marci@478: // -*- C++ -*-
marci@478: 
marci@478: /*
marci@615:   Heuristics:
marci@485:   2 phase
marci@485:   gap
marci@485:   list 'level_list' on the nodes on level i implemented by hand
marci@485:   stack 'active' on the active nodes on level i
marci@485:   runs heuristic 'highest label' for H1*n relabels
marci@485:   runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label'
marci@615: 
marci@485:   Parameters H0 and H1 are initialized to 20 and 1.
marci@478: 
marci@485:   Constructors:
marci@478: 
marci@615:   Preflow(Graph, Node, Node, CapMap, FlowMap, bool) : bool must be false if
marci@485:   FlowMap is not constant zero, and should be true if it is
marci@478: 
marci@485:   Members:
marci@478: 
marci@485:   void run()
marci@478: 
marci@485:   Num flowValue() : returns the value of a maximum flow
marci@478: 
marci@615:   void minMinCut(CutMap& M) : sets M to the characteristic vector of the
marci@485:   minimum min cut. M should be a map of bools initialized to false. ??Is it OK?
marci@478: 
marci@615:   void maxMinCut(CutMap& M) : sets M to the characteristic vector of the
marci@485:   maximum min cut. M should be a map of bools initialized to false.
marci@478: 
marci@615:   void minCut(CutMap& M) : sets M to the characteristic vector of
marci@485:   a min cut. M should be a map of bools initialized to false.
marci@478: 
marci@478: */
marci@478: 
marci@480: #ifndef HUGO_MAX_FLOW_H
marci@480: #define HUGO_MAX_FLOW_H
marci@478: 
marci@478: #include <vector>
marci@478: #include <queue>
marci@478: #include <stack>
marci@478: 
marci@557: #include <hugo/graph_wrapper.h>
marci@602: #include <bfs_dfs.h>
marci@555: #include <hugo/invalid.h>
marci@555: #include <hugo/maps.h>
marci@478: #include <for_each_macros.h>
marci@478: 
marci@488: /// \file
marci@615: /// \brief Maximum flows.
marci@615: /// \ingroup galgs
marci@478: 
marci@478: namespace hugo {
marci@478: 
marci@488: 
marci@602:   //  ///\author Marton Makai, Jacint Szabo
marci@488:   /// A class for computing max flows and related quantities.
marci@615:   /// \ingroup galgs
marci@615:   template <typename Graph, typename Num,
marci@615: 	    typename CapMap=typename Graph::template EdgeMap<Num>,
marci@478:             typename FlowMap=typename Graph::template EdgeMap<Num> >
marci@478:   class MaxFlow {
marci@615:   protected:
marci@478:     typedef typename Graph::Node Node;
marci@478:     typedef typename Graph::NodeIt NodeIt;
marci@478:     typedef typename Graph::OutEdgeIt OutEdgeIt;
marci@478:     typedef typename Graph::InEdgeIt InEdgeIt;
marci@478: 
marci@478:     typedef typename std::vector<std::stack<Node> > VecStack;
marci@478:     typedef typename Graph::template NodeMap<Node> NNMap;
marci@478:     typedef typename std::vector<Node> VecNode;
marci@478: 
marci@478:     const Graph* g;
marci@478:     Node s;
marci@478:     Node t;
marci@615:     const CapMap* capacity;
marci@478:     FlowMap* flow;
marci@478:     int n;      //the number of nodes of G
marci@478:     typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW;
marci@478:     typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt;
marci@478:     typedef typename ResGW::Edge ResGWEdge;
marci@478:     //typedef typename ResGW::template NodeMap<bool> ReachedMap;
marci@478:     typedef typename Graph::template NodeMap<int> ReachedMap;
marci@478:     ReachedMap level;
marci@615:     //level works as a bool map in augmenting path algorithms
marci@478:     //and is used by bfs for storing reached information.
marci@478:     //In preflow, it shows levels of nodes.
marci@615:     //typename Graph::template NodeMap<int> level;
marci@615:     typename Graph::template NodeMap<Num> excess;
marci@602:     //   protected:
marci@602:     //     MaxFlow() { }
marci@615:     //     void set(const Graph& _G, Node _s, Node _t, const CapMap& _capacity,
marci@615:     // 	     FlowMap& _flow)
marci@602:     //       {
marci@615:     // 	g=&_G;
marci@615:     // 	s=_s;
marci@615:     // 	t=_t;
marci@602:     // 	capacity=&_capacity;
marci@602:     // 	flow=&_flow;
marci@602:     // 	n=_G.nodeNum;
marci@615:     // 	level.set (_G); //kellene vmi ilyesmi fv
marci@602:     // 	excess(_G,0); //itt is
marci@602:     //       }
marci@478: 
marci@615:     // constants used for heuristics
marci@615:     static const int H0=20;
marci@615:     static const int H1=1;
marci@615: 
marci@478:   public:
marci@615: 
alpar@586:     ///\todo Document this.
alpar@586:     ///\todo Maybe, it should be PRE_FLOW instead.
marci@615:     ///- \c NO_FLOW means nothing,
alpar@586:     ///- \c ZERO_FLOW means something,
alpar@586:     ///- \c GEN_FLOW means something else,
marci@615:     ///- \c PRE_FLOW is something different.
marci@478:     enum flowEnum{
marci@615:       ZERO_FLOW,
marci@615:       GEN_FLOW,
marci@615:       PRE_FLOW,
marci@615:       NO_FLOW
marci@478:     };
marci@478: 
marci@615:     MaxFlow(const Graph& _G, Node _s, Node _t, const CapMap& _capacity,
marci@478: 	    FlowMap& _flow) :
marci@615:       g(&_G), s(_s), t(_t), capacity(&_capacity),
marci@478:       flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0) {}
marci@478: 
marci@485:     /// A max flow algorithm is run.
