156 lines
5.6 KiB
C++
156 lines
5.6 KiB
C++
|
//
|
||
|
//=======================================================================
|
||
|
// Copyright 1997, 1998, 1999, 2000 University of Notre Dame.
|
||
|
// Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek
|
||
|
//
|
||
|
// 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)
|
||
|
//=======================================================================
|
||
|
//
|
||
|
#ifndef BOOST_GRAPH_MST_KRUSKAL_HPP
|
||
|
#define BOOST_GRAPH_MST_KRUSKAL_HPP
|
||
|
|
||
|
/*
|
||
|
*Minimum Spanning Tree
|
||
|
* Kruskal Algorithm
|
||
|
*
|
||
|
*Requirement:
|
||
|
* undirected graph
|
||
|
*/
|
||
|
|
||
|
#include <vector>
|
||
|
#include <queue>
|
||
|
#include <functional>
|
||
|
|
||
|
#include <boost/property_map/property_map.hpp>
|
||
|
#include <boost/graph/graph_concepts.hpp>
|
||
|
#include <boost/graph/named_function_params.hpp>
|
||
|
#include <boost/pending/disjoint_sets.hpp>
|
||
|
#include <boost/pending/indirect_cmp.hpp>
|
||
|
#include <boost/concept/assert.hpp>
|
||
|
|
||
|
|
||
|
namespace boost {
|
||
|
|
||
|
// Kruskal's algorithm for Minimum Spanning Tree
|
||
|
//
|
||
|
// This is a greedy algorithm to calculate the Minimum Spanning Tree
|
||
|
// for an undirected graph with weighted edges. The output will be a
|
||
|
// set of edges.
|
||
|
//
|
||
|
|
||
|
namespace detail {
|
||
|
|
||
|
template <class Graph, class OutputIterator,
|
||
|
class Rank, class Parent, class Weight>
|
||
|
void
|
||
|
kruskal_mst_impl(const Graph& G,
|
||
|
OutputIterator spanning_tree_edges,
|
||
|
Rank rank, Parent parent, Weight weight)
|
||
|
{
|
||
|
if (num_vertices(G) == 0) return; // Nothing to do in this case
|
||
|
typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
|
||
|
typedef typename graph_traits<Graph>::edge_descriptor Edge;
|
||
|
BOOST_CONCEPT_ASSERT(( VertexListGraphConcept<Graph> ));
|
||
|
BOOST_CONCEPT_ASSERT(( EdgeListGraphConcept<Graph> ));
|
||
|
BOOST_CONCEPT_ASSERT(( OutputIteratorConcept<OutputIterator, Edge> ));
|
||
|
BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<Rank, Vertex> ));
|
||
|
BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<Parent, Vertex> ));
|
||
|
BOOST_CONCEPT_ASSERT(( ReadablePropertyMapConcept<Weight, Edge> ));
|
||
|
typedef typename property_traits<Weight>::value_type W_value;
|
||
|
typedef typename property_traits<Rank>::value_type R_value;
|
||
|
typedef typename property_traits<Parent>::value_type P_value;
|
||
|
BOOST_CONCEPT_ASSERT(( ComparableConcept<W_value> ));
|
||
|
BOOST_CONCEPT_ASSERT(( ConvertibleConcept<P_value, Vertex> ));
|
||
|
BOOST_CONCEPT_ASSERT(( IntegerConcept<R_value> ));
|
||
|
|
||
|
disjoint_sets<Rank, Parent> dset(rank, parent);
|
||
|
|
||
|
typename graph_traits<Graph>::vertex_iterator ui, uiend;
|
||
|
for (boost::tie(ui, uiend) = vertices(G); ui != uiend; ++ui)
|
||
|
dset.make_set(*ui);
|
||
|
|
||
|
typedef indirect_cmp<Weight, std::greater<W_value> > weight_greater;
|
||
|
