[Lemon-commits] [lemon_svn] marci: r1163 - hugo/trunk/src/work/marci
Lemon SVN
svn at lemon.cs.elte.hu
Mon Nov 6 20:43:37 CET 2006
Author: marci
Date: Thu Sep 16 13:11:01 2004
New Revision: 1163
Added:
hugo/trunk/src/work/marci/tight_edge_filter_map.h
- copied, changed from r1162, /hugo/trunk/src/work/marci/augmenting_flow.h
Modified:
hugo/trunk/src/work/marci/augmenting_flow.h
Log:
An edge-map which shows the tight edges w.r.t a potential and an edge-distance function.
Modified: hugo/trunk/src/work/marci/augmenting_flow.h
==============================================================================
--- hugo/trunk/src/work/marci/augmenting_flow.h (original)
+++ hugo/trunk/src/work/marci/augmenting_flow.h Thu Sep 16 13:11:01 2004
@@ -3,14 +3,13 @@
#define HUGO_AUGMENTING_FLOW_H
#include <vector>
-//#include <queue>
-//#include <stack>
#include <iostream>
#include <hugo/graph_wrapper.h>
#include <bfs_dfs.h>
#include <hugo/invalid.h>
#include <hugo/maps.h>
+#include <tight_edge_filter_map.h>
/// \file
/// \brief Maximum flow algorithms.
@@ -18,43 +17,6 @@
namespace hugo {
- /// \brief A map for filtering the edge-set to those edges
- /// which are tight w.r.t. some node_potential map and
- /// edge_distance map.
- ///
- /// A node-map node_potential is said to be a potential w.r.t.
- /// an edge-map edge_distance
- /// if and only if for each edge e, node_potential[g.head(e)]
- /// <= edge_distance[e]+node_potential[g.tail(e)]
- /// (or the reverse inequality holds for each edge).
- /// An edge is said to be tight if this inequality holds with equality,
- /// and the map returns true exactly for those edges.
- /// To avoid rounding errors, it is recommended to use this class with exact
- /// types, e.g. with int.
- template<typename Graph,
- typename NodePotentialMap, typename EdgeDistanceMap>
- class TightEdgeFilterMap {
- protected:
- const Graph* g;
- NodePotentialMap* node_potential;
- EdgeDistanceMap* edge_distance;
- public:
- TightEdgeFilterMap(Graph& _g, NodePotentialMap& _node_potential,
- EdgeDistanceMap& _edge_distance) :
- g(&_g), node_potential(&_node_potential),
- edge_distance(&_edge_distance) { }
-// void set(const typename Graph::Node& n, int a) {
-// pot->set(n, a);
-// }
-// int operator[](const typename Graph::Node& n) const {
-// return (*node_potential)[n];
-// }
- bool operator[](const typename Graph::Edge& e) const {
- return ((*node_potential)[g->head(e)] ==
- (*edge_distance)[e]+(*node_potential)[g->tail(e)]);
- }
- };
-
/// \addtogroup galgs
/// @{
/// Class for augmenting path flow algorithms.
Copied: hugo/trunk/src/work/marci/tight_edge_filter_map.h (from r1162, /hugo/trunk/src/work/marci/augmenting_flow.h)
==============================================================================
--- /hugo/trunk/src/work/marci/augmenting_flow.h (original)
+++ hugo/trunk/src/work/marci/tight_edge_filter_map.h Thu Sep 16 13:11:01 2004
@@ -1,20 +1,10 @@
// -*- C++ -*-
-#ifndef HUGO_AUGMENTING_FLOW_H
-#define HUGO_AUGMENTING_FLOW_H
+#ifndef HUGO_TIGHT_EDGE_FILTER_MAP_H
+#define HUGO_TIGHT_EDGE_FILTER_MAP_H
-#include <vector>
-//#include <queue>
-//#include <stack>
-#include <iostream>
-
-#include <hugo/graph_wrapper.h>
-#include <bfs_dfs.h>
-#include <hugo/invalid.h>
-#include <hugo/maps.h>
-
-/// \file
-/// \brief Maximum flow algorithms.
