Changeset 703:bb3392fe91f2 in lemon1.2 for lemon/pairing_heap.h
 Timestamp:
 07/09/09 04:07:08 (10 years ago)
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 default
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 public
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lemon/pairing_heap.h
r702 r703 1 /* * C++*1 /* * mode: C++; indenttabsmode: nil; * 2 2 * 3 * This file is a part of LEMON, a generic C++ optimization library 3 * This file is a part of LEMON, a generic C++ optimization library. 4 4 * 5 * Copyright (C) 2003200 85 * Copyright (C) 20032009 6 6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport 7 7 * (Egervary Research Group on Combinatorial Optimization, EGRES). … … 21 21 22 22 ///\file 23 ///\ingroup auxdat24 ///\brief Pairing Heap implementation.23 ///\ingroup heaps 24 ///\brief Pairing heap implementation. 25 25 26 26 #include <vector> 27 #include <utility> 27 28 #include <functional> 28 29 #include <lemon/math.h> … … 30 31 namespace lemon { 31 32 32 /// \ingroup auxdat33 /// \ingroup heaps 33 34 /// 34 35 ///\brief Pairing Heap. 35 36 /// 36 ///This class implements the \e Pairing \e heap data structure. A \e heap 37 ///is a data structure for storing items with specified values called \e 38 ///priorities in such a way that finding the item with minimum priority is 39 ///efficient. \c Compare specifies the ordering of the priorities. In a heap 40 ///one can change the priority of an item, add or erase an item, etc. 37 /// This class implements the \e pairing \e heap data structure. 38 /// It fully conforms to the \ref concepts::Heap "heap concept". 41 39 /// 42 ///The methods \ref increase and \ref erase are not efficient in a Pairing 43 ///heap. In case of many calls to these operations, it is better to use a 44 ///\ref BinHeap "binary heap". 40 /// The methods \ref increase() and \ref erase() are not efficient 41 /// in a pairing heap. In case of many calls of these operations, 42 /// it is better to use other heap structure, e.g. \ref BinHeap 43 /// "binary heap". 45 44 /// 46 ///\param _Prio Type of the priority of the items. 47 ///\param _ItemIntMap A read and writable Item int map, used internally 48 ///to handle the cross references. 49 ///\param _Compare A class for the ordering of the priorities. The 50 ///default is \c std::less<_Prio>. 51 /// 52 ///\sa BinHeap 53 ///\sa Dijkstra 54 ///\author Dorian Batha 55 45 /// \tparam PR Type of the priorities of the items. 46 /// \tparam IM A readwritable item map with \c int values, used 47 /// internally to handle the cross references. 48 /// \tparam CMP A functor class for comparing the priorities. 49 /// The default is \c std::less<PR>. 56 50 #ifdef DOXYGEN 57 template <typename _Prio, 58 typename _ItemIntMap, 59 typename _Compare> 51 template <typename PR, typename IM, typename CMP> 60 52 #else 61 template <typename _Prio, 62 typename _ItemIntMap, 63 typename _Compare = std::less<_Prio> > 53 template <typename PR, typename IM, typename CMP = std::less<PR> > 64 54 #endif 65 55 class PairingHeap { 66 56 public: 67 typedef _ItemIntMap ItemIntMap; 68 typedef _Prio Prio; 57 /// Type of the itemint map. 58 typedef IM ItemIntMap; 59 /// Type of the priorities. 60 typedef PR Prio; 61 /// Type of the items stored in the heap. 69 62 typedef typename ItemIntMap::Key Item; 70 typedef std::pair<Item,Prio> Pair; 71 typedef _Compare Compare; 63 /// Functor type for comparing the priorities. 64 typedef CMP Compare; 65 66 /// \brief Type to represent the states of the items. 67 /// 68 /// Each item has a state associated to it. It can be "in heap", 69 /// "preheap" or "postheap". The latter two are indifferent from the 70 /// heap's point of view, but may be useful to the user. 71 /// 72 /// The itemint map must be initialized in such way that it assigns 73 /// \c PRE_HEAP (<tt>1</tt>) to any element to be put in the heap. 74 enum State { 75 IN_HEAP = 0, ///< = 0. 