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diff --git a/extern/quadriflow/3rd/lemon-1.3.1/lemon/binomial_heap.h b/extern/quadriflow/3rd/lemon-1.3.1/lemon/binomial_heap.h new file mode 100644 index 00000000000..5bc13787058 --- /dev/null +++ b/extern/quadriflow/3rd/lemon-1.3.1/lemon/binomial_heap.h @@ -0,0 +1,445 @@ +/* -*- mode: C++; indent-tabs-mode: nil; -*- + * + * This file is a part of LEMON, a generic C++ optimization library. + * + * Copyright (C) 2003-2010 + * 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_BINOMIAL_HEAP_H +#define LEMON_BINOMIAL_HEAP_H + +///\file +///\ingroup heaps +///\brief Binomial Heap implementation. + +#include <vector> +#include <utility> +#include <functional> +#include <lemon/math.h> +#include <lemon/counter.h> + +namespace lemon { + + /// \ingroup heaps + /// + ///\brief Binomial heap data structure. + /// + /// This class implements the \e binomial \e heap data structure. + /// It fully conforms to the \ref concepts::Heap "heap concept". + /// + /// The methods \ref increase() and \ref erase() are not efficient + /// in a binomial heap. In case of many calls of these operations, + /// it is better to use other heap structure, e.g. \ref BinHeap + /// "binary heap". + /// + /// \tparam PR Type of the priorities of the items. + /// \tparam IM A read-writable item map with \c int values, used + /// internally to handle the cross references. + /// \tparam CMP A functor class for comparing the priorities. + /// The default is \c std::less<PR>. +#ifdef DOXYGEN + template <typename PR, typename IM, typename CMP> +#else + template <typename PR, typename IM, typename CMP = std::less<PR> > +#endif + class BinomialHeap { + public: + /// Type of the item-int map. + typedef IM ItemIntMap; + /// Type of the priorities. + typedef PR Prio; + /// Type of the items stored in the heap. + typedef typename ItemIntMap::Key Item; + /// Functor type for comparing the priorities. + typedef CMP Compare; + + /// \brief Type to represent the states of the items. + /// + /// Each item has a state associated to it. It can be "in heap", + /// "pre-heap" or "post-heap". The latter two are indifferent from the + /// heap's point of view, but may be useful to the user. + /// + /// The item-int map must be initialized in such way that it assigns + /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap. + enum State { + IN_HEAP = 0, ///< = 0. + PRE_HEAP = -1, ///< = -1. + POST_HEAP = -2 ///< = -2. + }; + + private: + class Store; + + std::vector<Store> _data; + int _min, _head; + ItemIntMap &_iim; + Compare _comp; + int _num_items; + + public: + /// \brief Constructor. + /// + /// Constructor. + /// \param map A map that assigns \c int values to the items. + /// It is used internally to handle the cross references. + /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. + explicit BinomialHeap(ItemIntMap &map) + : _min(0), _head(-1), _iim(map), _num_items(0) {} + + /// \brief Constructor. + /// + /// Constructor. + /// \param map A map that assigns \c int values to the items. + /// It is used internally to handle the cross references. + /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. + /// \param comp The function object used for comparing the priorities. + BinomialHeap(ItemIntMap &map, const Compare &comp) + : _min(0), _head(-1), _iim(map), _comp(comp), _num_items(0) {} + + /// \brief The number of items stored in the heap. + /// + /// This function returns the number of items stored in the heap. + int size() const { return _num_items; } + + /// \brief Check if the heap is empty. + /// + /// This function returns \c true if the heap is empty. + bool empty() const { return _num_items==0; } + + /// \brief Make the heap empty. + /// + /// This functon makes the heap empty. + /// It does not change the cross reference map. If you want to reuse + /// a heap that is not surely empty, you should first clear it and + /// then you should