marci@615:     /// \pre The flow have to satisfy the requirements
marci@615:     /// stated in fe.
marci@615:     void run(flowEnum fe=ZERO_FLOW) {
marci@615:       preflow(fe);
marci@478:     }
marci@615: 
marci@615:     /// A preflow algorithm is run.
marci@615:     /// \pre The initial edge-map have to be a
marci@487:     /// zero flow if \c fe is \c ZERO_FLOW,
marci@615:     /// a flow if \c fe is \c GEN_FLOW,
marci@615:     /// a pre-flow if fe is \c PRE_FLOW and
marci@615:     /// anything if fe is NO_FLOW.
marci@488:     void preflow(flowEnum fe) {
marci@478:       preflowPhase0(fe);
marci@478:       preflowPhase1();
marci@478:     }
marci@478: 
marci@615:     /// Run the first phase of preflow, starting from a 0 flow, from a flow,
marci@615:     /// or from a preflow, of from undefined value according to \c fe.
marci@615:     void preflowPhase0(flowEnum fe);
marci@478: 
marci@485:     /// Second phase of preflow.
marci@478:     void preflowPhase1();
marci@478: 
marci@615:     /// Starting from a flow, this method searches for an augmenting path
marci@615:     /// according to the Edmonds-Karp algorithm
marci@615:     /// and augments the flow on if any.
marci@487:     /// The return value shows if the augmentation was succesful.
marci@478:     bool augmentOnShortestPath();
marci@478: 
marci@615:     /// Starting from a flow, this method searches for an augmenting blocking
marci@615:     /// flow according to Dinits' algorithm and augments the flow on if any.
marci@615:     /// The blocking flow is computed in a physically constructed
marci@485:     /// residual graph of type \c Mutablegraph.
marci@487:     /// The return value show sif the augmentation was succesful.
marci@478:     template<typename MutableGraph> bool augmentOnBlockingFlow();
marci@478: 
marci@615:     /// The same as \c augmentOnBlockingFlow<MutableGraph> but the
marci@485:     /// residual graph is not constructed physically.
marci@487:     /// The return value shows if the augmentation was succesful.
marci@478:     bool augmentOnBlockingFlow2();
marci@478: 
marci@478:     /// Returns the actual flow value.
marci@615:     /// More precisely, it returns the negative excess of s, thus
marci@478:     /// this works also for preflows.
marci@615:     Num flowValue() {
marci@478:       Num a=0;
marci@615:       FOR_EACH_INC_LOC(InEdgeIt, e, *g, t) a+=(*flow)[e];
marci@615:       FOR_EACH_INC_LOC(OutEdgeIt, e, *g, t) a-=(*flow)[e];
marci@478:       return a;
marci@478:     }
marci@478: 
marci@485:     /// Should be used between preflowPhase0 and preflowPhase1.
marci@615:     /// \todo We have to make some status variable which shows the
marci@615:     /// actual state
marci@615:     /// of the class. This enables us to determine which methods are valid
marci@485:     /// for MinCut computation
marci@478:     template<typename _CutMap>
marci@478:     void actMinCut(_CutMap& M) {
marci@478:       NodeIt v;
marci@485:       for(g->first(v); g->valid(v); g->next(v)) {
marci@485: 	if ( level[v] < n ) {
marci@485: 	  M.set(v,false);
marci@485: 	} else {
marci@485: 	  M.set(v,true);
marci@485: 	}
marci@478:       }
marci@478:     }
marci@478: 
marci@615:     /// The unique inclusionwise minimum cut is computed by
marci@485:     /// processing a bfs from s in the residual graph.
marci@615:     /// \pre flow have to be a max flow otherwise it will the whole node-set.
marci@478:     template<typename _CutMap>
marci@478:     void minMinCut(_CutMap& M) {
marci@615: 
marci@478:       std::queue<Node> queue;
marci@615: 
marci@615:       M.set(s,true);
marci@478:       queue.push(s);
marci@478: 
marci@478:       while (!queue.empty()) {
marci@478:         Node w=queue.front();
marci@478: 	queue.pop();
marci@478: 
marci@478: 	OutEdgeIt e;
marci@478: 	for(g->first(e,w) ; g->valid(e); g->next(e)) {
marci@478: 	  Node v=g->head(e);
marci@478: 	  if (!M[v] && (*flow)[e] < (*capacity)[e] ) {
marci@478: 	    queue.push(v);
marci@478: 	    M.set(v, true);
marci@478: 	  }
marci@615: 	}
marci@478: 
marci@478: 	InEdgeIt f;
marci@478: 	for(g->first(f,w) ; g->valid(f); g->next(f)) {
marci@478: 	  Node v=g->tail(f);
marci@478: 	  if (!M[v] && (*flow)[f] > 0 ) {
marci@478: 	    queue.push(v);
marci@478: 	    M.set(v, true);
marci@478: 	  }
marci@615: 	}
marci@478:       }
marci@478:     }
marci@478: 
marci@478: 
marci@615:     /// The unique inclusionwise maximum cut is computed by
marci@485:     /// processing a reverse bfs from t in the residual graph.
marci@615:     /// \pre flow have to be a max flow otherwise it will be empty.