76 PRE_HEAP = 1, ///< = 1. 77 POST_HEAP = 2 ///< = 2. 78 }; 72 79 73 80 private: 74 81 class store; 75 82 76 std::vector<store> container;77 int minimum;78 ItemIntMap & iimap;79 Compare comp;80 int num_items;83 std::vector<store> _data; 84 int _min; 85 ItemIntMap &_iim; 86 Compare _comp; 87 int _num_items; 81 88 82 89 public: 83 ///Status of the nodes 84 enum State { 85 ///The node is in the heap 86 IN_HEAP = 0, 87 ///The node has never been in the heap 88 PRE_HEAP = 1, 89 ///The node was in the heap but it got out of it 90 POST_HEAP = 2 91 }; 92 93 /// \brief The constructor 94 /// 95 /// \c _iimap should be given to the constructor, since it is 96 /// used internally to handle the cross references. 97 explicit PairingHeap(ItemIntMap &_iimap) 98 : minimum(0), iimap(_iimap), num_items(0) {} 99 100 /// \brief The constructor 101 /// 102 /// \c _iimap should be given to the constructor, since it is used 103 /// internally to handle the cross references. \c _comp is an 104 /// object for ordering of the priorities. 105 PairingHeap(ItemIntMap &_iimap, const Compare &_comp) 106 : minimum(0), iimap(_iimap), comp(_comp), num_items(0) {} 90 /// \brief Constructor. 91 /// 92 /// Constructor. 93 /// \param map A map that assigns \c int values to the items. 94 /// It is used internally to handle the cross references. 95 /// The assigned value must be \c PRE_HEAP (<tt>1</tt>) for each item. 96 explicit PairingHeap(ItemIntMap &map) 97 : _min(0), _iim(map), _num_items(0) {} 98 99 /// \brief Constructor. 100 /// 101 /// Constructor. 102 /// \param map A map that assigns \c int values to the items. 103 /// It is used internally to handle the cross references. 104 /// The assigned value must be \c PRE_HEAP (<tt>1</tt>) for each item. 105 /// \param comp The function object used for comparing the priorities. 106 PairingHeap(ItemIntMap &map, const Compare &comp) 107 : _min(0), _iim(map), _comp(comp), _num_items(0) {} 107 108 108 109 /// \brief The number of items stored in the heap. 109 110 /// 110 /// Returns the number of items stored in the heap. 111 int size() const { return num_items; } 112 113 /// \brief Checks if the heap stores no items. 114 /// 115 /// Returns \c true if and only if the heap stores no items. 116 bool empty() const { return num_items==0; } 117 118 /// \brief Make empty this heap. 119 /// 120 /// Make empty this heap. It does not change the cross reference 121 /// map. If you want to reuse a heap what is not surely empty you 122 /// should first clear the heap and after that you should set the 123 /// cross reference map for each item to \c PRE_HEAP. 111 /// This function returns the number of items stored in the heap. 112 int size() const { return _num_items; } 113 114 /// \brief Check if the heap is empty. 115 /// 116 /// This function returns \c true if the heap is empty. 117 bool empty() const { return _num_items==0; } 118 119 /// \brief Make the heap empty. 120 /// 121 /// This functon makes the heap empty. 122 /// It does not change the cross reference map. If you want to reuse 123 /// a heap that is not surely empty, you should first clear it and 124 /// then you should set the cross reference map to \c PRE_HEAP 125 /// for each item. 124 126 void clear() { 125 container.clear(); 126 minimum = 0; 127 num_items = 0; 128 } 129 130 /// \brief \c item gets to the heap with priority \c value independently 131 /// if \c item was already there. 132 /// 133 /// This method calls \ref push(\c item, \c value) if \c item is not 134 /// stored in the heap and it calls \ref decrease(\c item, \c value) or 135 /// \ref increase(\c item, \c value) otherwise. 