set the cross reference map to \c PRE_HEAP + /// for each item. + void clear() { + _data.clear(); _min=0; _num_items=0; _head=-1; + } + + /// \brief Set the priority of an item or insert it, if it is + /// not stored in the heap. + /// + /// This method sets the priority of the given item if it is + /// already stored in the heap. Otherwise it inserts the given + /// item into the heap with the given priority. + /// \param item The item. + /// \param value The priority. + void set (const Item& item, const Prio& value) { + int i=_iim[item]; + if ( i >= 0 && _data[i].in ) { + if ( _comp(value, _data[i].prio) ) decrease(item, value); + if ( _comp(_data[i].prio, value) ) increase(item, value); + } else push(item, value); + } + + /// \brief Insert an item into the heap with the given priority. + /// + /// This function inserts the given item into the heap with the + /// given priority. + /// \param item The item to insert. + /// \param value The priority of the item. + /// \pre \e item must not be stored in the heap. + void push (const Item& item, const Prio& value) { + int i=_iim[item]; + if ( i<0 ) { + int s=_data.size(); + _iim.set( item,s ); + Store st; + st.name=item; + st.prio=value; + _data.push_back(st); + i=s; + } + else { + _data[i].parent=_data[i].right_neighbor=_data[i].child=-1; + _data[i].degree=0; + _data[i].in=true; + _data[i].prio=value; + } + + if( 0==_num_items ) { + _head=i; + _min=i; + } else { + merge(i); + if( _comp(_data[i].prio, _data[_min].prio) ) _min=i; + } + ++_num_items; + } + + /// \brief Return the item having minimum priority. + /// + /// This function returns the item having minimum priority. + /// \pre The heap must be non-empty. + Item top() const { return _data[_min].name; } + + /// \brief The minimum priority. + /// + /// This function returns the minimum priority. + /// \pre The heap must be non-empty. + Prio prio() const { return _data[_min].prio; } + + /// \brief The priority of the given item. + /// + /// This function returns the priority of the given item. + /// \param item The item. + /// \pre \e item must be in the heap. + const Prio& operator[](const Item& item) const { + return _data[_iim[item]].prio; + } + + /// \brief Remove the item having minimum priority. + /// + /// This function removes the item having minimum priority. + /// \pre The heap must be non-empty. + void pop() { + _data[_min].in=false; + + int head_child=-1; + if ( _data[_min].child!=-1 ) { + int child=_data[_min].child; + int neighb; + while( child!=-1 ) { + neighb=_data[child].right_neighbor; + _data[child].parent=-1; + _data[child].right_neighbor=head_child; + head_child=child; + child=neighb; + } + } + + if ( _data[_head].right_neighbor==-1 ) { + // there was only one root + _head=head_child; + } + else { + // there were more roots + if( _head!=_min ) { unlace(_min); } + else { _head=_data[_head].right_neighbor; } + merge(head_child); + } + _min=findMin(); + --_num_items; + } + + /// \brief Remove the given item from the heap. + /// + /// This function removes the given item from the heap if it is + /// already stored. + /// \param item The item to delete. + /// \pre \e item must be in the heap. + void erase (const Item& item) { + int i=_iim[item]; + if ( i >= 0 && _data[i].in ) { + decrease( item, _data[_min].prio-1 ); + pop(); + } + } + + /// \brief Decrease the priority of an item to the given value. + /// + /// This function decreases the priority of an item to the given value. + /// \param item The item. + /// \param value The priority. + /// \pre \e item must be stored in the heap with priority at least \e value. + void decrease (Item item, const Prio& value) { + int i=_iim[item]; + int p=_data[i].parent; + _data[i].prio=value; + + while( p!