marci@478:     template<typename _CutMap>
marci@478:     void maxMinCut(_CutMap& M) {
marci@478: 
marci@478:       NodeIt v;
marci@478:       for(g->first(v) ; g->valid(v); g->next(v)) {
marci@478: 	M.set(v, true);
marci@478:       }
marci@478: 
marci@478:       std::queue<Node> queue;
marci@615: 
marci@615:       M.set(t,false);
marci@478:       queue.push(t);
marci@478: 
marci@478:       while (!queue.empty()) {
marci@478:         Node w=queue.front();
marci@478: 	queue.pop();
marci@478: 
marci@478: 	InEdgeIt e;
marci@478: 	for(g->first(e,w) ; g->valid(e); g->next(e)) {
marci@478: 	  Node v=g->tail(e);
marci@478: 	  if (M[v] && (*flow)[e] < (*capacity)[e] ) {
marci@478: 	    queue.push(v);
marci@478: 	    M.set(v, false);
marci@478: 	  }
marci@478: 	}
marci@615: 
marci@478: 	OutEdgeIt f;
marci@478: 	for(g->first(f,w) ; g->valid(f); g->next(f)) {
marci@478: 	  Node v=g->head(f);
marci@478: 	  if (M[v] && (*flow)[f] > 0 ) {
marci@478: 	    queue.push(v);
marci@478: 	    M.set(v, false);
marci@478: 	  }
marci@478: 	}
marci@478:       }
marci@478:     }
marci@478: 
marci@478: 
marci@485:     /// A minimum cut is computed.
marci@478:     template<typename CutMap>
marci@485:     void minCut(CutMap& M) { minMinCut(M); }
marci@478: 
marci@485:     ///
marci@487:     void resetSource(Node _s) { s=_s; }
marci@487:     ///
marci@487:     void resetTarget(Node _t) { t=_t; }
marci@615: 
marci@485:     /// capacity-map is changed.
marci@485:     void resetCap(const CapMap& _cap) { capacity=&_cap; }
marci@615: 
marci@615:     /// flow-map is changed.
marci@485:     void resetFlow(FlowMap& _flow) { flow=&_flow; }
marci@478: 
marci@478: 
marci@478:   private:
marci@478: 
marci@478:     int push(Node w, VecStack& active) {
marci@615: 
marci@478:       int lev=level[w];
marci@478:       Num exc=excess[w];
marci@478:       int newlevel=n;       //bound on the next level of w
marci@615: 
marci@478:       OutEdgeIt e;
marci@478:       for(g->first(e,w); g->valid(e); g->next(e)) {
marci@615: 
marci@615: 	if ( (*flow)[e] >= (*capacity)[e] ) continue;
marci@615: 	Node v=g->head(e);
marci@615: 
marci@478: 	if( lev > level[v] ) { //Push is allowed now
marci@615: 
marci@478: 	  if ( excess[v]<=0 && v!=t && v!=s ) {
marci@478: 	    int lev_v=level[v];
marci@478: 	    active[lev_v].push(v);
marci@478: 	  }
marci@615: 
marci@478: 	  Num cap=(*capacity)[e];
marci@478: 	  Num flo=(*flow)[e];
marci@478: 	  Num remcap=cap-flo;
marci@615: 
marci@478: 	  if ( remcap >= exc ) { //A nonsaturating push.
marci@615: 
marci@478: 	    flow->set(e, flo+exc);
marci@478: 	    excess.set(v, excess[v]+exc);
marci@478: 	    exc=0;
marci@615: 	    break;
marci@615: 
marci@478: 	  } else { //A saturating push.
marci@478: 	    flow->set(e, cap);
marci@478: 	    excess.set(v, excess[v]+remcap);
marci@478: 	    exc-=remcap;
marci@478: 	  }
marci@478: 	} else if ( newlevel > level[v] ) newlevel = level[v];
marci@615:       } //for out edges wv
marci@615: 
marci@615:       if ( exc > 0 ) {
marci@478: 	InEdgeIt e;
marci@478: 	for(g->first(e,w); g->valid(e); g->next(e)) {
marci@615: 
marci@615: 	  if( (*flow)[e] <= 0 ) continue;
marci@615: 	  Node v=g->tail(e);
marci@615: 
marci@478: 	  if( lev > level[v] ) { //Push is allowed now
marci@615: 
marci@478: 	    if ( excess[v]<=0 && v!=t && v!=s ) {
marci@478: 	      int lev_v=level[v];
marci@478: 	      active[lev_v].push(v);
marci@478: 	    }
marci@615: 
marci@478: 	    Num flo=(*flow)[e];
marci@615: 
marci@478: 	    if ( flo >= exc ) { //A nonsaturating push.
marci@615: 
marci@478: 	      flow->set(e, flo-exc);
marci@478: 	      excess.set(v, excess[v]+exc);
marci@478: 	      exc=0;
marci@615: 	      break;
marci@478: 	    } else {  //A saturating push.
marci@615: 
marci@478: 	      excess.set(v, excess[v]+flo);
marci@478: 	      exc-=flo;
marci@478: 	      flow->set(e,0);
marci@615: 	    }
marci@478: 	  } else if ( newlevel > level[v] ) newlevel = level[v];
marci@478: 	} //for in edges vw
marci@615: 
marci@478:       } // if w still has excess after the out edge for cycle
marci@615: 
marci@478:       excess.set(w, exc);
marci@615: 
marci@478:       return newlevel;
marci@485:     }
marci@478: 
marci@478: 
marci@615:     void preflowPreproc(flowEnum fe, VecStack& active,
marci@615: 			VecNode& level_list, NNMap& left, NNMap& right)
marci@602:     {
marci@615:       std::queue<Node> bfs_queue;
marci@478: 
marci@615:       switch (fe) {
marci@615:       case ZERO_FLOW:
marci@602: 	{
marci@602: 	  //Reverse_bfs from t, to find the starting level.
