1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/binomial_heap.h Tue Sep 29 13:32:01 2009 +0200
1.3 @@ -0,0 +1,445 @@
1.4 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
1.5 + *
1.6 + * This file is a part of LEMON, a generic C++ optimization library.
1.7 + *
1.8 + * Copyright (C) 2003-2009
1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.11 + *
1.12 + * Permission to use, modify and distribute this software is granted
1.13 + * provided that this copyright notice appears in all copies. For
1.14 + * precise terms see the accompanying LICENSE file.
1.15 + *
1.16 + * This software is provided "AS IS" with no warranty of any kind,
1.17 + * express or implied, and with no claim as to its suitability for any
1.18 + * purpose.
1.19 + *
1.20 + */
1.21 +
1.22 +#ifndef LEMON_BINOMIAL_HEAP_H
1.23 +#define LEMON_BINOMIAL_HEAP_H
1.24 +
1.25 +///\file
1.26 +///\ingroup heaps
1.27 +///\brief Binomial Heap implementation.
1.28 +
1.29 +#include <vector>
1.30 +#include <utility>
1.31 +#include <functional>
1.32 +#include <lemon/math.h>
1.33 +#include <lemon/counter.h>
1.34 +
1.35 +namespace lemon {
1.36 +
1.37 + /// \ingroup heaps
1.38 + ///
1.39 + ///\brief Binomial heap data structure.
1.40 + ///
1.41 + /// This class implements the \e binomial \e heap data structure.
1.42 + /// It fully conforms to the \ref concepts::Heap "heap concept".
1.43 + ///
1.44 + /// The methods \ref increase() and \ref erase() are not efficient
1.45 + /// in a binomial heap. In case of many calls of these operations,
1.46 + /// it is better to use other heap structure, e.g. \ref BinHeap
1.47 + /// "binary heap".
1.48 + ///
1.49 + /// \tparam PR Type of the priorities of the items.
1.50 + /// \tparam IM A read-writable item map with \c int values, used
1.51 + /// internally to handle the cross references.
1.52 + /// \tparam CMP A functor class for comparing the priorities.
1.53 + /// The default is \c std::less<PR>.
1.54 +#ifdef DOXYGEN
1.55 + template <typename PR, typename IM, typename CMP>
1.56 +#else
1.57 + template <typename PR, typename IM, typename CMP = std::less<PR> >
1.58 +#endif
1.59 + class BinomialHeap {
1.60 + public:
1.61 + /// Type of the item-int map.
1.62 + typedef IM ItemIntMap;
1.63 + /// Type of the priorities.
1.64 + typedef PR Prio;
1.65 + /// Type of the items stored in the heap.
1.66 + typedef typename ItemIntMap::Key Item;
1.67 + /// Functor type for comparing the priorities.
1.68 + typedef CMP Compare;
1.69 +
1.70 + /// \brief Type to represent the states of the items.
1.71 + ///
1.72 + /// Each item has a state associated to it. It can be "in heap",
1.73 + /// "pre-heap" or "post-heap". The latter two are indifferent from the
1.74 + /// heap's point of view, but may be useful to the user.
1.75 + ///
1.76 + /// The item-int map must be initialized in such way that it assigns
1.77 + /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
1.78 + enum State {
1.79 + IN_HEAP = 0, ///< = 0.
1.80 + PRE_HEAP = -1, ///< = -1.
1.81 + POST_HEAP = -2 ///< = -2.
1.82 + };
1.83 +
1.84 + private:
1.85 + class Store;
1.86 +
1.87 + std::vector<Store> _data;
1.88 + int _min, _head;
1.89 + ItemIntMap &_iim;
1.90 + Compare _comp;
1.91 + int _num_items;
1.92 +
1.93 + public:
1.94 + /// \brief Constructor.
1.95 + ///
1.96 + /// Constructor.
1.97 + /// \param map A map that assigns \c int values to the items.
1.98 + /// It is used internally to handle the cross references.
1.99 + /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
1.100 + explicit BinomialHeap(ItemIntMap &map)
1.101 + : _min(0), _head(-1), _iim(map), _num_items(0) {}
1.102 +
1.103 + /// \brief Constructor.
1.104 + ///
1.105 + /// Constructor.
1.106 + /// \param map A map that assigns \c int values to the items.
1.107 + /// It is used internally to handle the cross references.
1.108 + /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
1.109 + /// \param comp The function object used for comparing the priorities.
