template <typename T>
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unsigned int Graph<T>::size(void) const
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{
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return isMarked_.size();
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}
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// tests ///////////////////////////////////////////////////////////////////////
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template <typename T>
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bool Graph<T>::gotValue(const T &value) const
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{
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try
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{
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isMarked_.at(value);
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}
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catch (std::out_of_range &)
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{
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return false;
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}
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return true;
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}
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// vertex marking //////////////////////////////////////////////////////////////
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template <typename T>
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void Graph<T>::mark(const T &value, const bool doMark)
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{
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try
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{
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isMarked_.at(value) = doMark;
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}
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catch (std::out_of_range &)
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{
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HADRON_ERROR("vertex " << value << " does not exists");
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}
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}
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template <typename T>
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void Graph<T>::markAll(const bool doMark)
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{
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for (auto &v: isMarked_)
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{
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mark(v.first, doMark);
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}
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}
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template <typename T>
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void Graph<T>::unmark(const T &value)
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{
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mark(value, false);
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}
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template <typename T>
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void Graph<T>::unmarkAll(void)
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{
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markAll(false);
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}
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template <typename T>
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bool Graph<T>::isMarked(const T &value) const
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{
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try
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{
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return isMarked_.at(value);
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}
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catch (std::out_of_range &)
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{
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HADRON_ERROR("vertex " << value << " does not exists");
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return false;
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}
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}
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template <typename T>
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const T * Graph<T>::getFirstMarked(const bool isMarked) const
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{
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auto pred = [&isMarked](const std::pair<T, bool> &v)
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{
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return (v.second == isMarked);
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};
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auto vIt = std::find_if(isMarked_.begin(), isMarked_.end(), pred);
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if (vIt != isMarked_.end())
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{
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return &(vIt->first);
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}
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else
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{
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return nullptr;
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}
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}
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template <typename T>
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const T * Graph<T>::getFirstUnmarked(void) const
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{
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return getFirstMarked(false);
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}
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// prune marked/unmarked vertices //////////////////////////////////////////////
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template <typename T>
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void Graph<T>::removeMarked(const bool isMarked)
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{
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auto isMarkedCopy = isMarked_;
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for (auto &v: isMarkedCopy)
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{
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if (v.second == isMarked)
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{
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removeVertex(v.first);
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}
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}
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}
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template <typename T>
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void Graph<T>::removeUnmarked(void)
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{
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removeMarked(false);
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}
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// depth-first search marking //////////////////////////////////////////////////
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template <typename T>
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void Graph<T>::depthFirstSearch(void)
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{
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depthFirstSearch(isMarked_.begin()->first);
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}
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template <typename T>
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void Graph<T>::depthFirstSearch(const T &root)
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{
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std::vector<T> adjacentVertex;
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mark(root);
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adjacentVertex = getAdjacentVertices(root);
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for (auto &v: adjacentVertex)
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{
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if (!isMarked(v))
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{
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depthFirstSearch(v);
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}
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}
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}
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// graph topological manipulations /////////////////////////////////////////////
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template <typename T>
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std::vector<T> Graph<T>::getAdjacentVertices(const T &value) const
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{
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std::vector<T> adjacentVertex;
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auto pred = [&value](const Edge &e)
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{
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return ((e.first == value) or (e.second == value));
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};
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auto eIt = find_if(edgeSet_.begin(), edgeSet_.end(), pred);
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while (eIt != edgeSet_.end())
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{
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if (eIt->first == value)
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{
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adjacentVertex.push_back((*eIt).second);
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}
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else if (eIt->second == value)
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{
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adjacentVertex.push_back((*eIt).first);
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}
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eIt = find_if(++eIt, edgeSet_.end(), pred);
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}
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return adjacentVertex;
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}
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template <typename T>
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std::vector<T> Graph<T>::getChildren(const T &value) const
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{
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std::vector<T> child;
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auto pred = [&value](const Edge &e)
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{
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return (e.first == value);
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};
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auto eIt = find_if(edgeSet_.begin(), edgeSet_.end(), pred);
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while (eIt != edgeSet_.end())
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{
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child.push_back((*eIt).second);
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eIt = find_if(++eIt, edgeSet_.end(), pred);
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}
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return child;
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}
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template <typename T>
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std::vector<T> Graph<T>::getParents(const T &value) const
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{
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std::vector<T> parent;
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auto pred = [&value](const Edge &e)
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{
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return (e.second == value);
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};
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auto eIt = find_if(edgeSet_.begin(), edgeSet_.end(), pred);
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while (eIt != edgeSet_.end())
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{
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parent.push_back((*eIt).first);
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eIt = find_if(++eIt, edgeSet_.end(), pred);
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}
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return parent;
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}
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template <typename T>
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std::vector<T> Graph<T>::getRoots(void) const
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{
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std::vector<T> root;
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for (auto &v: isMarked_)
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{
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auto parent = getParents(v.first);
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if (parent.size() == 0)
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{
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root.push_back(v.first);
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}
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}
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return root;
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}
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template <typename T>
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std::vector<Graph<T>> Graph<T>::getConnectedComponents(void) const
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{
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std::vector<Graph<T>> res;
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Graph<T> copy(*this);
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while (copy.size() > 0)
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{
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copy.depthFirstSearch();
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res.push_back(copy);
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res.back().removeUnmarked();
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res.back().unmarkAll();
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copy.removeMarked();
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copy.unmarkAll();
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}
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return res;
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}
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// topological sort using Tarjan's algorithm
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template <typename T>
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std::vector<T> Graph<T>::topoSort(void)
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{
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std::stack<T> buf;
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std::vector<T> res;
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const T *vPt;
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std::map<T, bool> tmpMarked(isMarked_);
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// visit function
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std::function<void(const T &)> visit = [&](const T &v)
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{
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if (tmpMarked.at(v))
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{
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HADRON_ERROR("cannot topologically sort a cyclic graph");
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}
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if (!this->isMarked(v))
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{
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std::vector<T> child = this->getChildren(v);
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tmpMarked[v] = true;
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for (auto &c: child)
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{
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visit(c);
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}
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this->mark(v);
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tmpMarked[v] = false;
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buf.push(v);
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}
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};
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// reset temporary marks
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for (auto &v: tmpMarked)
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{
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tmpMarked.at(v.first) = false;
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}
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// loop on unmarked vertices
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vPt = getFirstUnmarked();
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while (vPt)
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{
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visit(*vPt);
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vPt = getFirstUnmarked();
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}
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unmarkAll();
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// create result vector
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while (!buf.empty())
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{
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res.push_back(buf.top());
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buf.pop();
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}
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return res;
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}
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// generate all possible topological sorts
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// Y. L. Varol & D. Rotem, Comput. J. 24(1), pp. 83–84, 1981
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// http://comjnl.oupjournals.org/cgi/doi/10.1093/comjnl/24.1.83
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template <typename T>
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std::vector<std::vector<T>> Graph<T>::allTopoSort(void)
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{
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std::vector<std::vector<T>> res;
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std::map<T, std::map<T, bool>> iMat;
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// create incidence matrix
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for (auto &v1: isMarked_)
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for (auto &v2: isMarked_)
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{
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iMat[v1.first][v2.first] = false;
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}
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for (auto &v: isMarked_)
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{
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auto cVec = getChildren(v.first);
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for (auto &c: cVec)
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{
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iMat[v.first][c] = true;
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}
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}
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// generate initial topological sort
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res.push_back(topoSort());
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// generate all other topological sorts by permutation
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std::vector<T> p = res[0];
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const unsigned int n = size();
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std::vector<unsigned int> loc(n);
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unsigned int i, k, k1;
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T obj_k, obj_k1;
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bool isFinal;
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for (unsigned int j = 0; j < n; ++j)
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{
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loc[j] = j;
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}
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i = 0;
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while (i < n-1)
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{
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k = loc[i];
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k1 = k + 1;
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obj_k = p[k];
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if (k1 >= n)
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{
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isFinal = true;
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obj_k1 = obj_k;
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}
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else
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{
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isFinal = false;
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obj_k1 = p[k1];
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}
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if (iMat[res[0][i]][obj_k1] or isFinal)
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{
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for (unsigned int l = k; l >= i + 1; --l)
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{
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p[l] = p[l-1];
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}
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p[i] = obj_k;
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loc[i] = i;
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i++;
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}
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else
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{
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p[k] = obj_k1;
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p[k1] = obj_k;
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loc[i] = k1;
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i = 0;
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res.push_back(p);
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}
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}
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return res;
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}
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// build depedency matrix from topological sorts ///////////////////////////////
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template <typename T>
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std::map<T, std::map<T, bool>>
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makeDependencyMatrix(const std::vector<std::vector<T>> &topSort)
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{
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std::map<T, std::map<T, bool>> m;
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const std::vector<T> &vList = topSort[0];
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for (auto &v1: vList)
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for (auto &v2: vList)
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{
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bool dep = true;
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for (auto &t: topSort)
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{
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auto i1 = std::find(t.begin(), t.end(), v1);
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auto i2 = std::find(t.begin(), t.end(), v2);
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dep = dep and (i1 - i2 > 0);
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if (!dep) break;
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}
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m[v1][v2] = dep;
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}
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return m;
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}
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END_HADRONS_NAMESPACE
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#endif // Hadrons_Graph_hpp_
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