127 _data.clear(); 128 _min = 0; 129 _num_items = 0; 130 } 131 132 /// \brief Set the priority of an item or insert it, if it is 133 /// not stored in the heap. 134 /// 135 /// This method sets the priority of the given item if it is 136 /// already stored in the heap. Otherwise it inserts the given 137 /// item into the heap with the given priority. 138 /// \param item The item. 139 /// \param value The priority. 136 140 void set (const Item& item, const Prio& value) { 137 int i= iimap[item];138 if ( i>=0 && container[i].in ) {139 if ( comp(value, container[i].prio) ) decrease(item, value);140 if ( comp(container[i].prio, value) ) increase(item, value);141 int i=_iim[item]; 142 if ( i>=0 && _data[i].in ) { 143 if ( _comp(value, _data[i].prio) ) decrease(item, value); 144 if ( _comp(_data[i].prio, value) ) increase(item, value); 141 145 } else push(item, value); 142 146 } 143 147 144 /// \brief Adds \c item to the heap with priority \c value. 145 /// 146 /// Adds \c item to the heap with priority \c value. 147 /// \pre \c item must not be stored in the heap. 148 /// \brief Insert an item into the heap with the given priority. 149 /// 150 /// This function inserts the given item into the heap with the 151 /// given priority. 152 /// \param item The item to insert. 153 /// \param value The priority of the item. 154 /// \pre \e item must not be stored in the heap. 148 155 void push (const Item& item, const Prio& value) { 149 int i= iimap[item];156 int i=_iim[item]; 150 157 if( i<0 ) { 151 int s= container.size();152 iimap.set(item, s);158 int s=_data.size(); 159 _iim.set(item, s); 153 160 store st; 154 161 st.name=item; 155 container.push_back(st);162 _data.push_back(st); 156 163 i=s; 157 164 } else { 158 container[i].parent=container[i].child=1;159 container[i].left_child=false;160 container[i].degree=0;161 container[i].in=true;162 } 163 164 container[i].prio=value;165 166 if ( num_items!=0 ) {167 if ( comp( value, container[minimum].prio) ) {168 fuse(i, minimum);169 minimum=i;170 } 171 else fuse( minimum,i);172 } 173 else minimum=i;174 175 ++ num_items;176 } 177 178 /// \brief Return s the item with minimum priority relative to \c Compare.179 /// 180 /// This method returns the item with minimum priority relative to \c181 /// Compare.182 /// \pre The heap must be nonempty.183 Item top() const { return container[minimum].name; } 184 185 /// \brief Returns the minimum priority relative to \c Compare.186 /// 187 /// It returns the minimum priority relative to \c Compare.188 /// \pre The heap must be nonempty.189 const Prio& prio() const { return container[minimum].prio; } 190 191 /// \brief Returns the priority of \c item.192 /// 193 /// It returns the priority of \citem.194 /// \pre \ citem must be in the heap.165 _data[i].parent=_data[i].child=1; 166 _data[i].left_child=false; 167 _data[i].degree=0; 168 _data[i].in=true; 169 } 170 171 _data[i].prio=value; 172 173 if ( _num_items!=0 ) { 174 if ( _comp( value, _data[_min].prio) ) { 175 fuse(i,_min); 176 _min=i; 177 } 178 else fuse(_min,i); 179 } 180 else _min=i; 181 182 ++_num_items; 183 } 184 185 /// \brief Return the item having minimum priority. 186 /// 187 /// This function returns the item having minimum priority. 188 /// \pre The heap must be nonempty. 189 Item top() const { return _data[_min].name; } 190 191 /// \brief The minimum priority. 192 /// 193 /// This function returns the minimum priority. 194 /// \pre The heap must be nonempty. 195 const Prio& prio() const { return _data[_min].prio; } 196 197 /// \brief The priority of the given item. 198 /// 199 /// This function returns the priority of the given item. 200 /// \param item The item. 201 /// \pre \e item must be in the heap. 195 202 const Prio& operator[](const Item& item) const { 196 return container[iimap[item]].prio; 197 } 198 199 /// \brief Deletes the item with minimum priority relative to \c Compare. 