1.110 + BinomialHeap(ItemIntMap &map, const Compare &comp)
1.111 + : _min(0), _head(-1), _iim(map), _comp(comp), _num_items(0) {}
1.112 +
1.113 + /// \brief The number of items stored in the heap.
1.114 + ///
1.115 + /// This function returns the number of items stored in the heap.
1.116 + int size() const { return _num_items; }
1.117 +
1.118 + /// \brief Check if the heap is empty.
1.119 + ///
1.120 + /// This function returns \c true if the heap is empty.
1.121 + bool empty() const { return _num_items==0; }
1.122 +
1.123 + /// \brief Make the heap empty.
1.124 + ///
1.125 + /// This functon makes the heap empty.
1.126 + /// It does not change the cross reference map. If you want to reuse
1.127 + /// a heap that is not surely empty, you should first clear it and
1.128 + /// then you should set the cross reference map to \c PRE_HEAP
1.129 + /// for each item.
1.130 + void clear() {
1.131 + _data.clear(); _min=0; _num_items=0; _head=-1;
1.132 + }
1.133 +
1.134 + /// \brief Set the priority of an item or insert it, if it is
1.135 + /// not stored in the heap.
1.136 + ///
1.137 + /// This method sets the priority of the given item if it is
1.138 + /// already stored in the heap. Otherwise it inserts the given
1.139 + /// item into the heap with the given priority.
1.140 + /// \param item The item.
1.141 + /// \param value The priority.
1.142 + void set (const Item& item, const Prio& value) {
1.143 + int i=_iim[item];
1.144 + if ( i >= 0 && _data[i].in ) {
1.145 + if ( _comp(value, _data[i].prio) ) decrease(item, value);
1.146 + if ( _comp(_data[i].prio, value) ) increase(item, value);
1.147 + } else push(item, value);
1.148 + }
1.149 +
1.150 + /// \brief Insert an item into the heap with the given priority.
1.151 + ///
1.152 + /// This function inserts the given item into the heap with the
1.153 + /// given priority.
1.154 + /// \param item The item to insert.
1.155 + /// \param value The priority of the item.
1.156 + /// \pre \e item must not be stored in the heap.
1.157 + void push (const Item& item, const Prio& value) {
1.158 + int i=_iim[item];
1.159 + if ( i<0 ) {
1.160 + int s=_data.size();
1.161 + _iim.set( item,s );
1.162 + Store st;
1.163 + st.name=item;
1.164 + st.prio=value;
1.165 + _data.push_back(st);
1.166 + i=s;
1.167 + }
1.168 + else {
1.169 + _data[i].parent=_data[i].right_neighbor=_data[i].child=-1;
1.170 + _data[i].degree=0;
1.171 + _data[i].in=true;
1.172 + _data[i].prio=value;
1.173 + }
1.174 +
1.175 + if( 0==_num_items ) {
1.176 + _head=i;
1.177 + _min=i;
1.178 + } else {
1.179 + merge(i);
1.180 + if( _comp(_data[i].prio, _data[_min].prio) ) _min=i;
1.181 + }
1.182 + ++_num_items;
1.183 + }
1.184 +
1.185 + /// \brief Return the item having minimum priority.
1.186 + ///
1.187 + /// This function returns the item having minimum priority.
1.188 + /// \pre The heap must be non-empty.
1.189 + Item top() const { return _data[_min].name; }
1.190 +
1.191 + /// \brief The minimum priority.
1.192 + ///
1.193 + /// This function returns the minimum priority.
1.194 + /// \pre The heap must be non-empty.
1.195 + Prio prio() const { return _data[_min].prio; }
1.196 +
1.197 + /// \brief The priority of the given item.
1.198 + ///
1.199 + /// This function returns the priority of the given item.
1.200 + /// \param item The item.
1.201 + /// \pre \e item must be in the heap.
1.202 + const Prio& operator[](const Item& item) const {
1.203 + return _data[_iim[item]].prio;
1.204 + }
1.205 +
1.206 + /// \brief Remove the item having minimum priority.
1.207 + ///
1.208 + /// This function removes the item having minimum priority.
1.209 + /// \pre The heap must be non-empty.