-/// \ingroup galgs
+// /// \file
+// /// \brief Maximum flow algorithms.
+// /// \ingroup galgs
namespace hugo {
@@ -43,591 +33,14 @@
EdgeDistanceMap& _edge_distance) :
g(&_g), node_potential(&_node_potential),
edge_distance(&_edge_distance) { }
-// void set(const typename Graph::Node& n, int a) {
-// pot->set(n, a);
-// }
-// int operator[](const typename Graph::Node& n) const {
-// return (*node_potential)[n];
-// }
bool operator[](const typename Graph::Edge& e) const {
return ((*node_potential)[g->head(e)] ==
(*edge_distance)[e]+(*node_potential)[g->tail(e)]);
}
};
- /// \addtogroup galgs
- /// @{
- /// Class for augmenting path flow algorithms.
-
- /// This class provides various algorithms for finding a flow of
- /// maximum value in a directed graph. The \e source node, the \e
- /// target node, the \e capacity of the edges and the \e starting \e
- /// flow value of the edges should be passed to the algorithm through the
- /// constructor.
-// /// It is possible to change these quantities using the
-// /// functions \ref resetSource, \ref resetTarget, \ref resetCap and
-// /// \ref resetFlow. Before any subsequent runs of any algorithm of
-// /// the class \ref resetFlow should be called.
-
- /// After running an algorithm of the class, the actual flow value
- /// can be obtained by calling \ref flowValue(). The minimum
- /// value cut can be written into a \c node map of \c bools by
- /// calling \ref minCut. (\ref minMinCut and \ref maxMinCut writes
- /// the inclusionwise minimum and maximum of the minimum value
- /// cuts, resp.)
- ///\param Graph The directed graph type the algorithm runs on.
- ///\param Num The number type of the capacities and the flow values.
- ///\param CapMap The capacity map type.
- ///\param FlowMap The flow map type.
- ///\author Marton Makai
- template <typename Graph, typename Num,
- typename CapMap=typename Graph::template EdgeMap<Num>,
- typename FlowMap=typename Graph::template EdgeMap<Num> >
- class AugmentingFlow {
- protected:
- typedef typename Graph::Node Node;
- typedef typename Graph::NodeIt NodeIt;
- typedef typename Graph::EdgeIt EdgeIt;
- typedef typename Graph::OutEdgeIt OutEdgeIt;
- typedef typename Graph::InEdgeIt InEdgeIt;
-
- const Graph* g;
- Node s;
- Node t;
- const CapMap* capacity;
- FlowMap* flow;
-// int n; //the number of nodes of G
- typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW;
- //typedef ExpResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW;
- typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt;
- typedef typename ResGW::Edge ResGWEdge;
- //typedef typename ResGW::template NodeMap<bool> ReachedMap;
- typedef typename Graph::template NodeMap<int> ReachedMap;
-
- //level works as a bool map in augmenting path algorithms and is
- //used by bfs for storing reached information. In preflow, it
- //shows the levels of nodes.
- ReachedMap level;
-
- public:
- ///Indicates the property of the starting flow.
-
- ///Indicates the property of the starting flow. The meanings are as follows:
- ///- \c ZERO_FLOW: constant zero flow
- ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to
- ///the sum of the out-flows in every node except the \e source and
- ///the \e target.
- ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at
- ///least the sum of the out-flows in every node except the \e source.
- ///- \c NO_FLOW: indicates an unspecified edge map. \ref flow will be
- ///set to the constant zero flow in the beginning of the algorithm in this case.
- enum FlowEnum{
- ZERO_FLOW,
- GEN_FLOW,
- PRE_FLOW,
- NO_FLOW
- };
-
- enum StatusEnum {
- AFTER_NOTHING,
- AFTER_AUGMENTING,
- AFTER_FAST_AUGMENTING,
- AFTER_PRE_FLOW_PHASE_1,
- AFTER_PRE_FLOW_PHASE_2
- };
-
- /// Don not needle this flag only if necessary.