marci@602: 	  level.set(t,0);
marci@602: 	  bfs_queue.push(t);
marci@615: 
marci@602: 	  while (!bfs_queue.empty()) {
marci@615: 
marci@615: 	    Node v=bfs_queue.front();
marci@602: 	    bfs_queue.pop();
marci@602: 	    int l=level[v]+1;
marci@615: 
marci@602: 	    InEdgeIt e;
marci@602: 	    for(g->first(e,v); g->valid(e); g->next(e)) {
marci@602: 	      Node w=g->tail(e);
marci@602: 	      if ( level[w] == n && w != s ) {
marci@602: 		bfs_queue.push(w);
marci@602: 		Node first=level_list[l];
marci@602: 		if ( g->valid(first) ) left.set(first,w);
marci@602: 		right.set(w,first);
marci@602: 		level_list[l]=w;
marci@602: 		level.set(w, l);
marci@602: 	      }
marci@602: 	    }
marci@602: 	  }
marci@615: 
marci@602: 	  //the starting flow
marci@602: 	  OutEdgeIt e;
marci@615: 	  for(g->first(e,s); g->valid(e); g->next(e))
marci@602: 	    {
marci@602: 	      Num c=(*capacity)[e];
marci@602: 	      if ( c <= 0 ) continue;
marci@602: 	      Node w=g->head(e);
marci@615: 	      if ( level[w] < n ) {
marci@602: 		if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w);
marci@615: 		flow->set(e, c);
marci@602: 		excess.set(w, excess[w]+c);
marci@602: 	      }
marci@602: 	    }
marci@602: 	  break;
marci@602: 	}
marci@615: 
marci@602:       case GEN_FLOW:
marci@615:       case PRE_FLOW:
marci@602: 	{
marci@615: 	  //Reverse_bfs from t in the residual graph,
marci@602: 	  //to find the starting level.
marci@602: 	  level.set(t,0);
marci@602: 	  bfs_queue.push(t);
marci@615: 
marci@602: 	  while (!bfs_queue.empty()) {
marci@615: 
marci@615: 	    Node v=bfs_queue.front();
marci@602: 	    bfs_queue.pop();
marci@602: 	    int l=level[v]+1;
marci@615: 
marci@602: 	    InEdgeIt e;
marci@602: 	    for(g->first(e,v); g->valid(e); g->next(e)) {
marci@602: 	      if ( (*capacity)[e] <= (*flow)[e] ) continue;
marci@602: 	      Node w=g->tail(e);
marci@602: 	      if ( level[w] == n && w != s ) {
marci@602: 		bfs_queue.push(w);
marci@602: 		Node first=level_list[l];
marci@602: 		if ( g->valid(first) ) left.set(first,w);
marci@602: 		right.set(w,first);
marci@602: 		level_list[l]=w;
marci@602: 		level.set(w, l);
marci@602: 	      }
marci@602: 	    }
marci@615: 
marci@602: 	    OutEdgeIt f;
marci@602: 	    for(g->first(f,v); g->valid(f); g->next(f)) {
marci@602: 	      if ( 0 >= (*flow)[f] ) continue;
marci@602: 	      Node w=g->head(f);
marci@602: 	      if ( level[w] == n && w != s ) {
marci@602: 		bfs_queue.push(w);
marci@602: 		Node first=level_list[l];
marci@602: 		if ( g->valid(first) ) left.set(first,w);
marci@602: 		right.set(w,first);
marci@602: 		level_list[l]=w;
marci@602: 		level.set(w, l);
marci@602: 	      }
marci@602: 	    }
marci@602: 	  }
marci@615: 
marci@615: 
marci@602: 	  //the starting flow
marci@602: 	  OutEdgeIt e;
marci@615: 	  for(g->first(e,s); g->valid(e); g->next(e))
marci@602: 	    {
marci@602: 	      Num rem=(*capacity)[e]-(*flow)[e];
marci@602: 	      if ( rem <= 0 ) continue;
marci@602: 	      Node w=g->head(e);
marci@615: 	      if ( level[w] < n ) {
marci@602: 		if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w);
marci@615: 		flow->set(e, (*capacity)[e]);
marci@602: 		excess.set(w, excess[w]+rem);
marci@602: 	      }
marci@602: 	    }
marci@615: 
marci@602: 	  InEdgeIt f;
marci@615: 	  for(g->first(f,s); g->valid(f); g->next(f))
marci@602: 	    {
marci@602: 	      if ( (*flow)[f] <= 0 ) continue;
marci@602: 	      Node w=g->tail(f);
marci@615: 	      if ( level[w] < n ) {
marci@602: 		if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w);
marci@602: 		excess.set(w, excess[w]+(*flow)[f]);
marci@615: 		flow->set(f, 0);
marci@602: 	      }
marci@615: 	    }
marci@602: 	  break;
marci@615: 	} //case PRE_FLOW
marci@602:       }
marci@602:     } //preflowPreproc
marci@478: 
marci@478: 
marci@478: 
marci@615:     void relabel(Node w, int newlevel, VecStack& active,
marci@615: 		 VecNode& level_list, NNMap& left,
marci@615: 		 NNMap& right, int& b, int& k, bool what_heur )
marci@478:     {
marci@478: 
marci@615:       Num lev=level[w];
marci@615: 
marci@478:       Node right_n=right[w];
marci@478:       Node left_n=left[w];
marci@615: 
marci@478:       //unlacing starts
marci@478:       if ( g->valid(right_n) ) {
marci@478: 	if ( g->valid(left_n) ) {
marci@478: 	  right.set(left_n, right_n);
marci@478: 	  left.set(right_n, left_n);
marci@478: 	} else {
marci@615: 	  level_list[lev]=right_n;
marci@478: 	  left.set(right_n, INVALID);
marci@615: 	}
marci@478:       } else {
marci@478: 	if ( g->valid(left_n) ) {
marci@478: 	  right.set(left_n, INVALID);
marci@615: 	} else {
marci@615: 	  level_list[lev]=INVALID;
marci@615: 	}
marci@615:       }
marci@478:       //unlacing ends
marci@615: 
marci@478:       if ( !g->valid(level_list[lev]) ) {
marci@615: 
marci@478: 	//gapping starts
marci@478: 	for (int i=lev; i!=k ; ) {
marci@478: 	  Node v=level_list[++i];
