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// Copyright (C) 2001 Vladimir Prus <ghost@cs.msu.su>
// Copyright (C) 2001 Jeremy Siek <jsiek@cs.indiana.edu>
// Distributed under the Boost Software License, Version 1.0. (See
// accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
// NOTE: this final is generated by libs/graph/doc/transitive_closure.w
#ifndef BOOST_GRAPH_TRANSITIVE_CLOSURE_HPP
#define BOOST_GRAPH_TRANSITIVE_CLOSURE_HPP
#include <vector>
#include <algorithm> // for std::min and std::max
#include <functional>
#include <boost/config.hpp>
#include <boost/bind.hpp>
#include <boost/graph/strong_components.hpp>
#include <boost/graph/topological_sort.hpp>
#include <boost/graph/graph_concepts.hpp>
#include <boost/graph/named_function_params.hpp>
#include <boost/graph/adjacency_list.hpp>
#include <boost/concept/assert.hpp>
namespace boost
{
namespace detail
{
inline void
union_successor_sets(const std::vector < std::size_t > &s1,
const std::vector < std::size_t > &s2,
std::vector < std::size_t > &s3)
{
BOOST_USING_STD_MIN();
for (std::size_t k = 0; k < s1.size(); ++k)
s3[k] = min BOOST_PREVENT_MACRO_SUBSTITUTION(s1[k], s2[k]);
}
} // namespace detail
namespace detail
{
template < typename TheContainer, typename ST = std::size_t,
typename VT = typename TheContainer::value_type >
struct subscript_t
{
typedef ST argument_type;
typedef VT& result_type;
subscript_t(TheContainer & c):container(&c)
{
}
VT & operator() (const ST & i) const
{
return (*container)[i];
}
protected:
TheContainer * container;
};
template < typename TheContainer >
subscript_t < TheContainer > subscript(TheContainer & c) {
return subscript_t < TheContainer > (c);
}
} // namespace detail
template < typename Graph, typename GraphTC,
typename G_to_TC_VertexMap,
typename VertexIndexMap >
void transitive_closure(const Graph & g, GraphTC & tc,
G_to_TC_VertexMap g_to_tc_map,
VertexIndexMap index_map)
{
if (num_vertices(g) == 0)
return;
typedef typename graph_traits < Graph >::vertex_descriptor vertex;
typedef typename graph_traits < Graph >::vertex_iterator vertex_iterator;
typedef typename property_traits < VertexIndexMap >::value_type size_type;
typedef typename graph_traits <
Graph >::adjacency_iterator adjacency_iterator;
BOOST_CONCEPT_ASSERT(( VertexListGraphConcept < Graph > ));
BOOST_CONCEPT_ASSERT(( AdjacencyGraphConcept < Graph > ));
BOOST_CONCEPT_ASSERT(( VertexMutableGraphConcept < GraphTC > ));
BOOST_CONCEPT_ASSERT(( EdgeMutableGraphConcept < GraphTC > ));
BOOST_CONCEPT_ASSERT(( ReadablePropertyMapConcept < VertexIndexMap,
vertex > ));
typedef size_type cg_vertex;
std::vector < cg_vertex > component_number_vec(num_vertices(g));
iterator_property_map < cg_vertex *, VertexIndexMap, cg_vertex, cg_vertex& >
component_number(&component_number_vec[0], index_map);
int num_scc = strong_components(g, component_number,
vertex_index_map(index_map));
std::vector < std::vector < vertex > >components;
build_component_lists(g, num_scc, component_number, components);
typedef boost::adjacency_list<boost::vecS, boost::vecS, boost::directedS> CG_t;
CG_t CG(num_scc);
for (cg_vertex s = 0; s < components.size(); ++s) {
std::vector < cg_vertex > adj;
for (size_type i = 0; i < components[s].size(); ++i) {
vertex u = components[s][i];
adjacency_iterator v, v_end;
for (boost::tie(v, v_end) = adjacent_vertices(u, g); v != v_end; ++v) {
cg_vertex t = component_number[*v];
if (s != t) // Avoid loops in the condensation graph
adj.push_back(t);
}
}
std::sort(adj.begin(), adj.end());
typename std::vector<cg_vertex>::iterator di =
std::unique(adj.begin(), adj.end());
if (di != adj.end())
adj.erase(di, adj.end());
for (typename std::vector<cg_vertex>::const_iterator i = adj.begin();
i != adj.end(); ++i) {
add_edge(s, *i, CG);
}
}
std::vector<cg_vertex> topo_order;
std::vector<cg_vertex> topo_number(num_vertices(CG));