- StatusEnum status;
- int number_of_augmentations;
-
-
- template<typename IntMap>
- class TrickyReachedMap {
- protected:
- IntMap* map;
- int* number_of_augmentations;
- public:
- TrickyReachedMap(IntMap& _map, int& _number_of_augmentations) :
- map(&_map), number_of_augmentations(&_number_of_augmentations) { }
- void set(const Node& n, bool b) {
- if (b)
- map->set(n, *number_of_augmentations);
- else
- map->set(n, *number_of_augmentations-1);
- }
- bool operator[](const Node& n) const {
- return (*map)[n]==*number_of_augmentations;
- }
- };
-
- AugmentingFlow(const Graph& _G, Node _s, Node _t, const CapMap& _capacity,
- FlowMap& _flow) :
- g(&_G), s(_s), t(_t), capacity(&_capacity),
- flow(&_flow), //n(_G.nodeNum()),
- level(_G), //excess(_G,0),
- status(AFTER_NOTHING), number_of_augmentations(0) { }
-
- /// Starting from a flow, this method searches for an augmenting path
- /// according to the Edmonds-Karp algorithm
- /// and augments the flow on if any.
- /// The return value shows if the augmentation was succesful.
- bool augmentOnShortestPath();
- bool augmentOnShortestPath2();
-
- /// Starting from a flow, this method searches for an augmenting blocking
- /// flow according to Dinits' algorithm and augments the flow on if any.
- /// The blocking flow is computed in a physically constructed
- /// residual graph of type \c Mutablegraph.
- /// The return value show sif the augmentation was succesful.
- template<typename MutableGraph> bool augmentOnBlockingFlow();
-
- /// The same as \c augmentOnBlockingFlow<MutableGraph> but the
- /// residual graph is not constructed physically.
- /// The return value shows if the augmentation was succesful.
- bool augmentOnBlockingFlow2();
-
- template<typename _CutMap>
- void actMinCut(_CutMap& M) const {
- NodeIt v;
- switch (status) {
- case AFTER_PRE_FLOW_PHASE_1:
-// std::cout << "AFTER_PRE_FLOW_PHASE_1" << std::endl;
-// for(g->first(v); g->valid(v); g->next(v)) {
-// if (level[v] < n) {
-// M.set(v, false);
-// } else {
-// M.set(v, true);
-// }
-// }
- break;
- case AFTER_PRE_FLOW_PHASE_2:
-// std::cout << "AFTER_PRE_FLOW_PHASE_2" << std::endl;
- break;
- case AFTER_NOTHING:
-// std::cout << "AFTER_NOTHING" << std::endl;
- minMinCut(M);
- break;
- case AFTER_AUGMENTING:
-// std::cout << "AFTER_AUGMENTING" << std::endl;
- for(g->first(v); v!=INVALID; ++v) {
- if (level[v]) {
- M.set(v, true);
- } else {
- M.set(v, false);
- }
- }
- break;
- case AFTER_FAST_AUGMENTING:
-// std::cout << "AFTER_FAST_AUGMENTING" << std::endl;
- for(g->first(v); v!=INVALID; ++v) {
- if (level[v]==number_of_augmentations) {
- M.set(v, true);
- } else {
- M.set(v, false);
- }
- }
- break;
- }
- }
-
- template<typename _CutMap>
- void minMinCut(_CutMap& M) const {
- std::queue<Node> queue;
-
- M.set(s,true);
- queue.push(s);
-
- while (!queue.empty()) {
- Node w=queue.front();
- queue.pop();
-
- OutEdgeIt e;
- for(g->first(e,w) ; e!=INVALID; ++e) {
- Node v=g->head(e);
- if (!M[v] && (*flow)[e] < (*capacity)[e] ) {
- queue.push(v);
- M.set(v, true);
- }
- }
-
- InEdgeIt f;
- for(g->first(f,w) ; f!=INVALID; ++f) {
- Node v=g->tail(f);
- if (!M[v] && (*flow)[f] > 0 ) {
- queue.push(v);
- M.set(v, true);
- }
- }
- }
- }
-
- template<typename _CutMap>
- void minMinCut2(_CutMap& M) const {
- ResGW res_graph(*g, *capacity, *flow);
- BfsIterator<ResGW, _CutMap> bfs(res_graph, M);
- bfs.pushAndSetReached(s);
- while (!bfs.finished()) ++bfs;
- }
-
- Num flowValue() const {
- Num a=0;
- for (InEdgeIt e(*g, t); e!=INVALID; ++e) a+=(*flow)[e];
- for (OutEdgeIt e(*g, t); e!=INVALID; ++e) a-=(*flow)[e];
- return a;
- //marci figyu: excess[t] epp ezt adja preflow 1. fazisa utan
- }
-
- };
-
-
-
- template <typename Graph, typename Num, typename CapMap, typename FlowMap>
- bool AugmentingFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath()
- {
- ResGW res_graph(*g, *capacity, *flow);
- bool _augment=false;
-
- //ReachedMap level(res_graph);
- for (typename Graph::NodeIt n(*g); n!=INVALID; ++n) level.set(n, 0);
- BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);
- bfs.pushAndSetReached(s);
-
- typename ResGW::template NodeMap<ResGWEdge> pred(res_graph);
- pred.set(s, INVALID);
-
- typename ResGW::template NodeMap<Num> free(res_graph);
-
- //searching for augmenting path
- while ( !bfs.finished() ) {
- ResGWEdge e=bfs;
- if (e!=INVALID && bfs.isBNodeNewlyReached()) {
- Node v=res_graph.tail(e);
- Node w=res_graph.head(e);
- pred.set(w, e);
- if (pred[v]!=INVALID) {
- free.set(w, std::min(free[v], res_graph.resCap(e)));
- } else {
- free.set(w, res_graph.resCap(e));
- }
- if (res_graph.head(e)==t) { _augment=true; break; }
- }
-
- ++bfs;
- } //end of searching augmenting path
-
- if (_augment) {
- Node n=t;
- Num augment_value=free[t];
- while (pred[n]!=INVALID) {
- ResGWEdge e=pred[n];
- res_graph.augment(e, augment_value);
- n=res_graph.tail(e);
- }
- }
-
- status=AFTER_AUGMENTING;
- return _augment;
- }
-
- template <typename Graph, typename Num, typename CapMap, typename FlowMap>
- bool AugmentingFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath2()
- {
- ResGW res_graph(*g, *capacity, *flow);
- bool _augment=false;
-
- if (status!=AFTER_FAST_AUGMENTING) {
- for (typename Graph::NodeIt n(*g); n!=INVALID; ++n) level.set(n, 0);
- number_of_augmentations=1;
- } else {
- ++number_of_augmentations;
- }
- TrickyReachedMap<ReachedMap>
- tricky_reached_map(level, number_of_augmentations);
- //ReachedMap level(res_graph);
-// FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
- BfsIterator<ResGW, TrickyReachedMap<ReachedMap> >
- bfs(res_graph, tricky_reached_map);
- bfs.pushAndSetReached(s);
-
- typename ResGW::template NodeMap<ResGWEdge> pred(res_graph);
- pred.set(s, INVALID);
-
- typename ResGW::template NodeMap<Num> free(res_graph);
-
- //searching for augmenting path
- while ( !bfs.finished() ) {
- ResGWEdge e=bfs;
- if (e!=INVALID && bfs.isBNodeNewlyReached()) {
- Node v=res_graph.tail(e);
- Node w=res_graph.head(e);
- pred.set(w, e);
- if (pred[v]!=INVALID) {
- free.set(w, std::min(free[v], res_graph.resCap(e)));
- } else {
- free.set(w, res_graph.resCap(e));
- }
- if (res_graph.head(e)==t) { _augment=true; break; }
- }
-
- ++bfs;
- } //end of searching augmenting path
-
- if (_augment) {
- Node n=t;
- Num augment_value=free[t];
- while (pred[n]!=INVALID) {
- ResGWEdge e=pred[n];
- res_graph.augment(e, augment_value);
- n=res_graph.tail(e);
- }
- }
-
- status=AFTER_FAST_AUGMENTING;
- return _augment;
- }
-
-
