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Diffstat (limited to 'extern/quadriflow/3rd/lemon-1.3.1/lemon/fib_heap.h')
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diff --git a/extern/quadriflow/3rd/lemon-1.3.1/lemon/fib_heap.h b/extern/quadriflow/3rd/lemon-1.3.1/lemon/fib_heap.h new file mode 100644 index 00000000000..3441722a034 --- /dev/null +++ b/extern/quadriflow/3rd/lemon-1.3.1/lemon/fib_heap.h @@ -0,0 +1,475 @@ +/* -*- mode: C++; indent-tabs-mode: nil; -*- + * + * This file is a part of LEMON, a generic C++ optimization library. + * + * Copyright (C) 2003-2009 + * 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_FIB_HEAP_H +#define LEMON_FIB_HEAP_H + +///\file +///\ingroup heaps +///\brief Fibonacci heap implementation. + +#include <vector> +#include <utility> +#include <functional> +#include <lemon/math.h> + +namespace lemon { + + /// \ingroup heaps + /// + /// \brief Fibonacci heap data structure. + /// + /// This class implements the \e Fibonacci \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 + /// Fibonacci 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 FibHeap { + 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; + /// Type of the item-priority pairs. + typedef std::pair<Item,Prio> Pair; + /// Functor type for comparing the priorities. + typedef CMP Compare; + + private: + class Store; + + std::vector<Store> _data; + int _minimum; + ItemIntMap &_iim; + Compare _comp; + int _num; + + public: + + /// \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. + }; + + /// \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 FibHeap(ItemIntMap &map) + : _minimum(0), _iim(map), _num() {} + + /// \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. + FibHeap(ItemIntMap &map, const Compare &comp) + : _minimum(0), _iim(map), _comp(comp), _num() {} + + /// \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; } + + /// \brief Check if the heap is empty. + /// + /// This function returns \c true if the heap is empty. + bool empty() const { return _num==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(); _minimum = 0; _num = 0; + } + + /// \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 prio The priority of the item. + /// \pre \e item must not be stored in the heap. + void push (const Item& item, const Prio& prio) { + int i=_iim[item]; + if ( i < 0 ) { + int s=_data.size(); + _iim.set( item, s ); + Store st; + st.name=item; + _data.push_back(st); + i=s; + } else { + _data[i].parent=_data[i].child=-1; + _data[i].degree=0; + _data[i].in=true; + _data[i].marked=false; + } + + if ( _num ) { + _data[_data[_minimum].right_neighbor].left_neighbor=i; + _data[i].right_neighbor=_data[_minimum].right_neighbor; + _data[_minimum].right_neighbor=i; + _data[i].left_neighbor=_minimum; + if ( _comp( prio, _data[_minimum].prio) ) _minimum=i; + } else { + _data[i].right_neighbor=_data[i].left_neighbor=i; + _minimum=i; + } + _data[i].prio=prio; + ++_num; + } + + /// \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[_minimum].name; } + + /// \brief The minimum priority. + /// + /// This function returns the minimum priority. + /// \pre The heap must be non-empty. + Prio prio() const { return _data[_minimum].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() { + /*The first case is that there are only one root.*/ + if ( _data[_minimum].left_neighbor==_minimum ) { + _data[_minimum].in=false; + if ( _data[_minimum].degree!=0 ) { + makeRoot(_data[_minimum].child); + _minimum=_data[_minimum].child; + balance(); + } + } else { + int right=_data[_minimum].right_neighbor; + unlace(_minimum); + _data[_minimum].in=false; + if ( _data[_minimum].degree > 0 ) { + int left=_data[_minimum].left_neighbor; + int child=_data[_minimum].child; + int last_child=_data[child].left_neighbor; + + makeRoot(child); + + _data[left].right_neighbor=child; + _data[child].left_neighbor=left; + _data[right].left_neighbor=last_child; + _data[last_child].right_neighbor=right; + } + _minimum=right; + balance(); + } // the case where there are more roots + --_num; + } + + /// \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 ) { + if ( _data[i].parent!