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< a href = "eulerian__path_8h.html" > Go to the documentation of this file.< / a > < div class = "fragment" > < div class = "line" > < a name = "l00001" > < / a > < span class = "lineno" > 1< / span >   < span class = "comment" > // Copyright 2010-2018 Google LLC< / span > < / div >
< div class = "line" > < a name = "l00002" > < / a > < span class = "lineno" > 2< / span >   < span class = "comment" > // Licensed under the Apache License, Version 2.0 (the " License" );< / span > < / div >
< div class = "line" > < a name = "l00003" > < / a > < span class = "lineno" > 3< / span >   < span class = "comment" > // you may not use this file except in compliance with the License.< / span > < / div >
< div class = "line" > < a name = "l00004" > < / a > < span class = "lineno" > 4< / span >   < span class = "comment" > // You may obtain a copy of the License at< / span > < / div >
< div class = "line" > < a name = "l00005" > < / a > < span class = "lineno" > 5< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00006" > < / a > < span class = "lineno" > 6< / span >   < span class = "comment" > // http://www.apache.org/licenses/LICENSE-2.0< / span > < / div >
< div class = "line" > < a name = "l00007" > < / a > < span class = "lineno" > 7< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00008" > < / a > < span class = "lineno" > 8< / span >   < span class = "comment" > // Unless required by applicable law or agreed to in writing, software< / span > < / div >
< div class = "line" > < a name = "l00009" > < / a > < span class = "lineno" > 9< / span >   < span class = "comment" > // distributed under the License is distributed on an " AS IS" BASIS,< / span > < / div >
< div class = "line" > < a name = "l00010" > < / a > < span class = "lineno" > 10< / span >   < span class = "comment" > // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.< / span > < / div >
< div class = "line" > < a name = "l00011" > < / a > < span class = "lineno" > 11< / span >   < span class = "comment" > // See the License for the specific language governing permissions and< / span > < / div >
< div class = "line" > < a name = "l00012" > < / a > < span class = "lineno" > 12< / span >   < span class = "comment" > // limitations under the License.< / span > < / div >
< div class = "line" > < a name = "l00013" > < / a > < span class = "lineno" > 13< / span >   < / div >
< div class = "line" > < a name = "l00014" > < / a > < span class = "lineno" > 14< / span >   < span class = "comment" > // Utility to build Eulerian paths and tours on a graph. For more information,< / span > < / div >
< div class = "line" > < a name = "l00015" > < / a > < span class = "lineno" > 15< / span >   < span class = "comment" > // see https://en.wikipedia.org/wiki/Eulerian_path.< / span > < / div >
< div class = "line" > < a name = "l00016" > < / a > < span class = "lineno" > 16< / span >   < span class = "comment" > // As of 10/2015, only undirected graphs are supported.< / span > < / div >
< div class = "line" > < a name = "l00017" > < / a > < span class = "lineno" > 17< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00018" > < / a > < span class = "lineno" > 18< / span >   < span class = "comment" > // Usage:< / span > < / div >
< div class = "line" > < a name = "l00019" > < / a > < span class = "lineno" > 19< / span >   < span class = "comment" > // - Building an Eulerian tour on a ReverseArcListGraph:< / span > < / div >
< div class = "line" > < a name = "l00020" > < / a > < span class = "lineno" > 20< / span >   < span class = "comment" > // ReverseArcListGraph< int, int> graph;< / span > < / div >
< div class = "line" > < a name = "l00021" > < / a > < span class = "lineno" > 21< / span >   < span class = "comment" > // // Fill graph< / span > < / div >
< div class = "line" > < a name = "l00022" > < / a > < span class = "lineno" > 22< / span >   < span class = "comment" > // std::vector< int> tour = BuildEulerianTour(graph);< / span > < / div >