weight_greater wl(weight);
|
||
|
std::priority_queue<Edge, std::vector<Edge>, weight_greater> Q(wl);
|
||
|
/*push all edge into Q*/
|
||
|
typename graph_traits<Graph>::edge_iterator ei, eiend;
|
||
|
for (boost::tie(ei, eiend) = edges(G); ei != eiend; ++ei)
|
||
|
Q.push(*ei);
|
||
|
|
||
|
while (! Q.empty()) {
|
||
|
Edge e = Q.top();
|
||
|
Q.pop();
|
||
|
Vertex u = dset.find_set(source(e, G));
|
||
|
Vertex v = dset.find_set(target(e, G));
|
||
|
if ( u != v ) {
|
||
|
*spanning_tree_edges++ = e;
|
||
|
dset.link(u, v);
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
|
||
|
} // namespace detail
|
||
|
|
||
|
// Named Parameters Variants
|
||
|
|
||
|
template <class Graph, class OutputIterator>
|
||
|
inline void
|
||
|
kruskal_minimum_spanning_tree(const Graph& g,
|
||
|
OutputIterator spanning_tree_edges)
|
||
|
{
|
||
|
typedef typename graph_traits<Graph>::vertices_size_type size_type;
|
||
|
typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
|
||
|
if (num_vertices(g) == 0) return; // Nothing to do in this case
|
||
|
typename graph_traits<Graph>::vertices_size_type
|
||
|
n = num_vertices(g);
|
||
|
std::vector<size_type> rank_map(n);
|
||
|
std::vector<vertex_t> pred_map(n);
|
||
|
|
||
|
detail::kruskal_mst_impl
|
||
|
(g, spanning_tree_edges,
|
||
|
make_iterator_property_map(rank_map.begin(), get(vertex_index, g), rank_map[0]),
|
||
|
make_iterator_property_map(pred_map.begin(), get(vertex_index, g), pred_map[0]),
|
||
|
get(edge_weight, g));
|
||
|
}
|
||
|
|
||
|
template <class Graph, class OutputIterator, class P, class T, class R>
|
||
|
inline void
|
||
|
kruskal_minimum_spanning_tree(const Graph& g,
|
||
|
OutputIterator spanning_tree_edges,
|
||
|
const bgl_named_params<P, T, R>& params)
|
||
|
{
|
||
|
typedef typename graph_traits<Graph>::vertices_size_type size_type;
|
||
|
typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
|
||
|
if (num_vertices(g) == 0) return; // Nothing to do in this case
|
||
|
typename graph_traits<Graph>::vertices_size_type n;
|
||
|
n = is_default_param(get_param(params, vertex_rank))
|
||
|
? num_vertices(g) : 1;
|
||
|
std::vector<size_type> rank_map(n);
|
||
|
n = is_default_param(get_param(params, vertex_predecessor))
|
||
|
? num_vertices(g) : 1;
|
||
|
std::vector<vertex_t> pred_map(n);
|
||
|
|
||
|
detail::kruskal_mst_impl
|
||
|
(g, spanning_tree_edges,
|
||
|
choose_param
|
||
|
(get_param(params, vertex_rank),
|
||
|
make_iterator_property_map
|
||
|
(rank_map.begin(),
|
||
|
choose_pmap(get_param(params, vertex_index), g, vertex_index), rank_map[0])),
|
||
|
choose_param
|
||
|
(get_param(params, vertex_predecessor),
|
||
|
make_iterator_property_map
|
||
|
(pred_map.begin(),
|
||
|
choose_const_pmap(get_param(params, vertex_index), g, vertex_index),
|
||
|
pred_map[0])),
|
||
|
choose_const_pmap(get_param(params, edge_weight), g, edge_weight));
|
||
|
}
|
||
|
|
||
|
} // namespace boost
|
||
|
|
||
|
|
||
|
#endif // BOOST_GRAPH_MST_KRUSKAL_HPP
|
||
|
|