1.210 + void pop() {
1.211 + _data[_min].in=false;
1.212 +
1.213 + int head_child=-1;
1.214 + if ( _data[_min].child!=-1 ) {
1.215 + int child=_data[_min].child;
1.216 + int neighb;
1.217 + while( child!=-1 ) {
1.218 + neighb=_data[child].right_neighbor;
1.219 + _data[child].parent=-1;
1.220 + _data[child].right_neighbor=head_child;
1.221 + head_child=child;
1.222 + child=neighb;
1.223 + }
1.224 + }
1.225 +
1.226 + if ( _data[_head].right_neighbor==-1 ) {
1.227 + // there was only one root
1.228 + _head=head_child;
1.229 + }
1.230 + else {
1.231 + // there were more roots
1.232 + if( _head!=_min ) { unlace(_min); }
1.233 + else { _head=_data[_head].right_neighbor; }
1.234 + merge(head_child);
1.235 + }
1.236 + _min=findMin();
1.237 + --_num_items;
1.238 + }
1.239 +
1.240 + /// \brief Remove the given item from the heap.
1.241 + ///
1.242 + /// This function removes the given item from the heap if it is
1.243 + /// already stored.
1.244 + /// \param item The item to delete.
1.245 + /// \pre \e item must be in the heap.
1.246 + void erase (const Item& item) {
1.247 + int i=_iim[item];
1.248 + if ( i >= 0 && _data[i].in ) {
1.249 + decrease( item, _data[_min].prio-1 );
1.250 + pop();
1.251 + }
1.252 + }
1.253 +
1.254 + /// \brief Decrease the priority of an item to the given value.
1.255 + ///
1.256 + /// This function decreases the priority of an item to the given value.
1.257 + /// \param item The item.
1.258 + /// \param value The priority.
1.259 + /// \pre \e item must be stored in the heap with priority at least \e value.
1.260 + void decrease (Item item, const Prio& value) {
1.261 + int i=_iim[item];
1.262 + int p=_data[i].parent;
1.263 + _data[i].prio=value;
1.264 +
1.265 + while( p!=-1 && _comp(value, _data[p].prio) ) {
1.266 + _data[i].name=_data[p].name;
1.267 + _data[i].prio=_data[p].prio;
1.268 + _data[p].name=item;
1.269 + _data[p].prio=value;
1.270 + _iim[_data[i].name]=i;
1.271 + i=p;
1.272 + p=_data[p].parent;
1.273 + }
1.274 + _iim[item]=i;
1.275 + if ( _comp(value, _data[_min].prio) ) _min=i;
1.276 + }
1.277 +
1.278 + /// \brief Increase the priority of an item to the given value.
1.279 + ///
1.280 + /// This function increases the priority of an item to the given value.
1.281 + /// \param item The item.
1.282 + /// \param value The priority.
1.283 + /// \pre \e item must be stored in the heap with priority at most \e value.
1.284 + void increase (Item item, const Prio& value) {
1.285 + erase(item);
1.286 + push(item, value);
1.287 + }
1.288 +
1.289 + /// \brief Return the state of an item.
1.290 + ///
1.291 + /// This method returns \c PRE_HEAP if the given item has never
1.292 + /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
1.293 + /// and \c POST_HEAP otherwise.
1.294 + /// In the latter case it is possible that the item will get back
1.295 + /// to the heap again.
1.296 + /// \param item The item.
1.297 + State state(const Item &item) const {
1.298 + int i=_iim[item];
1.299 + if( i>=0 ) {
1.300 + if ( _data[i].in ) i=0;
1.301 + else i=-2;
1.302 + }
1.303 + return State(i);
1.304 + }
1.305 +
1.306 + /// \brief Set the state of an item in the heap.
1.307 + ///
1.308 + /// This function sets the state of the given item in the heap.
1.309 + /// It can be used to manually clear the heap when it is important
1.310 + /// to achive better time complexity.
1.311 + /// \param i The item.
1.312 + /// \param st The state. It should not be \c IN_HEAP.
