lemon-0.x: src/work/edmonds_karp.hh@970b265696b0

     1 #ifndef EDMONDS_KARP_HH

     2 #define EDMONDS_KARP_HH

     4 #include <algorithm>

     5 #include <list>

     6 #include <iterator>

     8 #include <bfs_iterator.hh>

     9 //#include <time_measure.h>

    11 namespace hugo {

    13   template<typename Graph, typename Number, typename FlowMap, typename CapacityMap>

    14   class ResGraph {

    15   public:

    16     typedef typename Graph::NodeIt NodeIt;

    17     typedef typename Graph::EachNodeIt EachNodeIt;

    18   private:

    19     typedef typename Graph::SymEdgeIt OldSymEdgeIt;

    20     const Graph& G;

    21     FlowMap& flow;

    22     const CapacityMap& capacity;

    23   public:

    24     ResGraph(const Graph& _G, FlowMap& _flow,

    25 	     const CapacityMap& _capacity) :

    26       G(_G), flow(_flow), capacity(_capacity) { }

    28     class EdgeIt;

    29     class OutEdgeIt;

    30     friend class EdgeIt;

    31     friend class OutEdgeIt;

    33     class EdgeIt {

    34       friend class ResGraph<Graph, Number, FlowMap, CapacityMap>;

    35     protected:

    36       const ResGraph<Graph, Number, FlowMap, CapacityMap>* resG;

    37       OldSymEdgeIt sym;

    38     public:

    39       EdgeIt() { }

    40       //EdgeIt(const EdgeIt& e) : resG(e.resG), sym(e.sym) { }

    41       Number free() const {

    42 	if (resG->G.aNode(sym)==resG->G.tail(sym)) {

    43 	  return (resG->capacity.get(sym)-resG->flow.get(sym));

    44 	} else {

    45 	  return (resG->flow.get(sym));

    46 	}

    47       }

    48       bool valid() const { return sym.valid(); }

    49       void augment(Number a) const {

    50 	if (resG->G.aNode(sym)==resG->G.tail(sym)) {

    51 	  resG->flow.set(sym, resG->flow.get(sym)+a);

    52 	  //resG->flow[sym]+=a;

    53 	} else {

    54 	  resG->flow.set(sym, resG->flow.get(sym)-a);

    55 	  //resG->flow[sym]-=a;

    56 	}

    57       }

    58     };

    60     class OutEdgeIt : public EdgeIt {

    61       friend class ResGraph<Graph, Number, FlowMap, CapacityMap>;

    62     public:

    63       OutEdgeIt() { }

    64       //OutEdgeIt(const OutEdgeIt& e) { resG=e.resG; sym=e.sym; }

    65     private:

    66       OutEdgeIt(const ResGraph<Graph, Number, FlowMap, CapacityMap>& _resG, NodeIt v) {

    67       	resG=&_resG;

    68 	sym=resG->G.template first<OldSymEdgeIt>(v);

    69 	while( sym.valid() && !(free()>0) ) { ++sym; }

    70       }

    71     public:

    72       OutEdgeIt& operator++() {

    73 	++sym;

    74 	while( sym.valid() && !(free()>0) ) { ++sym; }

    75 	return *this;

    76       }

    77     };

    79     void getFirst(OutEdgeIt& e, NodeIt v) const {

    80       e=OutEdgeIt(*this, v);

    81     }

    82     void getFirst(EachNodeIt& v) const { G.getFirst(v); }

    84     template< typename It >

    85     It first() const {

    86       It e;

    87       getFirst(e);

    88       return e;

    89     }

    91     template< typename It >

    92     It first(NodeIt v) const {

    93       It e;

    94       getFirst(e, v);

    95       return e;

    96     }

    98     NodeIt tail(EdgeIt e) const { return G.aNode(e.sym); }

    99     NodeIt head(EdgeIt e) const { return G.bNode(e.sym); }

   101     NodeIt aNode(OutEdgeIt e) const { return G.aNode(e.sym); }

   102     NodeIt bNode(OutEdgeIt e) const { return G.bNode(e.sym); }

   104     int id(NodeIt v) const { return G.id(v); }

   106     template <typename S>

   107     class NodeMap {

   108       typename Graph::NodeMap<S> node_map;