topological_sort(CG, std::back_inserter(topo_order),
vertex_index_map(identity_property_map()));
std::reverse(topo_order.begin(), topo_order.end());
size_type n = 0;
for (typename std::vector<cg_vertex>::iterator iter = topo_order.begin();
iter != topo_order.end(); ++iter)
topo_number[*iter] = n++;
std::vector<std::vector<cg_vertex> > CG_vec(num_vertices(CG));
for (size_type i = 0; i < num_vertices(CG); ++i) {
typedef typename boost::graph_traits<CG_t>::adjacency_iterator cg_adj_iter;
std::pair<cg_adj_iter, cg_adj_iter> pr = adjacent_vertices(i, CG);
CG_vec[i].assign(pr.first, pr.second);
std::sort(CG_vec[i].begin(), CG_vec[i].end(),
boost::bind(std::less<cg_vertex>(),
boost::bind(detail::subscript(topo_number), _1),
boost::bind(detail::subscript(topo_number), _2)));
}
std::vector<std::vector<cg_vertex> > chains;
{
std::vector<cg_vertex> in_a_chain(CG_vec.size());
for (typename std::vector<cg_vertex>::iterator i = topo_order.begin();
i != topo_order.end(); ++i) {
cg_vertex v = *i;
if (!in_a_chain[v]) {
chains.resize(chains.size() + 1);
std::vector<cg_vertex>& chain = chains.back();
for (;;) {
chain.push_back(v);
in_a_chain[v] = true;
typename std::vector<cg_vertex>::const_iterator next
= std::find_if(CG_vec[v].begin(), CG_vec[v].end(),
std::not1(detail::subscript(in_a_chain)));
if (next != CG_vec[v].end())
v = *next;
else
break; // end of chain, dead-end
}
}
}
}
std::vector<size_type> chain_number(CG_vec.size());
std::vector<size_type> pos_in_chain(CG_vec.size());
for (size_type i = 0; i < chains.size(); ++i)
for (size_type j = 0; j < chains[i].size(); ++j) {
cg_vertex v = chains[i][j];
chain_number[v] = i;
pos_in_chain[v] = j;
}
cg_vertex inf = (std::numeric_limits< cg_vertex >::max)();
std::vector<std::vector<cg_vertex> > successors(CG_vec.size(),
std::vector<cg_vertex>
(chains.size(), inf));
for (typename std::vector<cg_vertex>::reverse_iterator
i = topo_order.rbegin(); i != topo_order.rend(); ++i) {
cg_vertex u = *i;
typename std::vector<cg_vertex>::const_iterator adj, adj_last;
for (adj = CG_vec[u].begin(), adj_last = CG_vec[u].end();
adj != adj_last; ++adj) {
cg_vertex v = *adj;
if (topo_number[v] < successors[u][chain_number[v]]) {
// Succ(u) = Succ(u) U Succ(v)
detail::union_successor_sets(successors[u], successors[v],
successors[u]);
// Succ(u) = Succ(u) U {v}
successors[u][chain_number[v]] = topo_number[v];
}
}
}
for (size_type i = 0; i < CG_vec.size(); ++i)
CG_vec[i].clear();
for (size_type i = 0; i < CG_vec.size(); ++i)
for (size_type j = 0; j < chains.size(); ++j) {
size_type topo_num = successors[i][j];
if (topo_num < inf) {
cg_vertex v = topo_order[topo_num];
for (size_type k = pos_in_chain[v]; k < chains[j].size(); ++k)
CG_vec[i].push_back(chains[j][k]);
}
}
// Add vertices to the transitive closure graph
{
vertex_iterator i, i_end;
for (boost::tie(i, i_end) = vertices(g); i != i_end; ++i)
g_to_tc_map[*i] = add_vertex(tc);
}
// Add edges between all the vertices in two adjacent SCCs
typename std::vector<std::vector<cg_vertex> >::const_iterator si, si_end;
for (si = CG_vec.begin(), si_end = CG_vec.end(); si != si_end; ++si) {
cg_vertex s = si - CG_vec.begin();
typename std::vector<cg_vertex>::const_iterator i, i_end;
for (i = CG_vec[s].begin(), i_end = CG_vec[s].end(); i != i_end; ++i) {
cg_vertex t = *i;
for (size_type k = 0; k < components[s].size(); ++k)
for (size_type l = 0; l < components[t].size(); ++l)
add_edge(g_to_tc_map[components[s][k]],
g_to_tc_map[components[t][l]], tc);
}
}
// Add edges connecting all vertices in a SCC
for (size_type i = 0; i < components.size(); ++i)
if (components[i].size() > 1)
for (size_type k = 0; k < components[i].size(); ++k)
for (size_type l = 0; l < components[i].size(); ++l) {
vertex u = components[i][k], v = components[i][l];
add_edge(g_to_tc_map[u], g_to_tc_map[v], tc);
}
// Find loopbacks in the original graph.
// Need to add it to transitive closure.