marci@478: 	  while ( g->valid(v) ) {
marci@478: 	    level.set(v,n);
marci@478: 	    v=right[v];
marci@478: 	  }
marci@478: 	  level_list[i]=INVALID;
marci@478: 	  if ( !what_heur ) {
marci@478: 	    while ( !active[i].empty() ) {
marci@478: 	      active[i].pop();    //FIXME: ezt szebben kene
marci@478: 	    }
marci@615: 	  }
marci@478: 	}
marci@615: 
marci@478: 	level.set(w,n);
marci@478: 	b=lev-1;
marci@478: 	k=b;
marci@478: 	//gapping ends
marci@615: 
marci@478:       } else {
marci@615: 
marci@615: 	if ( newlevel == n ) level.set(w,n);
marci@478: 	else {
marci@478: 	  level.set(w,++newlevel);
marci@478: 	  active[newlevel].push(w);
marci@478: 	  if ( what_heur ) b=newlevel;
marci@478: 	  if ( k < newlevel ) ++k;      //now k=newlevel
marci@478: 	  Node first=level_list[newlevel];
marci@478: 	  if ( g->valid(first) ) left.set(first,w);
marci@478: 	  right.set(w,first);
marci@478: 	  left.set(w,INVALID);
marci@478: 	  level_list[newlevel]=w;
marci@478: 	}
marci@478:       }
marci@615: 
marci@478:     } //relabel
marci@478: 
marci@478: 
marci@615:     template<typename MapGraphWrapper>
marci@478:     class DistanceMap {
marci@478:     protected:
marci@478:       const MapGraphWrapper* g;
marci@615:       typename MapGraphWrapper::template NodeMap<int> dist;
marci@478:     public:
marci@478:       DistanceMap(MapGraphWrapper& _g) : g(&_g), dist(*g, g->nodeNum()) { }
marci@615:       void set(const typename MapGraphWrapper::Node& n, int a) {
marci@615: 	dist.set(n, a);
marci@478:       }
marci@615:       int operator[](const typename MapGraphWrapper::Node& n)
marci@485:       { return dist[n]; }
marci@615:       //       int get(const typename MapGraphWrapper::Node& n) const {
marci@485:       // 	return dist[n]; }
marci@615:       //       bool get(const typename MapGraphWrapper::Edge& e) const {
marci@485:       // 	return (dist.get(g->tail(e))<dist.get(g->head(e))); }
marci@615:       bool operator[](const typename MapGraphWrapper::Edge& e) const {
marci@615: 	return (dist[g->tail(e)]<dist[g->head(e)]);
marci@478:       }
marci@478:     };
marci@615: 
marci@478:   };
marci@478: 
marci@478: 
marci@478:   template <typename Graph, typename Num, typename CapMap, typename FlowMap>
marci@615:   void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase0( flowEnum fe )
marci@478:   {
marci@615: 
marci@615:     int heur0=(int)(H0*n);  //time while running 'bound decrease'
marci@485:     int heur1=(int)(H1*n);  //time while running 'highest label'
marci@485:     int heur=heur1;         //starting time interval (#of relabels)
marci@485:     int numrelabel=0;
marci@615: 
marci@615:     bool what_heur=1;
marci@485:     //It is 0 in case 'bound decrease' and 1 in case 'highest label'
marci@478: 
marci@615:     bool end=false;
marci@615:     //Needed for 'bound decrease', true means no active nodes are above bound
marci@615:     //b.
marci@478: 
marci@485:     int k=n-2;  //bound on the highest level under n containing a node
marci@485:     int b=k;    //bound on the highest level under n of an active node
marci@615: 
marci@485:     VecStack active(n);
marci@615: 
marci@485:     NNMap left(*g, INVALID);
marci@485:     NNMap right(*g, INVALID);
marci@485:     VecNode level_list(n,INVALID);
marci@485:     //List of the nodes in level i<n, set to n.
marci@478: 
marci@485:     NodeIt v;
marci@485:     for(g->first(v); g->valid(v); g->next(v)) level.set(v,n);
marci@485:     //setting each node to level n
marci@615: 
marci@615:     switch (fe) {
marci@615:     case PRE_FLOW:
marci@485:       {
marci@615: 	//computing the excess
marci@485: 	NodeIt v;
marci@485: 	for(g->first(v); g->valid(v); g->next(v)) {
marci@478: 	  Num exc=0;
marci@615: 
marci@478: 	  InEdgeIt e;
marci@485: 	  for(g->first(e,v); g->valid(e); g->next(e)) exc+=(*flow)[e];
marci@478: 	  OutEdgeIt f;
marci@485: 	  for(g->first(f,v); g->valid(f); g->next(f)) exc-=(*flow)[f];
marci@615: 
marci@615: 	  excess.set(v,exc);
marci@615: 
marci@485: 	  //putting the active nodes into the stack
marci@485: 	  int lev=level[v];
marci@485: 	  if ( exc > 0 && lev < n && v != t ) active[lev].push(v);
marci@478: 	}
marci@478: 	break;
marci@478:       }
marci@485:     case GEN_FLOW:
marci@485:       {
marci@615: 	//computing the excess of t
marci@485: 	Num exc=0;
marci@615: 
marci@485: 	InEdgeIt e;
marci@485: 	for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e];
marci@485: 	OutEdgeIt f;
marci@485: 	for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f];
marci@615: 
marci@615: 	excess.set(t,exc);
marci@615: 
marci@485: 	break;
marci@485:       }
marci@615:     default:;
marci@485:     }
marci@615: 
marci@615:     preflowPreproc(fe, active, level_list, left, right);
marci@615:     //End of preprocessing
marci@615: 
marci@615: 
marci@485:     //Push/relabel on the highest level active nodes.
