ecency-mobile/ios/Pods/boost-for-react-native/boost/graph/tiernan_all_cycles.hpp

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// (C) Copyright 2007-2009 Andrew Sutton
//
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0 (See accompanying file
// LICENSE_1_0.txt or http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_GRAPH_CYCLE_HPP
#define BOOST_GRAPH_CYCLE_HPP
#include <vector>
#include <boost/config.hpp>
#include <boost/graph/graph_concepts.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/properties.hpp>
#include <boost/concept/assert.hpp>
#include <boost/concept/detail/concept_def.hpp>
namespace boost {
namespace concepts {
BOOST_concept(CycleVisitor,(Visitor)(Path)(Graph))
{
BOOST_CONCEPT_USAGE(CycleVisitor)
{
vis.cycle(p, g);
}
private:
Visitor vis;
Graph g;
Path p;
};
} /* namespace concepts */
using concepts::CycleVisitorConcept;
} /* namespace boost */
#include <boost/concept/detail/concept_undef.hpp>
namespace boost
{
// The implementation of this algorithm is a reproduction of the Teirnan
// approach for directed graphs: bibtex follows
//
// @article{362819,
// author = {James C. Tiernan},
// title = {An efficient search algorithm to find the elementary circuits of a graph},
// journal = {Commun. ACM},
// volume = {13},
// number = {12},
// year = {1970},
// issn = {0001-0782},
// pages = {722--726},
// doi = {http://doi.acm.org/10.1145/362814.362819},
// publisher = {ACM Press},
// address = {New York, NY, USA},
// }
//
// It should be pointed out that the author does not provide a complete analysis for
// either time or space. This is in part, due to the fact that it's a fairly input
// sensitive problem related to the density and construction of the graph, not just
// its size.
//
// I've also taken some liberties with the interpretation of the algorithm - I've
// basically modernized it to use real data structures (no more arrays and matrices).
// Oh... and there's explicit control structures - not just gotos.
//
// The problem is definitely NP-complete, an unbounded implementation of this
// will probably run for quite a while on a large graph. The conclusions
// of this paper also reference a Paton algorithm for undirected graphs as being
// much more efficient (apparently based on spanning trees). Although not implemented,
// it can be found here:
//
// @article{363232,
// author = {Keith Paton},
// title = {An algorithm for finding a fundamental set of cycles of a graph},
// journal = {Commun. ACM},
// volume = {12},
// number = {9},
// year = {1969},
// issn = {0001-0782},
// pages = {514--518},
// doi = {http://doi.acm.org/10.1145/363219.363232},
// publisher = {ACM Press},
// address = {New York, NY, USA},
// }
/**
* The default cycle visitor provides an empty visit function for cycle
* visitors.
*/
struct cycle_visitor
{
template <typename Path, typename Graph>
inline void cycle(const Path& p, const Graph& g)
{ }
};
/**
* The min_max_cycle_visitor simultaneously records the minimum and maximum
* cycles in a graph.
*/
struct min_max_cycle_visitor
{
min_max_cycle_visitor(std::size_t& min_, std::size_t& max_)
: minimum(min_), maximum(max_)
{ }
template <typename Path, typename Graph>
inline void cycle(const Path& p, const Graph& g)
{
BOOST_USING_STD_MIN();
BOOST_USING_STD_MAX();
std::size_t len = p.size();
minimum = min BOOST_PREVENT_MACRO_SUBSTITUTION (minimum, len);
maximum = max BOOST_PREVENT_MACRO_SUBSTITUTION (maximum, len);
}
std::size_t& minimum;
std::size_t& maximum;
};
inline min_max_cycle_visitor
find_min_max_cycle(std::size_t& min_, std::size_t& max_)
{ return min_max_cycle_visitor(min_, max_); }
namespace detail
{
template <typename Graph, typename Path>
inline bool
is_vertex_in_path(const Graph&,
typename graph_traits<Graph>::vertex_descriptor v,
const Path& p)
{
return (std::find(p.begin(), p.end(), v) != p.end());
}
template <typename Graph, typename ClosedMatrix>
inline bool
is_path_closed(const Graph& g,
typename graph_traits<Graph>::vertex_descriptor u,
typename graph_traits<Graph>::vertex_descriptor v,
const ClosedMatrix& closed)
{
// the path from u to v is closed if v can be found in the list
// of closed vertices associated with u.
typedef typename ClosedMatrix::const_reference Row;
Row r = closed[get(vertex_index, g, u)];
if(find(r.begin(), r.end(), v) != r.end()) {
return true;
}
return false;
}
template <typename Graph, typename Path, typename ClosedMatrix>
inline bool
can_extend_path(const Graph& g,
typename graph_traits<Graph>::edge_descriptor e,
const Path& p,
const ClosedMatrix& m)
{
BOOST_CONCEPT_ASSERT(( IncidenceGraphConcept<Graph> ));
BOOST_CONCEPT_ASSERT(( VertexIndexGraphConcept<Graph> ));
typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
// get the vertices in question
Vertex
u = source(e, g),
v = target(e, g);
// conditions for allowing a traversal along this edge are:
// 1. the index of v must be greater than that at which the
// path is rooted (p.front()).
// 2. the vertex v cannot already be in the path
// 3. the vertex v cannot be closed to the vertex u
bool indices = get(vertex_index, g, p.front()) < get(vertex_index, g, v);
bool path = !is_vertex_in_path(g, v, p);
bool closed = !is_path_closed(g, u, v, m);
return indices && path && closed;
}
template <typename Graph, typename Path>
inline bool
can_wrap_path(const Graph& g, const Path& p)
{
BOOST_CONCEPT_ASSERT(( IncidenceGraphConcept<Graph> ));
typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
typedef typename graph_traits<Graph>::out_edge_iterator OutIterator;
// iterate over the out-edges of the back, looking for the
// front of the path. also, we can't travel along the same
// edge that we did on the way here, but we don't quite have the
// stringent requirements that we do in can_extend_path().