200 /// 201 /// This method deletes the item with minimum priority relative to \c 202 /// Compare from the heap. 203 return _data[_iim[item]].prio; 204 } 205 206 /// \brief Remove the item having minimum priority. 207 /// 208 /// This function removes the item having minimum priority. 203 209 /// \pre The heap must be nonempty. 204 210 void pop() { 205 int TreeArray[ num_items];211 int TreeArray[_num_items]; 206 212 int i=0, num_child=0, child_right = 0; 207 container[minimum].in=false;208 209 if( 1!= container[minimum].child ) {210 i= container[minimum].child;213 _data[_min].in=false; 214 215 if( 1!=_data[_min].child ) { 216 i=_data[_min].child; 211 217 TreeArray[num_child] = i; 212 container[i].parent = 1;213 container[minimum].child = 1;218 _data[i].parent = 1; 219 _data[_min].child = 1; 214 220 215 221 ++num_child; 216 222 int ch=1; 217 while( container[i].child!=1 ) {218 ch= container[i].child;219 if( container[ch].left_child && i==container[ch].parent ) {223 while( _data[i].child!=1 ) { 224 ch=_data[i].child; 225 if( _data[ch].left_child && i==_data[ch].parent ) { 220 226 i=ch; 221 227 //break; 222 228 } else { 223 if( container[ch].left_child ) {224 child_right= container[ch].parent;225 container[ch].parent = i;226  container[i].degree;229 if( _data[ch].left_child ) { 230 child_right=_data[ch].parent; 231 _data[ch].parent = i; 232 _data[i].degree; 227 233 } 228 234 else { 229 235 child_right=ch; 230 container[i].child=1;231 container[i].degree=0;236 _data[i].child=1; 237 _data[i].degree=0; 232 238 } 233 container[child_right].parent = 1;239 _data[child_right].parent = 1; 234 240 TreeArray[num_child] = child_right; 235 241 i = child_right; … … 240 246 int other; 241 247 for( i=0; i<num_child1; i+=2 ) { 242 if ( ! comp(container[TreeArray[i]].prio,243 container[TreeArray[i+1]].prio) ) {248 if ( !_comp(_data[TreeArray[i]].prio, 249 _data[TreeArray[i+1]].prio) ) { 244 250 other=TreeArray[i]; 245 251 TreeArray[i]=TreeArray[i+1]; … … 251 257 i = (0==(num_child % 2)) ? num_child2 : num_child1; 252 258 while(i>=2) { 253 if ( comp(container[TreeArray[i]].prio,254 container[TreeArray[i2]].prio) ) {259 if ( _comp(_data[TreeArray[i]].prio, 260 _data[TreeArray[i2]].prio) ) { 255 261 other=TreeArray[i]; 256 262 TreeArray[i]=TreeArray[i2]; … … 260 266 i=2; 261 267 } 262 minimum= TreeArray[0];268 _min = TreeArray[0]; 263 269 } 264 270 265 271 if ( 0==num_child ) { 266 minimum = container[minimum].child; 267 } 268 269 if (minimum >= 0) container[minimum].left_child = false; 270 271 num_items; 272 } 273 274 /// \brief Deletes \c item from the heap. 275 /// 276 /// This method deletes \c item from the heap, if \c item was already 277 /// stored in the heap. It is quite inefficient in Pairing heaps. 272 _min = _data[_min].child; 273 } 274 275 if (_min >= 0) _data[_min].left_child = false; 276 277 _num_items; 278 } 279 280 /// \brief Remove the given item from the heap. 281 /// 282 /// This function removes the given item from the heap if it is 283 /// already stored. 284 /// \param item The item to delete. 285 /// \pre \e item must be in the heap. 278 286 void erase (const Item& item) { 279 int i= iimap[item];280 if ( i>=0 && container[i].in ) {281 decrease( item, container[minimum].prio1 );287 int i=_iim[item]; 288 if ( i>=0 && _data[i].in ) { 289 decrease( item, _data[_min].prio1 ); 282 290 pop(); 283 291 } 284 292 } 285 293 286 /// \brief Decreases the priority of \c item to \c value. 287 /// 288 /// This method decreases the priority of \c item to \c value. 289 /// \pre \c item must be stored in the heap with priority at least \c 290 /// value relative to \c Compare. 294 /// \brief Decrease the priority of an item to the given value. 