=-1 ) { + int p=_data[i].parent; + cut(i,p); + cascade(p); + } + _minimum=i; //As if its prio would be -infinity + pop(); + } + } + + /// \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. + Prio operator[](const Item& item) const { + return _data[_iim[item]].prio; + } + + /// \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 prio The priority. + void set (const Item& item, const Prio& prio) { + int i=_iim[item]; + if ( i >= 0 && _data[i].in ) { + if ( _comp(prio, _data[i].prio) ) decrease(item, prio); + if ( _comp(_data[i].prio, prio) ) increase(item, prio); + } else push(item, prio); + } + + /// \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 prio The priority. + /// \pre \e item must be stored in the heap with priority at least \e prio. + void decrease (const Item& item, const Prio& prio) { + int i=_iim[item]; + _data[i].prio=prio; + int p=_data[i].parent; + + if ( p!=-1 && _comp(prio, _data[p].prio) ) { + cut(i,p); + cascade(p); + } + if ( _comp(prio, _data[_minimum].prio) ) _minimum=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 prio The priority. + /// \pre \e item must be stored in the heap with priority at most \e prio. + void increase (const Item& item, const Prio& prio) { + erase(item); + push(item, prio); + } + + /// \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: + + void balance() { + + int maxdeg=int( std::floor( 2.08*log(double(_data.size()))))+1; + + std::vector<int> A(maxdeg,-1); + + /* + *Recall that now minimum does not point to the minimum prio element. + *We set minimum to this during balance(). + */ + int anchor=_data[_minimum].left_neighbor; + int next=_minimum; + bool end=false; + + do { + int active=next; + if ( anchor==active ) end=true; + int d=_data[active].degree; + next=_data[active].right_neighbor; + + while (A[d]!=-1) { + if( _comp(_data[active].prio, _data[A[d]].prio) ) { + fuse(active,A[d]); + } else { + fuse(A[d],active); + active=A[d]; + } + A[d]=-1; + ++d; + } + A[d]=active; + } while ( !end ); + + + while ( _data[_minimum].parent >=0 ) + _minimum=_data[_minimum].parent; + int s=_minimum; + int m=_minimum; + do { + if ( _comp(_data[s].prio, _data[_minimum].prio) ) _minimum=s; + s=_data[s].right_neighbor; + } while ( s != m ); + } + + void makeRoot(int c) { + int s=c; + do { + _data[s].parent=-1; + s=_data[s].right_neighbor; + } while ( s != c ); + } + + void cut(int a, int b) { + /* + *Replacing a from the children of b. + */ + --_data[b].degree; + + if ( _data[b].degree !=0 ) { + int child=_data[b].child; + if ( child==a ) + _data[b].child=_data[child].right_neighbor; + unlace(a); + } + + + /*Lacing a to the roots.*/ + int right=_data[_minimum].right_neighbor; + _data[_minimum].right_neighbor=a; + _data[a].left_neighbor=_minimum; + _data[a].right_neighbor=right; + _data[right].left_neighbor=a; + + _data[a].parent=-1; + _data[a].marked=false; + } + + void cascade(int a) { + if ( _data[a].parent!=-1 ) { + int p=_data[a].parent; + + if ( _data[a].marked==false ) _data[a].marked=true; + else { + cut(a,p); + cascade(p); + } + } + } + + void fuse(int a, int b) { + unlace(b); + + /*Lacing b under a.*/ + _data[b].parent=a; + + if (_data[a].degree==0) { + _data[b].left_neighbor=b; + _data[b].right_neighbor=b; + _data[a].child=b; + } else { + int child=_data[a].child; + int last_child=_data[child].left_neighbor; + _data[child].left_neighbor=b; + _data[b].right_neighbor=child; + _data[last_child].right_neighbor=b; + _data[b].left_neighbor=last_child; + } + + ++_data[a].degree; + + _data[b].marked=false; + } + + /* + *It is invoked only if a has siblings. + */ + void unlace(int a) { + int leftn=_data[a].left_neighbor; + int rightn=_data[a].right_neighbor; + _data[leftn].right_neighbor=rightn; + _data[rightn].left_neighbor=leftn; + } + + + class Store { + friend class FibHeap; + + Item name; + int parent; + int left_neighbor; + int right_neighbor; + int child; + int degree; + bool marked; + bool in; + Prio prio; + + Store() : parent(-1), child(-1), degree(), marked(false), in(true) {} + }; + }; + +} //namespace lemon + +#endif //LEMON_FIB_HEAP_H + |