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extern/quadriflow/3rd/lemon-1.3.1/lemon/kruskal.h

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/* -*- mode: C++; indent-tabs-mode: nil; -*-
*
* This file is a part of LEMON, a generic C++ optimization library.
*
* Copyright (C) 2003-2013
* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
* (Egervary Research Group on Combinatorial Optimization, EGRES).
*
* Permission to use, modify and distribute this software is granted
* provided that this copyright notice appears in all copies. For
* precise terms see the accompanying LICENSE file.
*
* This software is provided "AS IS" with no warranty of any kind,
* express or implied, and with no claim as to its suitability for any
* purpose.
*
*/
#ifndef LEMON_KRUSKAL_H
#define LEMON_KRUSKAL_H
#include <algorithm>
#include <vector>
#include <lemon/unionfind.h>
#include <lemon/maps.h>
#include <lemon/core.h>
#include <lemon/bits/traits.h>
///\ingroup spantree
///\file
///\brief Kruskal's algorithm to compute a minimum cost spanning tree
namespace lemon {
namespace _kruskal_bits {
// Kruskal for directed graphs.
template <typename Digraph, typename In, typename Out>
typename disable_if<lemon::UndirectedTagIndicator<Digraph>,
typename In::value_type::second_type >::type
kruskal(const Digraph& digraph, const In& in, Out& out,dummy<0> = 0) {
typedef typename In::value_type::second_type Value;
typedef typename Digraph::template NodeMap<int> IndexMap;
typedef typename Digraph::Node Node;
IndexMap index(digraph);
UnionFind<IndexMap> uf(index);
for (typename Digraph::NodeIt it(digraph); it != INVALID; ++it) {
uf.insert(it);
}
Value tree_value = 0;
for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {
if (uf.join(digraph.target(it->first),digraph.source(it->first))) {
out.set(it->first, true);
tree_value += it->second;
}
else {
out.set(it->first, false);
}
}
return tree_value;
}
// Kruskal for undirected graphs.
template <typename Graph, typename In, typename Out>
typename enable_if<lemon::UndirectedTagIndicator<Graph>,
typename In::value_type::second_type >::type
kruskal(const Graph& graph, const In& in, Out& out,dummy<1> = 1) {
typedef typename In::value_type::second_type Value;
typedef typename Graph::template NodeMap<int> IndexMap;
typedef typename Graph::Node Node;
IndexMap index(graph);
UnionFind<IndexMap> uf(index);
for (typename Graph::NodeIt it(graph); it != INVALID; ++it) {
uf.insert(it);
}
Value tree_value = 0;
for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {
if (uf.join(graph.u(it->first),graph.v(it->first))) {
out.set(it->first, true);
tree_value += it->second;
}
else {
out.set(it->first, false);
}
}
return tree_value;
}
template <typename Sequence>
struct PairComp {
typedef typename Sequence::value_type Value;
bool operator()(const Value& left, const Value& right) {
return left.second < right.second;
}
};
template <typename In, typename Enable = void>
struct SequenceInputIndicator {
static const bool value = false;
};
template <typename In>
struct SequenceInputIndicator<In,
typename exists<typename In::value_type::first_type>::type> {
static const bool value = true;
};
template <typename In, typename Enable = void>
struct MapInputIndicator {
static const bool value = false;
};
template <typename In>
struct MapInputIndicator<In,
typename exists<typename In::Value>::type> {
static const bool value = true;
};
template <typename In, typename Enable = void>
struct SequenceOutputIndicator {
static const bool value = false;
};
template <typename Out>
struct SequenceOutputIndicator<Out,
typename exists<typename Out::value_type>::type> {
static const bool value = true;
};
template <typename Out, typename Enable = void>
struct MapOutputIndicator {
static const bool value = false;
};
template <typename Out>
struct MapOutputIndicator<Out,
typename exists<typename Out::Value>::type> {
static const bool value = true;
};
template <typename In, typename InEnable = void>
struct KruskalValueSelector {};
template <typename In>
struct KruskalValueSelector<In,
typename enable_if<SequenceInputIndicator<In>, void>::type>
{
typedef typename In::value_type::second_type Value;
};
template <typename In>
struct KruskalValueSelector<In,
typename enable_if<MapInputIndicator<In>, void>::type>
{
typedef typename In::Value Value;
};
template <typename Graph, typename In, typename Out,
typename InEnable = void>
struct KruskalInputSelector {};
template <typename Graph, typename In, typename Out,
typename InEnable = void>
struct KruskalOutputSelector {};
template <typename Graph, typename In, typename Out>
struct KruskalInputSelector<Graph, In, Out,
typename enable_if<SequenceInputIndicator<In>, void>::type >
{