295 /// 296 /// This function decreases the priority of an item to the given value. 297 /// \param item The item. 298 /// \param value The priority. 299 /// \pre \e item must be stored in the heap with priority at least \e value. 291 300 void decrease (Item item, const Prio& value) { 292 int i= iimap[item];293 container[i].prio=value;294 int p= container[i].parent;295 296 if( container[i].left_child && i!=container[p].child ) {297 p= container[p].parent;298 } 299 300 if ( p!=1 && comp(value,container[p].prio) ) {301 int i=_iim[item]; 302 _data[i].prio=value; 303 int p=_data[i].parent; 304 305 if( _data[i].left_child && i!=_data[p].child ) { 306 p=_data[p].parent; 307 } 308 309 if ( p!=1 && _comp(value,_data[p].prio) ) { 301 310 cut(i,p); 302 if ( comp(container[minimum].prio,value) ) {303 fuse( minimum,i);311 if ( _comp(_data[_min].prio,value) ) { 312 fuse(_min,i); 304 313 } else { 305 fuse(i,minimum); 306 minimum=i; 307 } 308 } 309 } 310 311 /// \brief Increases the priority of \c item to \c value. 312 /// 313 /// This method sets the priority of \c item to \c value. Though 314 /// there is no precondition on the priority of \c item, this 315 /// method should be used only if it is indeed necessary to increase 316 /// (relative to \c Compare) the priority of \c item, because this 317 /// method is inefficient. 314 fuse(i,_min); 315 _min=i; 316 } 317 } 318 } 319 320 /// \brief Increase the priority of an item to the given value. 321 /// 322 /// This function increases the priority of an item to the given value. 323 /// \param item The item. 324 /// \param value The priority. 325 /// \pre \e item must be stored in the heap with priority at most \e value. 318 326 void increase (Item item, const Prio& value) { 319 327 erase(item); … … 321 329 } 322 330 323 /// \brief Returns if \c item is in, has already been in, or has never 324 /// been in the heap. 325 /// 326 /// This method returns PRE_HEAP if \c item has never been in the 327 /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP 328 /// otherwise. In the latter case it is possible that \c item will 329 /// get back to the heap again. 331 /// \brief Return the state of an item. 332 /// 333 /// This method returns \c PRE_HEAP if the given item has never 334 /// been in the heap, \c IN_HEAP if it is in the heap at the moment, 335 /// and \c POST_HEAP otherwise. 336 /// In the latter case it is possible that the item will get back 337 /// to the heap again. 338 /// \param item The item. 330 339 State state(const Item &item) const { 331 int i= iimap[item];340 int i=_iim[item]; 332 341 if( i>=0 ) { 333 if( container[i].in ) i=0;342 if( _data[i].in ) i=0; 334 343 else i=2; 335 344 } … … 337 346 } 338 347 339 /// \brief Set s the state of the \citem in the heap.340 /// 341 /// Sets the state of the \c item in the heap. It can be used to342 /// manually clear the heap when it is important to achive the343 /// better time complexity.348 /// \brief Set the state of an item in the heap. 349 /// 350 /// This function sets the state of the given item in the heap. 351 /// It can be used to manually clear the heap when it is important 352 /// to achive better time complexity. 344 353 /// \param i The item. 345 354 /// \param st The state. It should not be \c IN_HEAP. … … 349 358 case PRE_HEAP: 350 359 if (state(i) == IN_HEAP) erase(i); 351 iimap[i]=st;360 _iim[i]=st; 352 361 break; 353 362 case IN_HEAP: … … 360 369 void cut(int a, int b) { 361 370 int child_a; 362 switch ( container[a].degree) {371 switch (_data[a].degree) { 363 372 case 2: 364 child_a = container[container[a].child].parent;365 if( container[a].left_child ) {366 container[child_a].left_child=true;367 container[b].child=child_a;368 container[child_a].parent=container[a].parent;373 child_a = _data[_data[a].child].parent; 374 if( _data[a].left_child ) { 375 _data[child_a].left_child=true; 376 _data[b].child=child_a; 377 _data[child_a].parent=_data[a].parent; 369 378 } 370 379 else { 371 container[child_a].left_child=false;372 container[child_a].parent=b;373 if( a!