1.313 + void state(const Item& i, State st) {
1.314 + switch (st) {
1.315 + case POST_HEAP:
1.316 + case PRE_HEAP:
1.317 + if (state(i) == IN_HEAP) {
1.318 + erase(i);
1.319 + }
1.320 + _iim[i] = st;
1.321 + break;
1.322 + case IN_HEAP:
1.323 + break;
1.324 + }
1.325 + }
1.326 +
1.327 + private:
1.328 +
1.329 + // Find the minimum of the roots
1.330 + int findMin() {
1.331 + if( _head!=-1 ) {
1.332 + int min_loc=_head, min_val=_data[_head].prio;
1.333 + for( int x=_data[_head].right_neighbor; x!=-1;
1.334 + x=_data[x].right_neighbor ) {
1.335 + if( _comp( _data[x].prio,min_val ) ) {
1.336 + min_val=_data[x].prio;
1.337 + min_loc=x;
1.338 + }
1.339 + }
1.340 + return min_loc;
1.341 + }
1.342 + else return -1;
1.343 + }
1.344 +
1.345 + // Merge the heap with another heap starting at the given position
1.346 + void merge(int a) {
1.347 + if( _head==-1 || a==-1 ) return;
1.348 + if( _data[a].right_neighbor==-1 &&
1.349 + _data[a].degree<=_data[_head].degree ) {
1.350 + _data[a].right_neighbor=_head;
1.351 + _head=a;
1.352 + } else {
1.353 + interleave(a);
1.354 + }
1.355 + if( _data[_head].right_neighbor==-1 ) return;
1.356 +
1.357 + int x=_head;
1.358 + int x_prev=-1, x_next=_data[x].right_neighbor;
1.359 + while( x_next!=-1 ) {
1.360 + if( _data[x].degree!=_data[x_next].degree ||
1.361 + ( _data[x_next].right_neighbor!=-1 &&
1.362 + _data[_data[x_next].right_neighbor].degree==_data[x].degree ) ) {
1.363 + x_prev=x;
1.364 + x=x_next;
1.365 + }
1.366 + else {
1.367 + if( _comp(_data[x_next].prio,_data[x].prio) ) {
1.368 + if( x_prev==-1 ) {
1.369 + _head=x_next;
1.370 + } else {
1.371 + _data[x_prev].right_neighbor=x_next;
1.372 + }
1.373 + fuse(x,x_next);
1.374 + x=x_next;
1.375 + }
1.376 + else {
1.377 + _data[x].right_neighbor=_data[x_next].right_neighbor;
1.378 + fuse(x_next,x);
1.379 + }
1.380 + }
1.381 + x_next=_data[x].right_neighbor;
1.382 + }
1.383 + }
1.384 +
1.385 + // Interleave the elements of the given list into the list of the roots
1.386 + void interleave(int a) {
1.387 + int p=_head, q=a;
1.388 + int curr=_data.size();
1.389 + _data.push_back(Store());
1.390 +
1.391 + while( p!=-1 || q!=-1 ) {
1.392 + if( q==-1 || ( p!=-1 && _data[p].degree<_data[q].degree ) ) {
1.393 + _data[curr].right_neighbor=p;
1.394 + curr=p;
1.395 + p=_data[p].right_neighbor;
1.396 + }
1.397 + else {
1.398 + _data[curr].right_neighbor=q;
1.399 + curr=q;
1.400 + q=_data[q].right_neighbor;
1.401 + }
1.402 + }
1.403 +
1.404 + _head=_data.back().right_neighbor;
1.405 + _data.pop_back();
1.406 + }
1.407 +
1.408 + // Lace node a under node b
1.409 + void fuse(int a, int b) {
1.410 + _data[a].parent=b;
1.411 + _data[a].right_neighbor=_data[b].child;
1.412 + _data[b].child=a;
1.413 +
1.414 + ++_data[b].degree;
1.415 + }
1.416 +
1.417 + // Unlace node a (if it has siblings)
1.418 + void unlace(int a) {
1.419 + int neighb=_data[a].right_neighbor;
1.420 + int other=_head;
1.421 +
1.422 + while( _data[other].right_neighbor!=a )
1.423 + other=_data[other].right_neighbor;
1.424 + _data[other].right_neighbor=neighb;
1.425 + }
1.426 +
1.427 + private:
1.428 +
1.429 + class Store {
1.430 + friend class BinomialHeap;
1.431 +
1.432 + Item name;
1.433 + int parent;
1.434 + int right_neighbor;
1.435 + int child;
1.436 + int degree;
1.437 + bool in;
1.438 + Prio prio;
1.439 +
1.440 + Store() : parent(-1), right_neighbor(-1), child(-1), degree(0),
1.441 + in(true) {}
1.442 + };
1.443 + };
1.444 +
1.445 +} //namespace lemon
1.446 +
1.447 +#endif //LEMON_BINOMIAL_HEAP_H
1.448 +