   109     public:

   110       NodeMap(const ResGraph<Graph, Number, FlowMap, CapacityMap>& _G) : node_map(_G.G) { }

   111       NodeMap(const ResGraph<Graph, Number, FlowMap, CapacityMap>& _G, S a) : node_map(_G.G, a) { }

   112       void set(NodeIt nit, S a) { node_map.set(nit, a); }

   113       S get(NodeIt nit) const { return node_map.get(nit); }

   114       S& operator[](NodeIt nit) { return node_map[nit]; }

   115       const S& operator[](NodeIt nit) const { return node_map[nit]; }

   116     };

   118   };

   121   template<typename Graph, typename Number, typename FlowMap, typename CapacityMap>

   122   class ResGraph2 {

   123   public:

   124     typedef typename Graph::NodeIt NodeIt;

   125     typedef typename Graph::EachNodeIt EachNodeIt;

   126   private:

   127     //typedef typename Graph::SymEdgeIt OldSymEdgeIt;

   128     typedef typename Graph::OutEdgeIt OldOutEdgeIt;

   129     typedef typename Graph::InEdgeIt OldInEdgeIt;

   131     const Graph& G;

   132     FlowMap& flow;

   133     const CapacityMap& capacity;

   134   public:

   135     ResGraph2(const Graph& _G, FlowMap& _flow,

   136 	     const CapacityMap& _capacity) :

   137       G(_G), flow(_flow), capacity(_capacity) { }

   139     class EdgeIt;

   140     class OutEdgeIt;

   141     friend class EdgeIt;

   142     friend class OutEdgeIt;

   144     class EdgeIt {

   145       friend class ResGraph2<Graph, Number, FlowMap, CapacityMap>;

   146     protected:

   147       const ResGraph2<Graph, Number, FlowMap, CapacityMap>* resG;

   148       //OldSymEdgeIt sym;

   149       OldOutEdgeIt out;

   150       OldInEdgeIt in;

   151       bool out_or_in; //true, iff out

   152     public:

   153       EdgeIt() : out_or_in(true) { }

   154       Number free() const {

   155 	if (out_or_in) {

   156 	  return (resG->capacity.get(out)-resG->flow.get(out));

   157 	} else {

   158 	  return (resG->flow.get(in));

   159 	}

   160       }

   161       bool valid() const {

   162 	return out_or_in && out.valid() || in.valid(); }

   163       void augment(Number a) const {

   164 	if (out_or_in) {

   165 	  resG->flow.set(out, resG->flow.get(out)+a);

   166 	} else {

   167 	  resG->flow.set(in, resG->flow.get(in)-a);

   168 	}

   169       }

   170     };

   172     class OutEdgeIt : public EdgeIt {

   173       friend class ResGraph2<Graph, Number, FlowMap, CapacityMap>;

   174     public:

   175       OutEdgeIt() { }

   176     private:

   177       OutEdgeIt(const ResGraph2<Graph, Number, FlowMap, CapacityMap>& _resG, NodeIt v) {

   178       	resG=&_resG;

   179 	out=resG->G.template first<OldOutEdgeIt>(v);

   180 	while( out.valid() && !(free()>0) ) { ++out; }

   181 	if (!out.valid()) {

   182 	  out_or_in=0;

   183 	  in=resG->G.template first<OldInEdgeIt>(v);

   184 	  while( in.valid() && !(free()>0) ) { ++in; }

   185 	}

   186       }

   187     public:

   188       OutEdgeIt& operator++() {

   189 	if (out_or_in) {

   190 	  NodeIt v=resG->G.aNode(out);

   191 	  ++out;

   192 	  while( out.valid() && !(free()>0) ) { ++out; }

   193 	  if (!out.valid()) {

   194 	    out_or_in=0;

   195 	    in=resG->G.template first<OldInEdgeIt>(v);

   196 	    while( in.valid() && !(free()>0) ) { ++in; }

   197 	  }

   198 	} else {

   199 	  ++in;

   200 	  while( in.valid() && !(free()>0) ) { ++in; }

   201 	}

   202 	return *this;

   203       }

   204     };

   206     void getFirst(OutEdgeIt& e, NodeIt v) const {

   207       e=OutEdgeIt(*this, v);

