COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/include/fib_heap.h @ 258:94bafec4f56f

Last change on this file since 258:94bafec4f56f was 255:45107782cbca, checked in by Alpar Juttner, 16 years ago

dijkstra.h and fib_heap.h has moved to include.
The versions of bin_heap.hh shuld be merged and renamed to bin_heap.h

File size: 8.9 KB
Line 
1// -*- C++ -*-
2/*
3 *template <typename Item,
4 *          typename Prio,
5 *          typename ItemIntMap,
6 *          typename Compare = std::less<Prio> >
7 *
8 *constructors:
9 *
10 *FibHeap(ItemIntMap),   FibHeap(ItemIntMap, Compare)
11 *
12 *Member functions:
13 *
14 *int size() : returns the number of elements in the heap
15 *
16 *bool empty() : true iff size()=0
17 *
18 *void set(Item, Prio) : calls push(Item, Prio) if Item is not
19 *     in the heap, and calls decrease/increase(Item, Prio) otherwise
20 *
21 *void push(Item, Prio) : pushes Item to the heap with priority Prio. Item
22 *     mustn't be in the heap.
23 *
24 *Item top() : returns the Item with least Prio.
25 *     Must be called only if heap is nonempty.
26 *
27 *Prio prio() : returns the least Prio
28 *     Must be called only if heap is nonempty.
29 *
30 *Prio get(Item) : returns Prio of Item
31 *     Must be called only if Item is in heap.
32 *
33 *void pop() : deletes the Item with least Prio
34 *
35 *void erase(Item) : deletes Item from the heap if it was already there
36 *
37 *void decrease(Item, P) : decreases prio of Item to P.
38 *     Item must be in the heap with prio at least P.
39 *
40 *void increase(Item, P) : sets prio of Item to P.
41 *
42 *state_enum state(Item) : returns PRE_HEAP if Item has not been in the
43 *     heap until now, IN_HEAP if it is in the heap at the moment, and
44 *     POST_HEAP otherwise. In the latter case it is possible that Item
45 *     will get back to the heap again.
46 *
47 *In Fibonacci heaps, increase and erase are not efficient, in case of
48 *many calls to these operations, it is better to use bin_heap.
49 */
50
51#ifndef FIB_HEAP_H
52#define FIB_HEAP_H
53
54///\file
55///\brief Fibonacci Heap implementation.
56
57#include <vector>
58#include <functional>
59#include <math.h>
60
61namespace hugo {
62 
63  /// A Fibonacci Heap implementation.
64  template <typename Item, typename Prio, typename ItemIntMap,
65            typename Compare = std::less<Prio> >
66  class FibHeap {
67   
68    typedef Prio PrioType;
69   
70    class store;
71   
72    std::vector<store> container;
73    int minimum;
74    ItemIntMap &iimap;
75    Compare comp;
76    int num_items;
77
78    ///\todo It is use nowhere
79    ///\todo It doesn't conform to the naming conventions.
80  public:
81    enum state_enum {
82      IN_HEAP = 0,
83      PRE_HEAP = -1,
84      POST_HEAP = -2
85    };
86   
87  public :
88   
89    FibHeap(ItemIntMap &_iimap) : minimum(), iimap(_iimap), num_items() {}
90    FibHeap(ItemIntMap &_iimap, const Compare &_comp) : minimum(),
91      iimap(_iimap), comp(_comp), num_items() {}
92   
93   
94    int size() const {
95      return num_items;
96    }
97
98
99    bool empty() const { return num_items==0; }
100
101
102    void set (Item const it, PrioType const value) {
103      int i=iimap[it];
104      if ( i >= 0 && container[i].in ) {
105        if ( comp(value, container[i].prio) ) decrease(it, value);
106        if ( comp(container[i].prio, value) ) increase(it, value);
107      } else push(it, value);
108    }
109   
110
111    void push (Item const it, PrioType const value) {
112      int i=iimap[it];     
113      if ( i < 0 ) {
114        int s=container.size();
115        iimap.set( it, s );     
116        store st;
117        st.name=it;
118        container.push_back(st);
119        i=s;
120      } else {
121        container[i].parent=container[i].child=-1;
122        container[i].degree=0;
123        container[i].in=true;
124        container[i].marked=false;
125      }
126
127      if ( num_items ) {
128        container[container[minimum].right_neighbor].left_neighbor=i;
129        container[i].right_neighbor=container[minimum].right_neighbor;
130        container[minimum].right_neighbor=i;
131        container[i].left_neighbor=minimum;
132        if ( comp( value, container[minimum].prio) ) minimum=i;
133      } else {
134        container[i].right_neighbor=container[i].left_neighbor=i;
135        minimum=i;     
136      }
137      container[i].prio=value;
138      ++num_items;
139    }
140   
141
142    Item top() const {
143      return container[minimum].name;
144    }
145   
146   
147    PrioType prio() const {
148      return container[minimum].prio;
149    }
150   
151
152
153
154    PrioType& operator[](const Item& it) {
155      return container[iimap[it]].prio;
156    }
157   
158    const PrioType& operator[](const Item& it) const {
159      return container[iimap[it]].prio;
160    }
161
162//     const PrioType get(const Item& it) const {
163//       return container[iimap[it]].prio;
164//     }
165
166    void pop() {
167      /*The first case is that there are only one root.*/
168      if ( container[minimum].left_neighbor==minimum ) {
169        container[minimum].in=false;
170        if ( container[minimum].degree!=0 ) {
171          makeroot(container[minimum].child);
172          minimum=container[minimum].child;
173          balance();
174        }
175      } else {
176        int right=container[minimum].right_neighbor;
177        unlace(minimum);
178        container[minimum].in=false;
179        if ( container[minimum].degree > 0 ) {
180          int left=container[minimum].left_neighbor;