= container[b].child )374 container[container[b].child].parent=child_a;380 _data[child_a].left_child=false; 381 _data[child_a].parent=b; 382 if( a!=_data[b].child ) 383 _data[_data[b].child].parent=child_a; 375 384 else 376 container[b].child=child_a;377 } 378  container[a].degree;379 container[container[a].child].parent=a;385 _data[b].child=child_a; 386 } 387 _data[a].degree; 388 _data[_data[a].child].parent=a; 380 389 break; 381 390 382 391 case 1: 383 child_a = container[a].child;384 if( ! container[child_a].left_child ) {385  container[a].degree;386 if( container[a].left_child ) {387 container[child_a].left_child=true;388 container[child_a].parent=container[a].parent;389 container[b].child=child_a;392 child_a = _data[a].child; 393 if( !_data[child_a].left_child ) { 394 _data[a].degree; 395 if( _data[a].left_child ) { 396 _data[child_a].left_child=true; 397 _data[child_a].parent=_data[a].parent; 398 _data[b].child=child_a; 390 399 } 391 400 else { 392 container[child_a].left_child=false;393 container[child_a].parent=b;394 if( a!= container[b].child )395 container[container[b].child].parent=child_a;401 _data[child_a].left_child=false; 402 _data[child_a].parent=b; 403 if( a!=_data[b].child ) 404 _data[_data[b].child].parent=child_a; 396 405 else 397 container[b].child=child_a;406 _data[b].child=child_a; 398 407 } 399 container[a].child=1;408 _data[a].child=1; 400 409 } 401 410 else { 402  container[b].degree;403 if( container[a].left_child ) {404 container[b].child =405 (1== container[b].degree) ? container[a].parent : 1;411 _data[b].degree; 412 if( _data[a].left_child ) { 413 _data[b].child = 414 (1==_data[b].degree) ? _data[a].parent : 1; 406 415 } else { 407 if (1== container[b].degree)408 container[container[b].child].parent=b;416 if (1==_data[b].degree) 417 _data[_data[b].child].parent=b; 409 418 else 410 container[b].child=1;419 _data[b].child=1; 411 420 } 412 421 } … … 414 423 415 424 case 0: 416  container[b].degree;417 if( container[a].left_child ) {418 container[b].child =419 (0!= container[b].degree) ? container[a].parent : 1;425 _data[b].degree; 426 if( _data[a].left_child ) { 427 _data[b].child = 428 (0!=_data[b].degree) ? _data[a].parent : 1; 420 429 } else { 421 if( 0!= container[b].degree )422 container[container[b].child].parent=b;430 if( 0!=_data[b].degree ) 431 _data[_data[b].child].parent=b; 423 432 else 424 container[b].child=1;433 _data[b].child=1; 425 434 } 426 435 break; 427 436 } 428 container[a].parent=1;429 container[a].left_child=false;437 _data[a].parent=1; 438 _data[a].left_child=false; 430 439 } 431 440 432 441 void fuse(int a, int b) { 433 int child_a = container[a].child;434 int child_b = container[b].child;435 container[a].child=b;436 container[b].parent=a;437 container[b].left_child=true;442 int child_a = _data[a].child; 443 int child_b = _data[b].child; 444 _data[a].child=b; 445 _data[b].parent=a; 446 _data[b].left_child=true; 438 447 439 448 if( 1!=child_a ) { 440 container[b].child=child_a;441 container[child_a].parent=b;442 container[child_a].left_child=false;443 ++ container[b].degree;449 _data[b].child=child_a; 450 _data[child_a].parent=b; 451 _data[child_a].left_child=false; 452 ++_data[b].degree; 444 453 445 454 if( 1!=child_b ) { 446 container[b].child=child_b;447 container[child_b].parent=child_a;448 } 449 } 450 else { ++ container[a].degree; }455 _data[b].child=child_b; 456 _data[child_b].parent=child_a; 457 } 458 } 459 else { ++_data[a].degree; } 451 460 } 452 461
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