Vertex
u = p.back(),
v = p.front();
OutIterator i, end;
for(boost::tie(i, end) = out_edges(u, g); i != end; ++i) {
if((target(*i, g) == v)) {
return true;
}
}
return false;
}
template <typename Graph,
typename Path,
typename ClosedMatrix>
inline typename graph_traits<Graph>::vertex_descriptor
extend_path(const Graph& g,
Path& p,
ClosedMatrix& closed)
{
BOOST_CONCEPT_ASSERT(( IncidenceGraphConcept<Graph> ));
typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
typedef typename graph_traits<Graph>::out_edge_iterator OutIterator;
// get the current vertex
Vertex u = p.back();
Vertex ret = graph_traits<Graph>::null_vertex();
// AdjacencyIterator i, end;
OutIterator i, end;
for(boost::tie(i, end) = out_edges(u, g); i != end; ++i) {
Vertex v = target(*i, g);
// if we can actually extend along this edge,
// then that's what we want to do
if(can_extend_path(g, *i, p, closed)) {
p.push_back(v); // add the vertex to the path
ret = v;
break;
}
}
return ret;
}
template <typename Graph, typename Path, typename ClosedMatrix>
inline bool
exhaust_paths(const Graph& g, Path& p, ClosedMatrix& closed)
{
BOOST_CONCEPT_ASSERT(( GraphConcept<Graph> ));
typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
// if there's more than one vertex in the path, this closes
// of some possible routes and returns true. otherwise, if there's
// only one vertex left, the vertex has been used up
if(p.size() > 1) {
// get the last and second to last vertices, popping the last
// vertex off the path
Vertex last, prev;
last = p.back();
p.pop_back();
prev = p.back();
// reset the closure for the last vertex of the path and
// indicate that the last vertex in p is now closed to
// the next-to-last vertex in p
closed[get(vertex_index, g, last)].clear();
closed[get(vertex_index, g, prev)].push_back(last);
return true;
}
else {
return false;
}
}
template <typename Graph, typename Visitor>
inline void
all_cycles_from_vertex(const Graph& g,
typename graph_traits<Graph>::vertex_descriptor v,
Visitor vis,
std::size_t minlen,
std::size_t maxlen)
{
BOOST_CONCEPT_ASSERT(( VertexListGraphConcept<Graph> ));
typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
typedef std::vector<Vertex> Path;
BOOST_CONCEPT_ASSERT(( CycleVisitorConcept<Visitor,Path,Graph> ));
typedef std::vector<Vertex> VertexList;
typedef std::vector<VertexList> ClosedMatrix;
Path p;
ClosedMatrix closed(num_vertices(g), VertexList());
Vertex null = graph_traits<Graph>::null_vertex();
// each path investigation starts at the ith vertex
p.push_back(v);
while(1) {
// extend the path until we've reached the end or the
// maxlen-sized cycle
Vertex j = null;
while(((j = detail::extend_path(g, p, closed)) != null)
&& (p.size() < maxlen))
; // empty loop
// if we're done extending the path and there's an edge
// connecting the back to the front, then we should have
// a cycle.
if(detail::can_wrap_path(g, p) && p.size() >= minlen) {
vis.cycle(p, g);
}
if(!detail::exhaust_paths(g, p, closed)) {
break;
}
}
}
// Select the minimum allowable length of a cycle based on the directedness
// of the graph - 2 for directed, 3 for undirected.
template <typename D> struct min_cycles { enum { value = 2 }; };
template <> struct min_cycles<undirected_tag> { enum { value = 3 }; };
} /* namespace detail */
template <typename Graph, typename Visitor>
inline void
tiernan_all_cycles(const Graph& g,
Visitor vis,
std::size_t minlen,
std::size_t maxlen)
{
BOOST_CONCEPT_ASSERT(( VertexListGraphConcept<Graph> ));
typedef typename graph_traits<Graph>::vertex_iterator VertexIterator;
VertexIterator i, end;
for(boost::tie(i, end) = vertices(g); i != end; ++i) {
detail::all_cycles_from_vertex(g, *i, vis, minlen, maxlen);
}
}
template <typename Graph, typename Visitor>
inline void
tiernan_all_cycles(const Graph& g, Visitor vis, std::size_t maxlen)
{
typedef typename graph_traits<Graph>::directed_category Dir;
tiernan_all_cycles(g, vis, detail::min_cycles<Dir>::value, maxlen);
}
template <typename Graph, typename Visitor>
inline void
tiernan_all_cycles(const Graph& g, Visitor vis)
{
typedef typename graph_traits<Graph>::directed_category Dir;
tiernan_all_cycles(g, vis, detail::min_cycles<Dir>::value,
(std::numeric_limits<std::size_t>::max)());
}
template <typename Graph>
inline std::pair<std::size_t, std::size_t>
tiernan_girth_and_circumference(const Graph& g)
{
std::size_t
min_ = (std::numeric_limits<std::size_t>::max)(),
max_ = 0;
tiernan_all_cycles(g, find_min_max_cycle(min_, max_));
// if this is the case, the graph is acyclic...
if(max_ == 0) max_ = min_;
return std::make_pair(min_, max_);
}
template <typename Graph>
inline std::size_t
tiernan_girth(const Graph& g)
{ return tiernan_girth_and_circumference(g).first; }
template <typename Graph>
inline std::size_t
tiernan_circumference(const Graph& g)
{ return tiernan_girth_and_circumference(g).second; }
} /* namespace boost */
#endif