marci@485:     while ( true ) {
marci@485:       if ( b == 0 ) {
marci@485: 	if ( !what_heur && !end && k > 0 ) {
marci@485: 	  b=k;
marci@485: 	  end=true;
marci@485: 	} else break;
marci@485:       }
marci@615: 
marci@615:       if ( active[b].empty() ) --b;
marci@485:       else {
marci@615: 	end=false;
marci@485: 	Node w=active[b].top();
marci@485: 	active[b].pop();
marci@485: 	int newlevel=push(w,active);
marci@615: 	if ( excess[w] > 0 ) relabel(w, newlevel, active, level_list,
marci@485: 				     left, right, b, k, what_heur);
marci@615: 
marci@615: 	++numrelabel;
marci@485: 	if ( numrelabel >= heur ) {
marci@485: 	  numrelabel=0;
marci@485: 	  if ( what_heur ) {
marci@485: 	    what_heur=0;
marci@485: 	    heur=heur0;
marci@485: 	    end=false;
marci@485: 	  } else {
marci@485: 	    what_heur=1;
marci@485: 	    heur=heur1;
marci@615: 	    b=k;
marci@485: 	  }
marci@478: 	}
marci@615:       }
marci@615:     }
marci@485:   }
marci@478: 
marci@478: 
marci@478: 
marci@478:   template <typename Graph, typename Num, typename CapMap, typename FlowMap>
marci@615:   void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase1()
marci@478:   {
marci@615: 
marci@485:     int k=n-2;  //bound on the highest level under n containing a node
marci@485:     int b=k;    //bound on the highest level under n of an active node
marci@615: 
marci@485:     VecStack active(n);
marci@485:     level.set(s,0);
marci@485:     std::queue<Node> bfs_queue;
marci@485:     bfs_queue.push(s);
marci@615: 
marci@485:     while (!bfs_queue.empty()) {
marci@615: 
marci@615:       Node v=bfs_queue.front();
marci@485:       bfs_queue.pop();
marci@485:       int l=level[v]+1;
marci@615: 
marci@485:       InEdgeIt e;
marci@485:       for(g->first(e,v); g->valid(e); g->next(e)) {
marci@485: 	if ( (*capacity)[e] <= (*flow)[e] ) continue;
marci@485: 	Node u=g->tail(e);
marci@615: 	if ( level[u] >= n ) {
marci@485: 	  bfs_queue.push(u);
marci@485: 	  level.set(u, l);
marci@485: 	  if ( excess[u] > 0 ) active[l].push(u);
marci@478: 	}
marci@478:       }
marci@615: 
marci@485:       OutEdgeIt f;
marci@485:       for(g->first(f,v); g->valid(f); g->next(f)) {
marci@485: 	if ( 0 >= (*flow)[f] ) continue;
marci@485: 	Node u=g->head(f);
marci@615: 	if ( level[u] >= n ) {
marci@485: 	  bfs_queue.push(u);
marci@485: 	  level.set(u, l);
marci@485: 	  if ( excess[u] > 0 ) active[l].push(u);
marci@485: 	}
marci@485:       }
marci@485:     }
marci@485:     b=n-2;
marci@478: 
marci@485:     while ( true ) {
marci@615: 
marci@485:       if ( b == 0 ) break;
marci@478: 
marci@615:       if ( active[b].empty() ) --b;
marci@485:       else {
marci@485: 	Node w=active[b].top();
marci@485: 	active[b].pop();
marci@615: 	int newlevel=push(w,active);
marci@478: 
marci@485: 	//relabel
marci@485: 	if ( excess[w] > 0 ) {
marci@485: 	  level.set(w,++newlevel);
marci@485: 	  active[newlevel].push(w);
marci@485: 	  b=newlevel;
marci@485: 	}
marci@485:       }  // if stack[b] is nonempty
marci@485:     } // while(true)
marci@485:   }
marci@478: 
marci@478: 
marci@478: 
marci@478:   template <typename Graph, typename Num, typename CapMap, typename FlowMap>
marci@615:   bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath()
marci@478:   {
marci@485:     ResGW res_graph(*g, *capacity, *flow);
marci@485:     bool _augment=false;
marci@615: 
marci@485:     //ReachedMap level(res_graph);
marci@485:     FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
marci@485:     BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);
marci@485:     bfs.pushAndSetReached(s);
marci@615: 
marci@615:     typename ResGW::template NodeMap<ResGWEdge> pred(res_graph);
marci@485:     pred.set(s, INVALID);
marci@615: 
marci@485:     typename ResGW::template NodeMap<Num> free(res_graph);
marci@615: 
marci@485:     //searching for augmenting path
marci@615:     while ( !bfs.finished() ) {
marci@485:       ResGWOutEdgeIt e=bfs;
marci@485:       if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {
marci@485: 	Node v=res_graph.tail(e);
marci@485: 	Node w=res_graph.head(e);
marci@485: 	pred.set(w, e);
marci@485: 	if (res_graph.valid(pred[v])) {
marci@485: 	  free.set(w, std::min(free[v], res_graph.resCap(e)));
marci@485: 	} else {
marci@615: 	  free.set(w, res_graph.resCap(e));
marci@478: 	}
marci@485: 	if (res_graph.head(e)==t) { _augment=true; break; }
marci@485:       }
marci@615: 
marci@485:       ++bfs;
marci@485:     } //end of searching augmenting path
marci@478: 
marci@485:     if (_augment) {
marci@485:       Node n=t;
marci@485:       Num augment_value=free[t];
marci@615:       while (res_graph.valid(pred[n])) {
marci@485: 	ResGWEdge e=pred[n];
marci@615: 	res_graph.augment(e, augment_value);
marci@485: 	n=res_graph.tail(e);
marci@478:       }
marci@485:     }
marci@478: 
marci@485:     return _augment;
marci@485:   }
marci@478: 
marci@478: 
marci@478: 
marci@478: 
marci@478: 
marci@478: 
marci@478: 
marci@478:   template <typename Graph, typename Num, typename CapMap, typename FlowMap>