typedef typename In::value_type::second_type Value;
static Value kruskal(const Graph& graph, const In& in, Out& out) {
return KruskalOutputSelector<Graph, In, Out>::
kruskal(graph, in, out);
}
};
template <typename Graph, typename In, typename Out>
struct KruskalInputSelector<Graph, In, Out,
typename enable_if<MapInputIndicator<In>, void>::type >
{
typedef typename In::Value Value;
static Value kruskal(const Graph& graph, const In& in, Out& out) {
typedef typename In::Key MapArc;
typedef typename In::Value Value;
typedef typename ItemSetTraits<Graph, MapArc>::ItemIt MapArcIt;
typedef std::vector<std::pair<MapArc, Value> > Sequence;
Sequence seq;
for (MapArcIt it(graph); it != INVALID; ++it) {
seq.push_back(std::make_pair(it, in[it]));
}
std::sort(seq.begin(), seq.end(), PairComp<Sequence>());
return KruskalOutputSelector<Graph, Sequence, Out>::
kruskal(graph, seq, out);
}
};
template <typename T>
struct RemoveConst {
typedef T type;
};
template <typename T>
struct RemoveConst<const T> {
typedef T type;
};
template <typename Graph, typename In, typename Out>
struct KruskalOutputSelector<Graph, In, Out,
typename enable_if<SequenceOutputIndicator<Out>, void>::type >
{
typedef typename In::value_type::second_type Value;
static Value kruskal(const Graph& graph, const In& in, Out& out) {
typedef LoggerBoolMap<typename RemoveConst<Out>::type> Map;
Map map(out);
return _kruskal_bits::kruskal(graph, in, map);
}
};
template <typename Graph, typename In, typename Out>
struct KruskalOutputSelector<Graph, In, Out,
typename enable_if<MapOutputIndicator<Out>, void>::type >
{
typedef typename In::value_type::second_type Value;
static Value kruskal(const Graph& graph, const In& in, Out& out) {
return _kruskal_bits::kruskal(graph, in, out);
}
};
}
/// \ingroup spantree
///
/// \brief Kruskal's algorithm for finding a minimum cost spanning tree of
/// a graph.
///
/// This function runs Kruskal's algorithm to find a minimum cost
/// spanning tree of a graph.
/// Due to some C++ hacking, it accepts various input and output types.
///
/// \param g The graph the algorithm runs on.
/// It can be either \ref concepts::Digraph "directed" or
/// \ref concepts::Graph "undirected".
/// If the graph is directed, the algorithm consider it to be
/// undirected by disregarding the direction of the arcs.
///
/// \param in This object is used to describe the arc/edge costs.
/// It can be one of the following choices.
/// - An STL compatible 'Forward Container' with
/// <tt>std::pair<GR::Arc,C></tt> or
/// <tt>std::pair<GR::Edge,C></tt> as its <tt>value_type</tt>, where
/// \c C is the type of the costs. The pairs indicates the arcs/edges
/// along with the assigned cost. <em>They must be in a
/// cost-ascending order.</em>
/// - Any readable arc/edge map. The values of the map indicate the
/// arc/edge costs.
///
/// \retval out Here we also have a choice.
/// - It can be a writable arc/edge map with \c bool value type. After
/// running the algorithm it will contain the found minimum cost spanning
/// tree: the value of an arc/edge will be set to \c true if it belongs
/// to the tree, otherwise it will be set to \c false. The value of
/// each arc/edge will be set exactly once.
/// - It can also be an iteraror of an STL Container with
/// <tt>GR::Arc</tt> or <tt>GR::Edge</tt> as its
/// <tt>value_type</tt>. The algorithm copies the elements of the
/// found tree into this sequence. For example, if we know that the
/// spanning tree of the graph \c g has say 53 arcs, then we can
/// put its arcs into an STL vector \c tree with a code like this.
///\code
/// std::vector<Arc> tree(53);
/// kruskal(g,cost,tree.begin());
///\endcode
/// Or if we don't know in advance the size of the tree, we can
/// write this.
///\code
/// std::vector<Arc> tree;
/// kruskal(g,cost,std::back_inserter(tree));
///\endcode
///
/// \return The total cost of the found spanning tree.
///
/// \note If the input graph is not (weakly) connected, a spanning
/// forest is calculated instead of a spanning tree.
#ifdef DOXYGEN
template <typename Graph, typename In, typename Out>
Value kruskal(const Graph& g, const In& in, Out& out)
#else
template <class Graph, class In, class Out>
inline typename _kruskal_bits::KruskalValueSelector<In>::Value
kruskal(const Graph& graph, const In& in, Out& out)
#endif
{
return _kruskal_bits::KruskalInputSelector<Graph, In, Out>::
kruskal(graph, in, out);
}
template <class Graph, class In, class Out>
inline typename _kruskal_bits::KruskalValueSelector<In>::Value
kruskal(const Graph& graph, const In& in, const Out& out)
{
return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>::
kruskal(graph, in, out);
}
} //namespace lemon
#endif //LEMON_KRUSKAL_H