{
vertex_iterator i, i_end;
for (boost::tie(i, i_end) = vertices(g); i != i_end; ++i)
{
adjacency_iterator ab, ae;
for (boost::tie(ab, ae) = adjacent_vertices(*i, g); ab != ae; ++ab)
{
if (*ab == *i)
if (components[component_number[*i]].size() == 1)
add_edge(g_to_tc_map[*i], g_to_tc_map[*i], tc);
}
}
}
}
template <typename Graph, typename GraphTC>
void transitive_closure(const Graph & g, GraphTC & tc)
{
if (num_vertices(g) == 0)
return;
typedef typename property_map<Graph, vertex_index_t>::const_type
VertexIndexMap;
VertexIndexMap index_map = get(vertex_index, g);
typedef typename graph_traits<GraphTC>::vertex_descriptor tc_vertex;
std::vector<tc_vertex> to_tc_vec(num_vertices(g));
iterator_property_map < tc_vertex *, VertexIndexMap, tc_vertex, tc_vertex&>
g_to_tc_map(&to_tc_vec[0], index_map);
transitive_closure(g, tc, g_to_tc_map, index_map);
}
namespace detail
{
template < typename Graph, typename GraphTC, typename G_to_TC_VertexMap,
typename VertexIndexMap>
void transitive_closure_dispatch
(const Graph & g, GraphTC & tc,
G_to_TC_VertexMap g_to_tc_map, VertexIndexMap index_map)
{
typedef typename graph_traits < GraphTC >::vertex_descriptor tc_vertex;
typename std::vector < tc_vertex >::size_type
n = is_default_param(g_to_tc_map) ? num_vertices(g) : 1;
std::vector < tc_vertex > to_tc_vec(n);
transitive_closure
(g, tc,
choose_param(g_to_tc_map, make_iterator_property_map
(to_tc_vec.begin(), index_map, to_tc_vec[0])),
index_map);
}
} // namespace detail
template < typename Graph, typename GraphTC,
typename P, typename T, typename R >
void transitive_closure(const Graph & g, GraphTC & tc,
const bgl_named_params < P, T, R > &params)
{
if (num_vertices(g) == 0)
return;
detail::transitive_closure_dispatch
(g, tc, get_param(params, orig_to_copy_t()),
choose_const_pmap(get_param(params, vertex_index), g, vertex_index) );
}
template < typename G > void warshall_transitive_closure(G & g)
{
typedef typename graph_traits < G >::vertex_iterator vertex_iterator;
BOOST_CONCEPT_ASSERT(( AdjacencyMatrixConcept < G > ));
BOOST_CONCEPT_ASSERT(( EdgeMutableGraphConcept < G > ));
// Matrix form:
// for k
// for i
// if A[i,k]
// for j
// A[i,j] = A[i,j] | A[k,j]
vertex_iterator ki, ke, ii, ie, ji, je;
for (boost::tie(ki, ke) = vertices(g); ki != ke; ++ki)
for (boost::tie(ii, ie) = vertices(g); ii != ie; ++ii)
if (edge(*ii, *ki, g).second)
for (boost::tie(ji, je) = vertices(g); ji != je; ++ji)
if (!edge(*ii, *ji, g).second && edge(*ki, *ji, g).second) {
add_edge(*ii, *ji, g);
}
}
template < typename G > void warren_transitive_closure(G & g)
{
using namespace boost;
typedef typename graph_traits < G >::vertex_iterator vertex_iterator;
BOOST_CONCEPT_ASSERT(( AdjacencyMatrixConcept < G > ));
BOOST_CONCEPT_ASSERT(( EdgeMutableGraphConcept < G > ));
// Make sure second loop will work
if (num_vertices(g) == 0)
return;
// for i = 2 to n
// for k = 1 to i - 1
// if A[i,k]
// for j = 1 to n
// A[i,j] = A[i,j] | A[k,j]
vertex_iterator ic, ie, jc, je, kc, ke;
for (boost::tie(ic, ie) = vertices(g), ++ic; ic != ie; ++ic)
for (boost::tie(kc, ke) = vertices(g); *kc != *ic; ++kc)
if (edge(*ic, *kc, g).second)
for (boost::tie(jc, je) = vertices(g); jc != je; ++jc)
if (!edge(*ic, *jc, g).second && edge(*kc, *jc, g).second) {
add_edge(*ic, *jc, g);
}
// for i = 1 to n - 1
// for k = i + 1 to n
// if A[i,k]
// for j = 1 to n
// A[i,j] = A[i,j] | A[k,j]
for (boost::tie(ic, ie) = vertices(g), --ie; ic != ie; ++ic)
for (kc = ic, ke = ie, ++kc; kc != ke; ++kc)
if (edge(*ic, *kc, g).second)
for (boost::tie(jc, je) = vertices(g); jc != je; ++jc)
if (!edge(*ic, *jc, g).second && edge(*kc, *jc, g).second) {
add_edge(*ic, *jc, g);
}
}
} // namespace boost
#endif // BOOST_GRAPH_TRANSITIVE_CLOSURE_HPP