marci@615:   template<typename MutableGraph>
marci@615:   bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow()
marci@615:   {
marci@485:     typedef MutableGraph MG;
marci@485:     bool _augment=false;
marci@478: 
marci@485:     ResGW res_graph(*g, *capacity, *flow);
marci@478: 
marci@485:     //bfs for distances on the residual graph
marci@485:     //ReachedMap level(res_graph);
marci@485:     FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
marci@485:     BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);
marci@485:     bfs.pushAndSetReached(s);
marci@615:     typename ResGW::template NodeMap<int>
marci@485:       dist(res_graph); //filled up with 0's
marci@478: 
marci@485:     //F will contain the physical copy of the residual graph
marci@485:     //with the set of edges which are on shortest paths
marci@485:     MG F;
marci@615:     typename ResGW::template NodeMap<typename MG::Node>
marci@485:       res_graph_to_F(res_graph);
marci@485:     {
marci@485:       typename ResGW::NodeIt n;
marci@485:       for(res_graph.first(n); res_graph.valid(n); res_graph.next(n)) {
marci@485: 	res_graph_to_F.set(n, F.addNode());
marci@478:       }
marci@485:     }
marci@478: 
marci@485:     typename MG::Node sF=res_graph_to_F[s];
marci@485:     typename MG::Node tF=res_graph_to_F[t];
marci@485:     typename MG::template EdgeMap<ResGWEdge> original_edge(F);
marci@485:     typename MG::template EdgeMap<Num> residual_capacity(F);
marci@478: 
marci@615:     while ( !bfs.finished() ) {
marci@485:       ResGWOutEdgeIt e=bfs;
marci@485:       if (res_graph.valid(e)) {
marci@485: 	if (bfs.isBNodeNewlyReached()) {
marci@485: 	  dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1);
marci@615: 	  typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)],
marci@615: 					res_graph_to_F[res_graph.head(e)]);
marci@485: 	  original_edge.update();
marci@485: 	  original_edge.set(f, e);
marci@485: 	  residual_capacity.update();
marci@485: 	  residual_capacity.set(f, res_graph.resCap(e));
marci@485: 	} else {
marci@485: 	  if (dist[res_graph.head(e)]==(dist[res_graph.tail(e)]+1)) {
marci@615: 	    typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)],
marci@615: 					  res_graph_to_F[res_graph.head(e)]);
marci@478: 	    original_edge.update();
marci@478: 	    original_edge.set(f, e);
marci@478: 	    residual_capacity.update();
marci@478: 	    residual_capacity.set(f, res_graph.resCap(e));
marci@478: 	  }
marci@478: 	}
marci@485:       }
marci@485:       ++bfs;
marci@485:     } //computing distances from s in the residual graph
marci@478: 
marci@485:     bool __augment=true;
marci@478: 
marci@485:     while (__augment) {
marci@485:       __augment=false;
marci@485:       //computing blocking flow with dfs
marci@485:       DfsIterator< MG, typename MG::template NodeMap<bool> > dfs(F);
marci@485:       typename MG::template NodeMap<typename MG::Edge> pred(F);
marci@485:       pred.set(sF, INVALID);
marci@485:       //invalid iterators for sources
marci@478: 
marci@485:       typename MG::template NodeMap<Num> free(F);
marci@478: 
marci@615:       dfs.pushAndSetReached(sF);
marci@485:       while (!dfs.finished()) {
marci@485: 	++dfs;
marci@485: 	if (F.valid(/*typename MG::OutEdgeIt*/(dfs))) {
marci@485: 	  if (dfs.isBNodeNewlyReached()) {
marci@485: 	    typename MG::Node v=F.aNode(dfs);
marci@485: 	    typename MG::Node w=F.bNode(dfs);
marci@485: 	    pred.set(w, dfs);
marci@485: 	    if (F.valid(pred[v])) {
marci@485: 	      free.set(w, std::min(free[v], residual_capacity[dfs]));
marci@485: 	    } else {
marci@615: 	      free.set(w, residual_capacity[dfs]);
marci@485: 	    }
marci@615: 	    if (w==tF) {
marci@615: 	      __augment=true;
marci@485: 	      _augment=true;
marci@615: 	      break;
marci@485: 	    }
marci@615: 
marci@485: 	  } else {
marci@485: 	    F.erase(/*typename MG::OutEdgeIt*/(dfs));
marci@485: 	  }
marci@615: 	}
marci@485:       }
marci@485: 
marci@485:       if (__augment) {
marci@485: 	typename MG::Node n=tF;
marci@485: 	Num augment_value=free[tF];
marci@615: 	while (F.valid(pred[n])) {
marci@485: 	  typename MG::Edge e=pred[n];
marci@615: 	  res_graph.augment(original_edge[e], augment_value);
marci@485: 	  n=F.tail(e);
marci@615: 	  if (residual_capacity[e]==augment_value)
marci@615: 	    F.erase(e);
marci@615: 	  else
marci@485: 	    residual_capacity.set(e, residual_capacity[e]-augment_value);
marci@478: 	}
marci@485:       }
marci@615: 
marci@485:     }
marci@615: 
marci@485:     return _augment;
marci@485:   }
marci@478: 
marci@478: 
marci@478: 
marci@478: 
marci@478:   template <typename Graph, typename Num, typename CapMap, typename FlowMap>
marci@615:   bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow2()
marci@478:   {
marci@485:     bool _augment=false;
marci@478: 
marci@485:     ResGW res_graph(*g, *capacity, *flow);
marci@615: 
marci@485:     //ReachedMap level(res_graph);
marci@485:     FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