181          int child=container[minimum].child;
182          int last_child=container[child].left_neighbor;
183       
184          makeroot(child);
185         
186          container[left].right_neighbor=child;
187          container[child].left_neighbor=left;
188          container[right].left_neighbor=last_child;
189          container[last_child].right_neighbor=right;
190        }
191        minimum=right;
192        balance();
193      } // the case where there are more roots
194      --num_items;   
195    }
196
197   
198    void erase (const Item& it) {
199      int i=iimap[it];
200     
201      if ( i >= 0 && container[i].in ) {       
202        if ( container[i].parent!=-1 ) {
203          int p=container[i].parent;
204          cut(i,p);         
205          cascade(p);
206        }
207        minimum=i;     //As if its prio would be -infinity
208        pop();
209      }
210    }
211   
212
213    void decrease (Item it, PrioType const value) {
214      int i=iimap[it];
215      container[i].prio=value;
216      int p=container[i].parent;
217     
218      if ( p!=-1 && comp(value, container[p].prio) ) {
219        cut(i,p);           
220        cascade(p);
221      }     
222      if ( comp(value, container[minimum].prio) ) minimum=i;
223    }
224   
225
226    void increase (Item it, PrioType const value) {
227      erase(it);
228      push(it, value);
229    }
230
231
232    state_enum state(const Item &it) const {
233      int i=iimap[it];
234      if( i>=0 ) {
235        if ( container[i].in ) i=0;
236        else i=-2;
237      }
238      return state_enum(i);
239    }
240
241
242  private:
243   
244    void balance() {     
245
246    int maxdeg=int( floor( 2.08*log(double(container.size()))))+1;
247 
248    std::vector<int> A(maxdeg,-1);
249   
250    /*
251     *Recall that now minimum does not point to the minimum prio element.
252     *We set minimum to this during balance().
253     */
254    int anchor=container[minimum].left_neighbor;
255    int next=minimum;
256    bool end=false;
257       
258       do {
259        int active=next;
260        if ( anchor==active ) end=true;
261        int d=container[active].degree;
262        next=container[active].right_neighbor;
263
264        while (A[d]!=-1) {       
265          if( comp(container[active].prio, container[A[d]].prio) ) {
266            fuse(active,A[d]);
267          } else {
268            fuse(A[d],active);
269            active=A[d];
270          }
271          A[d]=-1;
272          ++d;
273        }       
274        A[d]=active;
275       } while ( !end );
276
277
278       while ( container[minimum].parent >=0 ) minimum=container[minimum].parent;
279       int s=minimum;
280       int m=minimum;
281       do { 
282         if ( comp(container[s].prio, container[minimum].prio) ) minimum=s;
283         s=container[s].right_neighbor;
284       } while ( s != m );
285    }
286
287
288    void makeroot (int c) {
289      int s=c;
290      do { 
291        container[s].parent=-1;
292        s=container[s].right_neighbor;
293      } while ( s != c );
294    }
295   
296
297    void cut (int a, int b) {   
298      /*
299       *Replacing a from the children of b.
300       */
301      --container[b].degree;
302     
303      if ( container[b].degree !=0 ) {
304        int child=container[b].child;
305        if ( child==a )
306          container[b].child=container[child].right_neighbor;
307        unlace(a);
308      }
309     
310     
311      /*Lacing a to the roots.*/
312      int right=container[minimum].right_neighbor;
313      container[minimum].right_neighbor=a;
314      container[a].left_neighbor=minimum;
315      container[a].right_neighbor=right;
316      container[right].left_neighbor=a;
317
318      container[a].parent=-1;
319      container[a].marked=false;
320    }
321
322
323    void cascade (int a)
324    {
325      if ( container[a].parent!=-1 ) {
326        int p=container[a].parent;
327       
328        if ( container[a].marked==false ) container[a].marked=true;
329        else {
330          cut(a,p);
331          cascade(p);
332        }
333      }
334    }
335
336
337    void fuse (int a, int b) {
338      unlace(b);
339     
340      /*Lacing b under a.*/
341      container[b].parent=a;
342
343      if (container[a].degree==0) {
344        container[b].left_neighbor=b;
345        container[b].right_neighbor=b;
346        container[a].child=b;   
347      } else {
348        int child=container[a].child;
349        int last_child=container[child].left_neighbor;
350        container[child].left_neighbor=b;
351        container[b].right_neighbor=child;
352        container[last_child].right_neighbor=b;
353        container[b].left_neighbor=last_child;
354      }
355
356      ++container[a].degree;
357     
358      container[b].marked=false;
359    }
360
361
362    /*
363     *It is invoked only if a has siblings.
364     */
365    void unlace (int a) {     
366      int leftn=container[a].left_neighbor;
367      int rightn=container[a].right_neighbor;
368      container[leftn].right_neighbor=rightn;
369      container[rightn].left_neighbor=leftn;
370    }
371
372
373    class store {
374      friend class FibHeap;
375     
376      Item name;
377      int parent;
378      int left_neighbor;
379      int right_neighbor;
380      int child;
381      int degree; 
382      bool marked;
383      bool in;
384      PrioType prio;
385
386      store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
387    };
388   
389  };
390 
391} //namespace hugo
392#endif
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