1.1 --- a/lemon/binom_heap.h Tue Mar 02 10:27:47 2010 +0100
1.2 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000
1.3 @@ -1,445 +0,0 @@
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_BINOM_HEAP_H
1.23 -#define LEMON_BINOM_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 BinomHeap {
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 BinomHeap(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 - BinomHeap(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 BinomHeap;
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_BINOM_HEAP_H
1.448 -