   208     }

   209     void getFirst(EachNodeIt& v) const { G.getFirst(v); }

   211     template< typename It >

   212     It first() const {

   213       It e;

   214       getFirst(e);

   215       return e;

   216     }

   218     template< typename It >

   219     It first(NodeIt v) const {

   220       It e;

   221       getFirst(e, v);

   222       return e;

   223     }

   225     NodeIt tail(EdgeIt e) const {

   226       return ((e.out_or_in) ? G.aNode(e.out) : G.aNode(e.in)); }

   227     NodeIt head(EdgeIt e) const {

   228       return ((e.out_or_in) ? G.bNode(e.out) : G.bNode(e.in)); }

   230     NodeIt aNode(OutEdgeIt e) const {

   231       return ((e.out_or_in) ? G.aNode(e.out) : G.aNode(e.in)); }

   232     NodeIt bNode(OutEdgeIt e) const {

   233       return ((e.out_or_in) ? G.bNode(e.out) : G.bNode(e.in)); }

   235     int id(NodeIt v) const { return G.id(v); }

   237     template <typename S>

   238     class NodeMap {

   239       typename Graph::NodeMap<S> node_map;

   240     public:

   241       NodeMap(const ResGraph2<Graph, Number, FlowMap, CapacityMap>& _G) : node_map(_G.G) { }

   242       NodeMap(const ResGraph2<Graph, Number, FlowMap, CapacityMap>& _G, S a) : node_map(_G.G, a) { }

   243       void set(NodeIt nit, S a) { node_map.set(nit, a); }

   244       S get(NodeIt nit) const { return node_map.get(nit); }

   245     };

   246   };

   249   template <typename Graph, typename Number, typename FlowMap, typename CapacityMap>

   250   class MaxFlow {

   251   public:

   252     typedef typename Graph::NodeIt NodeIt;

   253     typedef typename Graph::EdgeIt EdgeIt;

   254     typedef typename Graph::EachEdgeIt EachEdgeIt;

   255     typedef typename Graph::OutEdgeIt OutEdgeIt;

   256     typedef typename Graph::InEdgeIt InEdgeIt;

   258   private:

   259     const Graph* G;

   260     NodeIt s;

   261     NodeIt t;

   262     FlowMap* flow;

   263     const CapacityMap* capacity;

   264     typedef ResGraphWrapper<Graph, Number, FlowMap, CapacityMap > AugGraph;

   265     typedef typename AugGraph::OutEdgeIt AugOutEdgeIt;

   266     typedef typename AugGraph::EdgeIt AugEdgeIt;

   268     //AugGraph res_graph;

   269     //typedef typename AugGraph::NodeMap<bool> ReachedMap;

   270     //typename AugGraph::NodeMap<AugEdgeIt> pred;

   271     //typename AugGraph::NodeMap<Number> free;

   272   public:

   273     MaxFlow(const Graph& _G, NodeIt _s, NodeIt _t, FlowMap& _flow, const CapacityMap& _capacity) :

   274       G(&_G), s(_s), t(_t), flow(&_flow), capacity(&_capacity) //,

   275       //res_graph(G, flow, capacity), pred(res_graph), free(res_graph)

   276       { }

   277     bool augmentOnShortestPath() {

   278       AugGraph res_graph(*G, *flow, *capacity);

   279       bool _augment=false;

   281       typedef typename AugGraph::NodeMap<bool> ReachedMap;

   282       BfsIterator5< AugGraph, AugOutEdgeIt, ReachedMap > res_bfs(res_graph);

   283       res_bfs.pushAndSetReached(s);

   285       typename AugGraph::NodeMap<AugEdgeIt> pred(res_graph);

   286       //filled up with invalid iterators

   287       //pred.set(s, AugEdgeIt());

   289       typename AugGraph::NodeMap<Number> free(res_graph);

   291       //searching for augmenting path

   292       while ( !res_bfs.finished() ) {

   293 	AugOutEdgeIt e=/*AugOutEdgeIt*/(res_bfs);

   294 	if (res_graph.valid(e) && res_bfs.isBNodeNewlyReached()) {

   295 	  NodeIt v=res_graph.tail(e);

   296 	  NodeIt w=res_graph.head(e);

   297 	  pred.set(w, e);