=-1 && _comp(value, _data[p].prio) ) { + _data[i].name=_data[p].name; + _data[i].prio=_data[p].prio; + _data[p].name=item; + _data[p].prio=value; + _iim[_data[i].name]=i; + i=p; + p=_data[p].parent; + } + _iim[item]=i; + if ( _comp(value, _data[_min].prio) ) _min=i; + } + + /// \brief Increase the priority of an item to the given value. + /// + /// This function increases the priority of an item to the given value. + /// \param item The item. + /// \param value The priority. + /// \pre \e item must be stored in the heap with priority at most \e value. + void increase (Item item, const Prio& value) { + erase(item); + push(item, value); + } + + /// \brief Return the state of an item. + /// + /// This method returns \c PRE_HEAP if the given item has never + /// been in the heap, \c IN_HEAP if it is in the heap at the moment, + /// and \c POST_HEAP otherwise. + /// In the latter case it is possible that the item will get back + /// to the heap again. + /// \param item The item. + State state(const Item &item) const { + int i=_iim[item]; + if( i>=0 ) { + if ( _data[i].in ) i=0; + else i=-2; + } + return State(i); + } + + /// \brief Set the state of an item in the heap. + /// + /// This function sets the state of the given item in the heap. + /// It can be used to manually clear the heap when it is important + /// to achive better time complexity. + /// \param i The item. + /// \param st The state. It should not be \c IN_HEAP. + void state(const Item& i, State st) { + switch (st) { + case POST_HEAP: + case PRE_HEAP: + if (state(i) == IN_HEAP) { + erase(i); + } + _iim[i] = st; + break; + case IN_HEAP: + break; + } + } + + private: + + // Find the minimum of the roots + int findMin() { + if( _head!=-1 ) { + int min_loc=_head, min_val=_data[_head].prio; + for( int x=_data[_head].right_neighbor; x!=-1; + x=_data[x].right_neighbor ) { + if( _comp( _data[x].prio,min_val ) ) { + min_val=_data[x].prio; + min_loc=x; + } + } + return min_loc; + } + else return -1; + } + + // Merge the heap with another heap starting at the given position + void merge(int a) { + if( _head==-1 || a==-1 ) return; + if( _data[a].right_neighbor==-1 && + _data[a].degree<=_data[_head].degree ) { + _data[a].right_neighbor=_head; + _head=a; + } else { + interleave(a); + } + if( _data[_head].right_neighbor==-1 ) return; + + int x=_head; + int x_prev=-1, x_next=_data[x].right_neighbor; + while( x_next!=-1 ) { + if( _data[x].degree!=_data[x_next].degree || + ( _data[x_next].right_neighbor!=-1 && + _data[_data[x_next].right_neighbor].degree==_data[x].degree ) ) { + x_prev=x; + x=x_next; + } + else { + if( _comp(_data[x_next].prio,_data[x].prio) ) { + if( x_prev==-1 ) { + _head=x_next; + } else { + _data[x_prev].right_neighbor=x_next; + } + fuse(x,x_next); + x=x_next; + } + else { + _data[x].right_neighbor=_data[x_next].right_neighbor; + fuse(x_next,x); + } + } + x_next=_data[x].right_neighbor; + } + } + + // Interleave the elements of the given list into the list of the roots + void interleave(int a) { + int p=_head, q=a; + int curr=_data.size(); + _data.push_back(Store()); + + while( p!=-1 || q!=-1 ) { + if( q==-1 || ( p!=-1 && _data[p].degree<_data[q].degree ) ) { + _data[curr].right_neighbor=p; + curr=p; + p=_data[p].right_neighbor; + } + else { + _data[curr].right_neighbor=q; + curr=q; + q=_data[q].right_neighbor; + } + } + + _head=_data.back().right_neighbor; + _data.pop_back(); + } + + // Lace node a under node b + void fuse(int a, int b) { + _data[a].parent=b; + _data[a].right_neighbor=_data[b].child; + _data[b].child=a; + + ++_data[b].degree; + } + + // Unlace node a (if it has siblings) + void unlace(int a) { + int neighb=_data[a].right_neighbor; + int other=_head; + + while( _data[other].right_neighbor!=a ) + other=_data[other].right_neighbor; + _data[other].right_neighbor=neighb; + } + + private: + + class Store { + friend class BinomialHeap; + + Item name; + int parent; + int right_neighbor; + int child; + int degree; + bool in; + Prio prio; + + Store() : parent(-1), right_neighbor(-1), child(-1), degree(0), + in(true) {} + }; + }; + +} //namespace lemon + +#endif //LEMON_BINOMIAL_HEAP_H + |