< div class = "line" > < a name = "l00023" > < / a > < span class = "lineno" > 23< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00024" > < / a > < span class = "lineno" > 24< / span >   < span class = "comment" > // - Building an Eulerian path on a ReverseArcListGraph:< / span > < / div >
< div class = "line" > < a name = "l00025" > < / a > < span class = "lineno" > 25< / span >   < span class = "comment" > // ReverseArcListGraph< int, int> graph;< / span > < / div >
< div class = "line" > < a name = "l00026" > < / a > < span class = "lineno" > 26< / span >   < span class = "comment" > // // Fill graph< / span > < / div >
< div class = "line" > < a name = "l00027" > < / a > < span class = "lineno" > 27< / span >   < span class = "comment" > // std::vector< int> tour = BuildEulerianPath(graph);< / span > < / div >
< div class = "line" > < a name = "l00028" > < / a > < span class = "lineno" > 28< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00029" > < / a > < span class = "lineno" > 29< / span >   < span class = "preprocessor" > #ifndef OR_TOOLS_GRAPH_EULERIAN_PATH_H_< / span > < / div >
< div class = "line" > < a name = "l00030" > < / a > < span class = "lineno" > 30< / span >   < span class = "preprocessor" > #define OR_TOOLS_GRAPH_EULERIAN_PATH_H_< / span > < / div >
< div class = "line" > < a name = "l00031" > < / a > < span class = "lineno" > 31< / span >   < / div >
< div class = "line" > < a name = "l00032" > < / a > < span class = "lineno" > 32< / span >   < span class = "preprocessor" > #include < vector> < / span > < / div >
< div class = "line" > < a name = "l00033" > < / a > < span class = "lineno" > 33< / span >   < / div >
< div class = "line" > < a name = "l00034" > < / a > < span class = "lineno" > 34< / span >   < span class = "preprocessor" > #include " ortools/base/logging.h" < / span > < / div >
< div class = "line" > < a name = "l00035" > < / a > < span class = "lineno" > 35< / span >   < / div >
< div class = "line" > < a name = "l00036" > < / a > < span class = "lineno" > 36< / span >   < span class = "keyword" > namespace < / span > < a class = "code" href = "namespaceoperations__research.html" > operations_research< / a > {< / div >
< div class = "line" > < a name = "l00037" > < / a > < span class = "lineno" > 37< / span >   < / div >
< div class = "line" > < a name = "l00038" > < / a > < span class = "lineno" > 38< / span >   < span class = "comment" > // Returns true if a graph is Eulerian, aka all its nodes are of even degree.< / span > < / div >
< div class = "line" > < a name = "l00039" > < / a > < span class = "lineno" > 39< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > Graph> < / div >
< div class = "line" > < a name = "l00040" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#ab1cf773de0cae72d0c44efe5b8f4bb89" > 40< / a > < / span >   < span class = "keywordtype" > bool< / span > < a class = "code" href = "namespaceoperations__research.html#ab1cf773de0cae72d0c44efe5b8f4bb89" > IsEulerianGraph< / a > (< span class = "keyword" > const< / span > < a class = "code" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > & graph) {< / div >
< div class = "line" > < a name = "l00041" > < / a > < span class = "lineno" > 41< / span >   < span class = "keyword" > typedef< / span > < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > Graph::NodeIndex< / a > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > ;< / div >
< div class = "line" > < a name = "l00042" > < / a > < span class = "lineno" > 42< / span >   < span class = "keywordflow" > for< / span > (< span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > node : graph.AllNodes()) {< / div >
< div class = "line" > < a name = "l00043" > < / a > < span class = "lineno" > 43< / span >   < span class = "keywordflow" > if< / span > ((graph.OutDegree(node) + graph.InDegree(node)) % 2 != 0) {< / div >
< div class = "line" > < a name = "l00044" > < / a > < span class = "lineno" > 44< / span >   < span class = "keywordflow" > return< / span > < span class = "keyword" > false< / span > ;< / div >