- template <typename Graph, typename Num, typename CapMap, typename FlowMap>
- template<typename MutableGraph>
- bool AugmentingFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow()
- {
- typedef MutableGraph MG;
- bool _augment=false;
-
- ResGW res_graph(*g, *capacity, *flow);
-
- //bfs for distances on the residual graph
- //ReachedMap level(res_graph);
- for (typename Graph::NodeIt n(*g); n!=INVALID; ++n) level.set(n, 0);
- BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);
- bfs.pushAndSetReached(s);
- typename ResGW::template NodeMap<int>
- dist(res_graph); //filled up with 0's
-
- //F will contain the physical copy of the residual graph
- //with the set of edges which are on shortest paths
- MG F;
- typename ResGW::template NodeMap<typename MG::Node>
- res_graph_to_F(res_graph);
- {
- typename ResGW::NodeIt n;
- for(res_graph.first(n); n!=INVALID; ++n)
- res_graph_to_F.set(n, F.addNode());
- }
-
- typename MG::Node sF=res_graph_to_F[s];
- typename MG::Node tF=res_graph_to_F[t];
- typename MG::template EdgeMap<ResGWEdge> original_edge(F);
- typename MG::template EdgeMap<Num> residual_capacity(F);
-
- while ( !bfs.finished() ) {
- ResGWEdge e=bfs;
- if (e!=INVALID) {
- if (bfs.isBNodeNewlyReached()) {
- dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1);
- typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)],
- res_graph_to_F[res_graph.head(e)]);
- //original_edge.update();
- original_edge.set(f, e);
- //residual_capacity.update();
- residual_capacity.set(f, res_graph.resCap(e));
- } else {
- if (dist[res_graph.head(e)]==(dist[res_graph.tail(e)]+1)) {
- typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)],
- res_graph_to_F[res_graph.head(e)]);
- //original_edge.update();
- original_edge.set(f, e);
- //residual_capacity.update();
- residual_capacity.set(f, res_graph.resCap(e));
- }
- }
- }
- ++bfs;
- } //computing distances from s in the residual graph
-
- bool __augment=true;
-
- while (__augment) {
- __augment=false;
- //computing blocking flow with dfs
- DfsIterator< MG, typename MG::template NodeMap<bool> > dfs(F);
- typename MG::template NodeMap<typename MG::Edge> pred(F);
- pred.set(sF, INVALID);
- //invalid iterators for sources
-
- typename MG::template NodeMap<Num> free(F);
-
- dfs.pushAndSetReached(sF);
- while (!dfs.finished()) {
- ++dfs;
- if (typename MG::Edge(dfs)!=INVALID) {
- if (dfs.isBNodeNewlyReached()) {
- typename MG::Node v=F.tail(dfs);
- typename MG::Node w=F.head(dfs);
- pred.set(w, dfs);
- if (pred[v]!=INVALID) {
- free.set(w, std::min(free[v], residual_capacity[dfs]));
- } else {
- free.set(w, residual_capacity[dfs]);
- }
- if (w==tF) {
- __augment=true;
- _augment=true;
- break;
- }
-
- } else {
- F.erase(typename MG::Edge(dfs));
- }
- }
- }
-
- if (__augment) {
- typename MG::Node n=tF;
- Num augment_value=free[tF];
- while (pred[n]!=INVALID) {
- typename MG::Edge e=pred[n];
- res_graph.augment(original_edge[e], augment_value);
- n=F.tail(e);
- if (residual_capacity[e]==augment_value)
- F.erase(e);
- else
- residual_capacity.set(e, residual_capacity[e]-augment_value);
- }
- }
-
- }
-
- status=AFTER_AUGMENTING;
- return _augment;
- }
-
- /// Blocking flow augmentation without constructing the layered
- /// graph physically in which the blocking flow is computed.