   298 	  if (res_graph.valid(pred.get(v))) {

   299 	    free.set(w, std::min(free.get(v), e.free()));

   300 	  } else {

   301 	    free.set(w, e.free());

   302 	  }

   303 	  if (res_graph.head(e)==t) { _augment=true; break; }

   304 	}

   306 	++res_bfs;

   307       } //end of searching augmenting path

   309       if (_augment) {

   310 	NodeIt n=t;

   311 	Number augment_value=free.get(t);

   312 	while (res_graph.valid(pred.get(n))) {

   313 	  AugEdgeIt e=pred.get(n);

   314 	  e.augment(augment_value);

   315 	  n=res_graph.tail(e);

   316 	}

   317       }

   319       return _augment;

   320     }

   322     template<typename MutableGraph> bool augmentOnBlockingFlow() {

   323       bool _augment=false;

   325       AugGraph res_graph(*G, *flow, *capacity);

   327       typedef typename AugGraph::NodeMap<bool> ReachedMap;

   328       BfsIterator4< AugGraph, AugOutEdgeIt, ReachedMap > bfs(res_graph);

   330       bfs.pushAndSetReached(s);

   331       typename AugGraph::NodeMap<int> dist(res_graph); //filled up with 0's

   332       while ( !bfs.finished() ) {

   333 	AugOutEdgeIt e=/*AugOutEdgeIt*/(bfs);

   334 	if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {

   335 	  dist.set(res_graph.head(e), dist.get(res_graph.tail(e))+1);

   336 	}

   338 	++bfs;

   339       } //computing distances from s in the residual graph

   341       MutableGraph F;

   342       typename AugGraph::NodeMap<NodeIt> res_graph_to_F(res_graph);

   343       for(typename AugGraph::EachNodeIt n=res_graph.template first<typename AugGraph::EachNodeIt>(); res_graph.valid(n); res_graph.next(n)) {

   344 	res_graph_to_F.set(n, F.addNode());

   345       }

   347       typename MutableGraph::NodeIt sF=res_graph_to_F.get(s);

   348       typename MutableGraph::NodeIt tF=res_graph_to_F.get(t);

   350       typename MutableGraph::EdgeMap<AugEdgeIt> original_edge(F);

   351       typename MutableGraph::EdgeMap<Number> residual_capacity(F);

   353       //Making F to the graph containing the edges of the residual graph

   354       //which are in some shortest paths

   355       for(typename AugGraph::EachEdgeIt e=res_graph.template first<typename AugGraph::EachEdgeIt>(); res_graph.valid(e); res_graph.next(e)) {

   356 	if (dist.get(res_graph.head(e))==dist.get(res_graph.tail(e))+1) {

   357 	  typename MutableGraph::EdgeIt f=F.addEdge(res_graph_to_F.get(res_graph.tail(e)), res_graph_to_F.get(res_graph.head(e)));

   358 	  original_edge.update();

   359 	  original_edge.set(f, e);

   360 	  residual_capacity.update();

   361 	  residual_capacity.set(f, e.free());

   362 	}

   363       }

   365       bool __augment=true;

   367       while (__augment) {

   368 	__augment=false;

   369 	//computing blocking flow with dfs

   370 	typedef typename MutableGraph::NodeMap<bool> BlockingReachedMap;

   371 	DfsIterator4< MutableGraph, typename MutableGraph::OutEdgeIt, BlockingReachedMap > dfs(F);

   372 	typename MutableGraph::NodeMap<EdgeIt> pred(F); //invalid iterators

   373 	typename MutableGraph::NodeMap<Number> free(F);

   375 	dfs.pushAndSetReached(sF);

   376 	while (!dfs.finished()) {

   377 	  ++dfs;

   378 	  if (F.valid(typename MutableGraph::OutEdgeIt(dfs))) {

   379 	    //std::cout << "OutEdgeIt: " << dfs;

   380 	    //std::cout << " aNode: " << F.aNode(dfs);

   381 	    //std::cout << " bNode: " << F.bNode(dfs) << " ";

   383 	    typename MutableGraph::NodeIt v=F.aNode(dfs);