marci@485:     BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);
marci@478: 
marci@485:     bfs.pushAndSetReached(s);
marci@485:     DistanceMap<ResGW> dist(res_graph);
marci@615:     while ( !bfs.finished() ) {
marci@485:       ResGWOutEdgeIt e=bfs;
marci@485:       if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {
marci@485: 	dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1);
marci@485:       }
marci@485:       ++bfs;
marci@485:     } //computing distances from s in the residual graph
marci@478: 
marci@478:       //Subgraph containing the edges on some shortest paths
marci@485:     ConstMap<typename ResGW::Node, bool> true_map(true);
marci@615:     typedef SubGraphWrapper<ResGW, ConstMap<typename ResGW::Node, bool>,
marci@485:       DistanceMap<ResGW> > FilterResGW;
marci@485:     FilterResGW filter_res_graph(res_graph, true_map, dist);
marci@478: 
marci@615:     //Subgraph, which is able to delete edges which are already
marci@485:     //met by the dfs
marci@615:     typename FilterResGW::template NodeMap<typename FilterResGW::OutEdgeIt>
marci@485:       first_out_edges(filter_res_graph);
marci@485:     typename FilterResGW::NodeIt v;
marci@615:     for(filter_res_graph.first(v); filter_res_graph.valid(v);
marci@615: 	filter_res_graph.next(v))
marci@478:       {
marci@478:  	typename FilterResGW::OutEdgeIt e;
marci@478:  	filter_res_graph.first(e, v);
marci@478:  	first_out_edges.set(v, e);
marci@478:       }
marci@485:     typedef ErasingFirstGraphWrapper<FilterResGW, typename FilterResGW::
marci@485:       template NodeMap<typename FilterResGW::OutEdgeIt> > ErasingResGW;
marci@485:     ErasingResGW erasing_res_graph(filter_res_graph, first_out_edges);
marci@478: 
marci@485:     bool __augment=true;
marci@478: 
marci@485:     while (__augment) {
marci@478: 
marci@485:       __augment=false;
marci@485:       //computing blocking flow with dfs
marci@615:       DfsIterator< ErasingResGW,
marci@615: 	typename ErasingResGW::template NodeMap<bool> >
marci@485: 	dfs(erasing_res_graph);
marci@485:       typename ErasingResGW::
marci@615: 	template NodeMap<typename ErasingResGW::OutEdgeIt>
marci@615: 	pred(erasing_res_graph);
marci@485:       pred.set(s, INVALID);
marci@485:       //invalid iterators for sources
marci@478: 
marci@615:       typename ErasingResGW::template NodeMap<Num>
marci@485: 	free1(erasing_res_graph);
marci@478: 
marci@615:       dfs.pushAndSetReached
marci@615: 	///\bug hugo 0.2
marci@615: 	(typename ErasingResGW::Node
marci@615: 	 (typename FilterResGW::Node
marci@615: 	  (typename ResGW::Node(s)
marci@615: 	   )
marci@615: 	  )
marci@615: 	 );
marci@485:       while (!dfs.finished()) {
marci@485: 	++dfs;
marci@615: 	if (erasing_res_graph.valid(typename ErasingResGW::OutEdgeIt(dfs)))
marci@615:  	  {
marci@478:   	    if (dfs.isBNodeNewlyReached()) {
marci@615: 
marci@478:  	      typename ErasingResGW::Node v=erasing_res_graph.aNode(dfs);
marci@478:  	      typename ErasingResGW::Node w=erasing_res_graph.bNode(dfs);
marci@478: 
marci@478:  	      pred.set(w, /*typename ErasingResGW::OutEdgeIt*/(dfs));
marci@478:  	      if (erasing_res_graph.valid(pred[v])) {
marci@615:  		free1.set
marci@615: 		  (w, std::min(free1[v], res_graph.resCap
marci@615: 			       (typename ErasingResGW::OutEdgeIt(dfs))));
marci@478:  	      } else {
marci@615:  		free1.set
marci@615: 		  (w, res_graph.resCap
marci@615: 		   (typename ErasingResGW::OutEdgeIt(dfs)));
marci@478:  	      }
marci@615: 
marci@615:  	      if (w==t) {
marci@615:  		__augment=true;
marci@478:  		_augment=true;
marci@615:  		break;
marci@478:  	      }
marci@478:  	    } else {
marci@478:  	      erasing_res_graph.erase(dfs);
marci@478: 	    }
marci@478: 	  }
marci@615:       }
marci@478: 
marci@485:       if (__augment) {
marci@615: 	typename ErasingResGW::Node
marci@615: 	  n=typename FilterResGW::Node(typename ResGW::Node(t));
marci@485: 	// 	  typename ResGW::NodeMap<Num> a(res_graph);
marci@485: 	// 	  typename ResGW::Node b;
marci@485: 	// 	  Num j=a[b];
marci@485: 	// 	  typename FilterResGW::NodeMap<Num> a1(filter_res_graph);
marci@485: 	// 	  typename FilterResGW::Node b1;
marci@485: 	// 	  Num j1=a1[b1];
marci@485: 	// 	  typename ErasingResGW::NodeMap<Num> a2(erasing_res_graph);
marci@485: 	// 	  typename ErasingResGW::Node b2;
marci@485: 	// 	  Num j2=a2[b2];
marci@485: 	Num augment_value=free1[n];
marci@615: 	while (erasing_res_graph.valid(pred[n])) {
marci@485: 	  typename ErasingResGW::OutEdgeIt e=pred[n];
marci@485: 	  res_graph.augment(e, augment_value);
marci@485: 	  n=erasing_res_graph.tail(e);
marci@485: 	  if (res_graph.resCap(e)==0)
marci@485: 	    erasing_res_graph.erase(e);
marci@478: 	}
marci@478:       }
marci@615: 
marci@615:     } //while (__augment)
marci@615: 
marci@485:     return _augment;
marci@485:   }
marci@478: 
marci@478: 
marci@478: } //namespace hugo
marci@478: 
marci@480: #endif //HUGO_MAX_FLOW_H
marci@478: 
marci@478: 
marci@478: 
marci@478: