404 lines
13 KiB
C++
404 lines
13 KiB
C++
/**
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*
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* Copyright (c) 2010 Matthias Walter (xammy@xammy.homelinux.net)
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*
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* Authors: Matthias Walter
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*
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* Distributed under the Boost Software License, Version 1.0. (See
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* accompanying file LICENSE_1_0.txt or copy at
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* http://www.boost.org/LICENSE_1_0.txt)
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*
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*/
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#ifndef BOOST_GRAPH_BIPARTITE_HPP
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#define BOOST_GRAPH_BIPARTITE_HPP
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#include <utility>
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#include <vector>
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#include <exception>
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#include <boost/graph/properties.hpp>
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#include <boost/graph/adjacency_list.hpp>
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#include <boost/graph/depth_first_search.hpp>
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#include <boost/graph/one_bit_color_map.hpp>
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namespace boost
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{
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namespace detail
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{
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/**
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* The bipartite_visitor_error is thrown if an edge cannot be colored.
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* The witnesses are the edges incident vertices.
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*/
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template < typename Vertex >
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struct BOOST_SYMBOL_VISIBLE bipartite_visitor_error : std::exception
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{
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std::pair< Vertex, Vertex > witnesses;
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bipartite_visitor_error(Vertex a, Vertex b) : witnesses(a, b) {}
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const char* what() const throw() { return "Graph is not bipartite."; }
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};
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/**
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* Functor which colors edges to be non-monochromatic.
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*/
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template < typename PartitionMap > struct bipartition_colorize
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{
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typedef on_tree_edge event_filter;
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bipartition_colorize(PartitionMap partition_map)
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: partition_map_(partition_map)
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{
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}
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template < typename Edge, typename Graph >
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void operator()(Edge e, const Graph& g)
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{
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typedef typename graph_traits< Graph >::vertex_descriptor
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vertex_descriptor_t;
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typedef color_traits<
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typename property_traits< PartitionMap >::value_type >
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color_traits;
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vertex_descriptor_t source_vertex = source(e, g);
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vertex_descriptor_t target_vertex = target(e, g);
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if (get(partition_map_, source_vertex) == color_traits::white())
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put(partition_map_, target_vertex, color_traits::black());
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else
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put(partition_map_, target_vertex, color_traits::white());
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}
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private:
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PartitionMap partition_map_;
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};
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/**
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* Creates a bipartition_colorize functor which colors edges
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* to be non-monochromatic.
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*
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* @param partition_map Color map for the bipartition
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* @return The functor.
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*/
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template < typename PartitionMap >
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inline bipartition_colorize< PartitionMap > colorize_bipartition(
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PartitionMap partition_map)
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{
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return bipartition_colorize< PartitionMap >(partition_map);
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}
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/**
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* Functor which tests an edge to be monochromatic.
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*/
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template < typename PartitionMap > struct bipartition_check
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{
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typedef on_back_edge event_filter;
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bipartition_check(PartitionMap partition_map)
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: partition_map_(partition_map)
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{
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}
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template < typename Edge, typename Graph >
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void operator()(Edge e, const Graph& g)
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{
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typedef typename graph_traits< Graph >::vertex_descriptor
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vertex_descriptor_t;
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vertex_descriptor_t source_vertex = source(e, g);
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vertex_descriptor_t target_vertex = target(e, g);
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if (get(partition_map_, source_vertex)
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== get(partition_map_, target_vertex))
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throw bipartite_visitor_error< vertex_descriptor_t >(
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source_vertex, target_vertex);
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}
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private:
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PartitionMap partition_map_;
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};
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/**
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* Creates a bipartition_check functor which raises an error if a
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* monochromatic edge is found.
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*
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* @param partition_map The map for a bipartition.
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* @return The functor.
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*/
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template < typename PartitionMap >
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inline bipartition_check< PartitionMap > check_bipartition(
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PartitionMap partition_map)
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{
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return bipartition_check< PartitionMap >(partition_map);
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}
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/**
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* Find the beginning of a common suffix of two sequences
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*
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* @param sequence1 Pair of bidirectional iterators defining the first
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* sequence.
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* @param sequence2 Pair of bidirectional iterators defining the second
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* sequence.
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* @return Pair of iterators pointing to the beginning of the common suffix.
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*/
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template < typename BiDirectionalIterator1,
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typename BiDirectionalIterator2 >
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inline std::pair< BiDirectionalIterator1, BiDirectionalIterator2 >
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reverse_mismatch(
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std::pair< BiDirectionalIterator1, BiDirectionalIterator1 > sequence1,
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std::pair< BiDirectionalIterator2, BiDirectionalIterator2 > sequence2)
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{
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if (sequence1.first == sequence1.second
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|| sequence2.first == sequence2.second)
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return std::make_pair(sequence1.first, sequence2.first);
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BiDirectionalIterator1 iter1 = sequence1.second;
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BiDirectionalIterator2 iter2 = sequence2.second;
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while (true)
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{
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--iter1;
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--iter2;
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if (*iter1 != *iter2)
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{
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++iter1;
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++iter2;
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break;
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}
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if (iter1 == sequence1.first)
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break;
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if (iter2 == sequence2.first)
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break;
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}
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return std::make_pair(iter1, iter2);
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}
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}
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/**
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* Checks a given graph for bipartiteness and fills the given color map with
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* white and black according to the bipartition. If the graph is not
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* bipartite, the contents of the color map are undefined. Runs in linear
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* time in the size of the graph, if access to the property maps is in
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* constant time.
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*
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* @param graph The given graph.
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* @param index_map An index map associating vertices with an index.
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* @param partition_map A color map to fill with the bipartition.
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* @return true if and only if the given graph is bipartite.
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*/
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template < typename Graph, typename IndexMap, typename PartitionMap >
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bool is_bipartite(
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const Graph& graph, const IndexMap index_map, PartitionMap partition_map)
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{
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/// General types and variables
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typedef
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typename property_traits< PartitionMap >::value_type partition_color_t;
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typedef
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typename graph_traits< Graph >::vertex_descriptor vertex_descriptor_t;
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/// Declare dfs visitor
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// detail::empty_recorder recorder;
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// typedef detail::bipartite_visitor <PartitionMap,
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// detail::empty_recorder> dfs_visitor_t; dfs_visitor_t dfs_visitor
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// (partition_map, recorder);
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/// Call dfs
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try
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{
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depth_first_search(graph,
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vertex_index_map(index_map).visitor(make_dfs_visitor(
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std::make_pair(detail::colorize_bipartition(partition_map),
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std::make_pair(detail::check_bipartition(partition_map),
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put_property(partition_map,
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color_traits< partition_color_t >::white(),
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on_start_vertex()))))));
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}
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catch (const detail::bipartite_visitor_error< vertex_descriptor_t >&)
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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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/**
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* Checks a given graph for bipartiteness.
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*
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* @param graph The given graph.
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* @param index_map An index map associating vertices with an index.
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* @return true if and only if the given graph is bipartite.
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*/
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template < typename Graph, typename IndexMap >
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bool is_bipartite(const Graph& graph, const IndexMap index_map)
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{
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typedef one_bit_color_map< IndexMap > partition_map_t;
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partition_map_t partition_map(num_vertices(graph), index_map);
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return is_bipartite(graph, index_map, partition_map);
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}
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/**
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* Checks a given graph for bipartiteness. The graph must
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* have an internal vertex_index property. Runs in linear time in the
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* size of the graph, if access to the property maps is in constant time.
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*
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* @param graph The given graph.
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* @return true if and only if the given graph is bipartite.
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*/
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template < typename Graph > bool is_bipartite(const Graph& graph)
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{
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return is_bipartite(graph, get(vertex_index, graph));
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}
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/**
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* Checks a given graph for bipartiteness and fills a given color map with
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* white and black according to the bipartition. If the graph is not
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* bipartite, a sequence of vertices, producing an odd-cycle, is written to
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* the output iterator. The final iterator value is returned. Runs in linear
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* time in the size of the graph, if access to the property maps is in
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* constant time.
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*
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* @param graph The given graph.
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* @param index_map An index map associating vertices with an index.
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* @param partition_map A color map to fill with the bipartition.
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* @param result An iterator to write the odd-cycle vertices to.
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* @return The final iterator value after writing.
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*/
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template < typename Graph, typename IndexMap, typename PartitionMap,
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typename OutputIterator >
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OutputIterator find_odd_cycle(const Graph& graph, const IndexMap index_map,
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PartitionMap partition_map, OutputIterator result)
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{
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/// General types and variables
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typedef
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typename property_traits< PartitionMap >::value_type partition_color_t;
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typedef
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typename graph_traits< Graph >::vertex_descriptor vertex_descriptor_t;
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typedef typename graph_traits< Graph >::vertex_iterator vertex_iterator_t;
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vertex_iterator_t vertex_iter, vertex_end;
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/// Declare predecessor map
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typedef std::vector< vertex_descriptor_t > predecessors_t;
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typedef iterator_property_map< typename predecessors_t::iterator, IndexMap,
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vertex_descriptor_t, vertex_descriptor_t& >
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predecessor_map_t;
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predecessors_t predecessors(
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num_vertices(graph), graph_traits< Graph >::null_vertex());
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predecessor_map_t predecessor_map(predecessors.begin(), index_map);
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/// Initialize predecessor map
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for (boost::tie(vertex_iter, vertex_end) = vertices(graph);
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vertex_iter != vertex_end; ++vertex_iter)
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{
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put(predecessor_map, *vertex_iter, *vertex_iter);
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}
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/// Call dfs
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try
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{
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depth_first_search(graph,
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vertex_index_map(index_map).visitor(make_dfs_visitor(
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std::make_pair(detail::colorize_bipartition(partition_map),
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std::make_pair(detail::check_bipartition(partition_map),
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std::make_pair(
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put_property(partition_map,
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color_traits< partition_color_t >::white(),
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on_start_vertex()),
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record_predecessors(
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predecessor_map, on_tree_edge())))))));
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}
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catch (const detail::bipartite_visitor_error< vertex_descriptor_t >& error)
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{
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typedef std::vector< vertex_descriptor_t > path_t;
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path_t path1, path2;
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vertex_descriptor_t next, current;
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/// First path
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next = error.witnesses.first;
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do
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{
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current = next;
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path1.push_back(current);
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next = predecessor_map[current];
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} while (current != next);
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/// Second path
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next = error.witnesses.second;
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do
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{
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current = next;
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path2.push_back(current);
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next = predecessor_map[current];
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} while (current != next);
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/// Find beginning of common suffix
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std::pair< typename path_t::iterator, typename path_t::iterator >
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mismatch = detail::reverse_mismatch(
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std::make_pair(path1.begin(), path1.end()),
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std::make_pair(path2.begin(), path2.end()));
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/// Copy the odd-length cycle
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result = std::copy(path1.begin(), mismatch.first + 1, result);
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return std::reverse_copy(path2.begin(), mismatch.second, result);
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}
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return result;
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}
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/**
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* Checks a given graph for bipartiteness. If the graph is not bipartite, a
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* sequence of vertices, producing an odd-cycle, is written to the output
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* iterator. The final iterator value is returned. Runs in linear time in the
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* size of the graph, if access to the property maps is in constant time.
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*
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* @param graph The given graph.
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* @param index_map An index map associating vertices with an index.
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* @param result An iterator to write the odd-cycle vertices to.
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* @return The final iterator value after writing.
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*/
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template < typename Graph, typename IndexMap, typename OutputIterator >
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OutputIterator find_odd_cycle(
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const Graph& graph, const IndexMap index_map, OutputIterator result)
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{
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typedef one_bit_color_map< IndexMap > partition_map_t;
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partition_map_t partition_map(num_vertices(graph), index_map);
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return find_odd_cycle(graph, index_map, partition_map, result);
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}
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/**
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* Checks a given graph for bipartiteness. If the graph is not bipartite, a
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* sequence of vertices, producing an odd-cycle, is written to the output
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* iterator. The final iterator value is returned. The graph must have an
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* internal vertex_index property. Runs in linear time in the size of the
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* graph, if access to the property maps is in constant time.
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*
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* @param graph The given graph.
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* @param result An iterator to write the odd-cycle vertices to.
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* @return The final iterator value after writing.
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*/
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template < typename Graph, typename OutputIterator >
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OutputIterator find_odd_cycle(const Graph& graph, OutputIterator result)
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{
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return find_odd_cycle(graph, get(vertex_index, graph), result);
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}
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}
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#endif /// BOOST_GRAPH_BIPARTITE_HPP
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