   384 	    typename MutableGraph::NodeIt w=F.bNode(dfs);

   385 	    pred.set(w, dfs);

   386 	    if (F.valid(pred.get(v))) {

   387 	      free.set(w, std::min(free.get(v), residual_capacity.get(dfs)));

   388 	    } else {

   389 	      free.set(w, residual_capacity.get(dfs)/*original_edge.get(dfs).free()*/);

   390 	    }

   391 	    if (w==tF) {

   392 	      //std::cout << "AUGMENTATION"<<std::endl;

   393 	      __augment=true;

   394 	      _augment=true;

   395 	      break;

   396 	    }

   397 	  } else {

   398 	    //std::cout << "OutEdgeIt: " << "invalid";

   399 	    //std::cout << " aNode: " << dfs.aNode();

   400 	    //std::cout << " bNode: " << "invalid" << " ";

   401 	  }

   402 	  if (dfs.isBNodeNewlyReached()) {

   403 	    //std::cout << "bNodeIsNewlyReached ";

   404 	  } else {

   405 	    //std::cout << "bNodeIsNotNewlyReached ";

   406 	    if (typename MutableGraph::OutEdgeIt(dfs).valid()) {

   407 	      //std::cout << "DELETE ";

   408 	      F.erase(typename MutableGraph::OutEdgeIt(dfs));

   409 	    }

   410 	  }

   411 	  //if (dfs.isANodeExamined()) {

   412 	    //std::cout << "aNodeIsExamined ";

   413 	    //} else {

   414 	    //std::cout << "aNodeIsNotExamined ";

   415 	    //}

   416 	  //std::cout<<std::endl;

   417 	}

   419 	if (__augment) {

   420 	  typename MutableGraph::NodeIt n=tF;

   421 	  Number augment_value=free.get(tF);

   422 	  while (F.valid(pred.get(n))) {

   423 	    typename MutableGraph::EdgeIt e=pred.get(n);

   424 	    original_edge.get(e).augment(augment_value);

   425 	    n=F.tail(e);

   426 	    if (residual_capacity.get(e)==augment_value)

   427 	      F.erase(e);

   428 	    else

   429 	      residual_capacity.set(e, residual_capacity.get(e)-augment_value);

   430 	  }

   431 	}

   433       }

   435       return _augment;

   436     }

   437     void run() {

   438       //int num_of_augmentations=0;

   439       while (augmentOnShortestPath()) {

   440 	//while (augmentOnBlockingFlow<MutableGraph>()) {

   441 	//std::cout << ++num_of_augmentations << " ";

   442 	//std::cout<<std::endl;

   443       }

   444     }

   445     template<typename MutableGraph> void run() {

   446       //int num_of_augmentations=0;

   447       //while (augmentOnShortestPath()) {

   448 	while (augmentOnBlockingFlow<MutableGraph>()) {

   449 	//std::cout << ++num_of_augmentations << " ";

   450 	//std::cout<<std::endl;

   451       }

   452     }

   453     Number flowValue() {

   454       Number a=0;

   455       OutEdgeIt e;

   456       for(G->getFirst(e, s); G->valid(e); G->next(e)) {

   457 	a+=flow->get(e);

   458       }

   459       return a;

   460     }

   461   };

   464 //   template <typename Graph, typename Number, typename FlowMap, typename CapacityMap>

   465 //   class MaxFlow2 {

   466 //   public:

   467 //     typedef typename Graph::NodeIt NodeIt;

   468 //     typedef typename Graph::EdgeIt EdgeIt;

   469 //     typedef typename Graph::EachEdgeIt EachEdgeIt;

   470 //     typedef typename Graph::OutEdgeIt OutEdgeIt;

   471 //     typedef typename Graph::InEdgeIt InEdgeIt;

   472 //   private:

   473 //     const Graph& G;

   474 //     std::list<NodeIt>& S;

   475 //     std::list<NodeIt>& T;

   476 //     FlowMap& flow;

   477 //     const CapacityMap& capacity;

   478 //     typedef ResGraphWrapper<Graph, Number, FlowMap, CapacityMap > AugGraph;

   479 //     typedef typename AugGraph::OutEdgeIt AugOutEdgeIt;

   480 //     typedef typename AugGraph::EdgeIt AugEdgeIt;