< div class = "line" > < a name = "l00045" > < / a > < span class = "lineno" > 45< / span >   }< / div >
< div class = "line" > < a name = "l00046" > < / a > < span class = "lineno" > 46< / span >   }< / div >
< div class = "line" > < a name = "l00047" > < / a > < span class = "lineno" > 47< / span >   < span class = "comment" > // TODO(user): Check graph connectivity.< / span > < / div >
< div class = "line" > < a name = "l00048" > < / a > < span class = "lineno" > 48< / span >   < span class = "keywordflow" > return< / span > < span class = "keyword" > true< / span > ;< / div >
< div class = "line" > < a name = "l00049" > < / a > < span class = "lineno" > 49< / span >   }< / div >
< div class = "line" > < a name = "l00050" > < / a > < span class = "lineno" > 50< / span >   < / div >
< div class = "line" > < a name = "l00051" > < / a > < span class = "lineno" > 51< / span >   < span class = "comment" > // Returns true if a graph is Semi-Eulerian, aka at most two of its nodes are of< / span > < / div >
< div class = "line" > < a name = "l00052" > < / a > < span class = "lineno" > 52< / span >   < span class = "comment" > // odd degree.< / span > < / div >
< div class = "line" > < a name = "l00053" > < / a > < span class = "lineno" > 53< / span >   < span class = "comment" > // odd_nodes is filled with odd nodes of the graph.< / span > < / div >
< div class = "line" > < a name = "l00054" > < / a > < span class = "lineno" > 54< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > NodeIndex, < span class = "keyword" > typename< / span > Graph> < / div >
< div class = "line" > < a name = "l00055" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a6b312dd19c90b2af099e6f159869f7ee" > 55< / a > < / span >   < span class = "keywordtype" > bool< / span > < a class = "code" href = "namespaceoperations__research.html#a6b312dd19c90b2af099e6f159869f7ee" > IsSemiEulerianGraph< / a > (< span class = "keyword" > const< / span > < a class = "code" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > & graph,< / div >
< div class = "line" > < a name = "l00056" > < / a > < span class = "lineno" > 56< / span >   std::vector< NodeIndex> * odd_nodes) {< / div >
< div class = "line" > < a name = "l00057" > < / a > < span class = "lineno" > 57< / span >   CHECK(odd_nodes != < span class = "keyword" > nullptr< / span > );< / div >
< div class = "line" > < a name = "l00058" > < / a > < span class = "lineno" > 58< / span >   < span class = "keywordflow" > for< / span > (< span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > node : graph.AllNodes()) {< / div >
< div class = "line" > < a name = "l00059" > < / a > < span class = "lineno" > 59< / span >   < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > degree = graph.OutDegree(node) + graph.InDegree(node);< / div >
< div class = "line" > < a name = "l00060" > < / a > < span class = "lineno" > 60< / span >   < span class = "keywordflow" > if< / span > (degree % 2 != 0) {< / div >
< div class = "line" > < a name = "l00061" > < / a > < span class = "lineno" > 61< / span >   odd_nodes-> push_back(node);< / div >
< div class = "line" > < a name = "l00062" > < / a > < span class = "lineno" > 62< / span >   }< / div >
< div class = "line" > < a name = "l00063" > < / a > < span class = "lineno" > 63< / span >   }< / div >
< div class = "line" > < a name = "l00064" > < / a > < span class = "lineno" > 64< / span >   < span class = "comment" > // TODO(user): Check graph connectivity.< / span > < / div >
< div class = "line" > < a name = "l00065" > < / a > < span class = "lineno" > 65< / span >   < span class = "keywordflow" > return< / span > odd_nodes-> size() < = 2;< / div >
< div class = "line" > < a name = "l00066" > < / a > < span class = "lineno" > 66< / span >   }< / div >
< div class = "line" > < a name = "l00067" > < / a > < span class = "lineno" > 67< / span >   < / div >