- template <typename Graph, typename Num, typename CapMap, typename FlowMap>
- bool AugmentingFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow2()
- {
- bool _augment=false;
-
- ResGW res_graph(*g, *capacity, *flow);
-
- //Potential map, for distances from s
- typename ResGW::template NodeMap<int> potential(res_graph, 0);
- typedef ConstMap<typename ResGW::Edge, int> Const1Map;
- Const1Map const_1_map(1);
- TightEdgeFilterMap<ResGW, typename ResGW::template NodeMap<int>,
- Const1Map> tight_edge_filter(res_graph, potential, const_1_map);
-
- for (typename Graph::NodeIt n(*g); n!=INVALID; ++n) level.set(n, 0);
- BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);
- bfs.pushAndSetReached(s);
-
- //computing distances from s in the residual graph
- while ( !bfs.finished() ) {
- ResGWEdge e=bfs;
- if (e!=INVALID && bfs.isBNodeNewlyReached())
- potential.set(res_graph.head(e), potential[res_graph.tail(e)]+1);
- ++bfs;
- }
-
- //Subgraph containing the edges on some shortest paths
- //(i.e. tight edges)
- ConstMap<typename ResGW::Node, bool> true_map(true);
- typedef SubGraphWrapper<ResGW, ConstMap<typename ResGW::Node, bool>,
- TightEdgeFilterMap<ResGW, typename ResGW::template NodeMap<int>,
- Const1Map> > FilterResGW;
- FilterResGW filter_res_graph(res_graph, true_map, tight_edge_filter);
-
- //Subgraph, which is able to delete edges which are already
- //met by the dfs
- typename FilterResGW::template NodeMap<typename FilterResGW::Edge>
- first_out_edges(filter_res_graph);
- for (typename FilterResGW::NodeIt v(filter_res_graph); v!=INVALID; ++v)
- first_out_edges.set
- (v, typename FilterResGW::OutEdgeIt(filter_res_graph, v));
-
- typedef ErasingFirstGraphWrapper<FilterResGW, typename FilterResGW::
- template NodeMap<typename FilterResGW::Edge> > ErasingResGW;
- ErasingResGW erasing_res_graph(filter_res_graph, first_out_edges);
-
- bool __augment=true;
-
- while (__augment) {
-
- __augment=false;
- //computing blocking flow with dfs
- DfsIterator< ErasingResGW,
- typename ErasingResGW::template NodeMap<bool> >
- dfs(erasing_res_graph);
- typename ErasingResGW::
- template NodeMap<typename ErasingResGW::Edge> pred(erasing_res_graph);
- pred.set(s, INVALID);
- //invalid iterators for sources
-
- typename ErasingResGW::template NodeMap<Num>
- free1(erasing_res_graph);
-
- dfs.pushAndSetReached
- /// \bug hugo 0.2
- (typename ErasingResGW::Node
- (typename FilterResGW::Node
- (typename ResGW::Node(s)
- )
- )
- );
-
- while (!dfs.finished()) {
- ++dfs;
- if (typename ErasingResGW::Edge(dfs)!=INVALID) {
- if (dfs.isBNodeNewlyReached()) {
-
- typename ErasingResGW::Node v=erasing_res_graph.tail(dfs);
- typename ErasingResGW::Node w=erasing_res_graph.head(dfs);
-
- pred.set(w, typename ErasingResGW::Edge(dfs));
- if (pred[v]!=INVALID) {
- free1.set
- (w, std::min(free1[v], res_graph.resCap
- (typename ErasingResGW::Edge(dfs))));
- } else {
- free1.set
- (w, res_graph.resCap
- (typename ErasingResGW::Edge(dfs)));
- }
-
- if (w==t) {
- __augment=true;
- _augment=true;
- break;
- }
- } else {
- erasing_res_graph.erase(dfs);
- }
- }
- }
-
- if (__augment) {
- typename ErasingResGW::Node
- n=typename FilterResGW::Node(typename ResGW::Node(t));
- Num augment_value=free1[n];
- while (pred[n]!=INVALID) {
- typename ErasingResGW::Edge e=pred[n];
- res_graph.augment(e, augment_value);
- n=erasing_res_graph.tail(e);
- if (res_graph.resCap(e)==0)
- erasing_res_graph.erase(e);
- }
- }
-
- } //while (__augment)
-
- status=AFTER_AUGMENTING;
- return _augment;
- }
-
-
} //namespace hugo
-#endif //HUGO_AUGMENTING_FLOW_H
+#endif //HUGO_TIGHT_EDGE_FILTER_MAP_H
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