   481 //     typename Graph::NodeMap<bool> SMap;

   482 //     typename Graph::NodeMap<bool> TMap;

   483 //   public:

   484 //     MaxFlow2(const Graph& _G, std::list<NodeIt>& _S, std::list<NodeIt>& _T, FlowMap& _flow, const CapacityMap& _capacity) : G(_G), S(_S), T(_T), flow(_flow), capacity(_capacity), SMap(_G), TMap(_G) {

   485 //       for(typename std::list<NodeIt>::const_iterator i=S.begin();

   486 // 	  i!=S.end(); ++i) {

   487 // 	SMap.set(*i, true);

   488 //       }

   489 //       for (typename std::list<NodeIt>::const_iterator i=T.begin();

   490 // 	   i!=T.end(); ++i) {

   491 // 	TMap.set(*i, true);

   492 //       }

   493 //     }

   494 //     bool augment() {

   495 //       AugGraph res_graph(G, flow, capacity);

   496 //       bool _augment=false;

   497 //       NodeIt reached_t_node;

   499 //       typedef typename AugGraph::NodeMap<bool> ReachedMap;

   500 //       BfsIterator4< AugGraph, AugOutEdgeIt, ReachedMap > res_bfs(res_graph);

   501 //       for(typename std::list<NodeIt>::const_iterator i=S.begin();

   502 // 	  i!=S.end(); ++i) {

   503 // 	res_bfs.pushAndSetReached(*i);

   504 //       }

   505 //       //res_bfs.pushAndSetReached(s);

   507 //       typename AugGraph::NodeMap<AugEdgeIt> pred(res_graph);

   508 //       //filled up with invalid iterators

   510 //       typename AugGraph::NodeMap<Number> free(res_graph);

   512 //       //searching for augmenting path

   513 //       while ( !res_bfs.finished() ) {

   514 // 	AugOutEdgeIt e=/*AugOutEdgeIt*/(res_bfs);

   515 // 	if (e.valid() && res_bfs.isBNodeNewlyReached()) {

   516 // 	  NodeIt v=res_graph.tail(e);

   517 // 	  NodeIt w=res_graph.head(e);

   518 // 	  pred.set(w, e);

   519 // 	  if (pred.get(v).valid()) {

   520 // 	    free.set(w, std::min(free.get(v), e.free()));

   521 // 	  } else {

   522 // 	    free.set(w, e.free());

   523 // 	  }

   524 // 	  if (TMap.get(res_graph.head(e))) {

   525 // 	    _augment=true;

   526 // 	    reached_t_node=res_graph.head(e);

   527 // 	    break;

   528 // 	  }

   529 // 	}

   531 // 	++res_bfs;

   532 //       } //end of searching augmenting path

   534 //       if (_augment) {

   535 // 	NodeIt n=reached_t_node;

   536 // 	Number augment_value=free.get(reached_t_node);

   537 // 	while (pred.get(n).valid()) {

   538 // 	  AugEdgeIt e=pred.get(n);

   539 // 	  e.augment(augment_value);

   540 // 	  n=res_graph.tail(e);

   541 // 	}

   542 //       }

   544 //       return _augment;

   545 //     }

   546 //     void run() {

   547 //       while (augment()) { }

   548 //     }

   549 //     Number flowValue() {

   550 //       Number a=0;

   551 //       for(typename std::list<NodeIt>::const_iterator i=S.begin();

   552 // 	  i!=S.end(); ++i) {

   553 // 	for(OutEdgeIt e=G.template first<OutEdgeIt>(*i); e.valid(); ++e) {

   554 // 	  a+=flow.get(e);

   555 // 	}

   556 // 	for(InEdgeIt e=G.template first<InEdgeIt>(*i); e.valid(); ++e) {

   557 // 	  a-=flow.get(e);

   558 // 	}

   559 //       }

   560 //       return a;

   561 //     }

   562 //   };

   566 } // namespace hugo

   568 #endif //EDMONDS_KARP_HH

author	alpar
	Wed, 10 Mar 2004 17:47:54 +0000
changeset 164	970b265696b0
parent 148	004fdf703abb
child 168	27fbd1559fb7
permissions	-rw-r--r--