< div class = "line" > < a name = "l00068" > < / a > < span class = "lineno" > 68< / span >   < span class = "comment" > // Builds an Eulerian path/trail on an undirected graph starting from node root.< / span > < / div >
< div class = "line" > < a name = "l00069" > < / a > < span class = "lineno" > 69< / span >   < span class = "comment" > // Supposes the graph is connected and is eulerian or semi-eulerian.< / span > < / div >
< div class = "line" > < a name = "l00070" > < / a > < span class = "lineno" > 70< / span >   < span class = "comment" > // This is an implementation of Hierholzer' s algorithm.< / span > < / div >
< div class = "line" > < a name = "l00071" > < / a > < span class = "lineno" > 71< / span >   < span class = "comment" > // If m is the number of edges in the graph and n the number of nodes, time< / span > < / div >
< div class = "line" > < a name = "l00072" > < / a > < span class = "lineno" > 72< / span >   < span class = "comment" > // and memory complexity is O(n + m).< / span > < / div >
< div class = "line" > < a name = "l00073" > < / a > < span class = "lineno" > 73< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > NodeIndex, < span class = "keyword" > typename< / span > Graph> < / div >
< div class = "line" > < a name = "l00074" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a743d8c9d6f64531bdeb7bbf18023e9d4" > 74< / a > < / span >   std::vector< NodeIndex> < a class = "code" href = "namespaceoperations__research.html#a743d8c9d6f64531bdeb7bbf18023e9d4" > BuildEulerianPathFromNode< / a > (< span class = "keyword" > const< / span > < a class = "code" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > & graph,< / div >
< div class = "line" > < a name = "l00075" > < / a > < span class = "lineno" > 75< / span >   < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > root) {< / div >
< div class = "line" > < a name = "l00076" > < / a > < span class = "lineno" > 76< / span >   < span class = "keyword" > typedef< / span > < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > Graph::ArcIndex< / a > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > ;< / div >
< div class = "line" > < a name = "l00077" > < / a > < span class = "lineno" > 77< / span >   std::vector< bool> unvisited_edges(graph.num_arcs(), < span class = "keyword" > true< / span > );< / div >
< div class = "line" > < a name = "l00078" > < / a > < span class = "lineno" > 78< / span >   std::vector< NodeIndex> tour;< / div >
< div class = "line" > < a name = "l00079" > < / a > < span class = "lineno" > 79< / span >   < span class = "keywordflow" > if< / span > (graph.IsNodeValid(root)) {< / div >
< div class = "line" > < a name = "l00080" > < / a > < span class = "lineno" > 80< / span >   std::vector< NodeIndex> tour_stack = {root};< / div >
< div class = "line" > < a name = "l00081" > < / a > < span class = "lineno" > 81< / span >   std::vector< ArcIndex> active_arcs(graph.num_nodes());< / div >
< div class = "line" > < a name = "l00082" > < / a > < span class = "lineno" > 82< / span >   < span class = "keywordflow" > for< / span > (< span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > node : graph.AllNodes()) {< / div >
< div class = "line" > < a name = "l00083" > < / a > < span class = "lineno" > 83< / span >   active_arcs[node] = *(graph.OutgoingOrOppositeIncomingArcs(node)).begin();< / div >
< div class = "line" > < a name = "l00084" > < / a > < span class = "lineno" > 84< / span >   }< / div >
< div class = "line" > < a name = "l00085" > < / a > < span class = "lineno" > 85< / span >   < span class = "keywordflow" > while< / span > (!tour_stack.empty()) {< / div >
< div class = "line" > < a name = "l00086" > < / a > < span class = "lineno" > 86< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > node = tour_stack.back();< / div >
< div class = "line" > < a name = "l00087" > < / a > < span class = "lineno" > 87< / span >   < span class = "keywordtype" > bool< / span > has_unvisited_edges = < span class = "keyword" > false< / span > ;< / div >
< div class = "line" > < a name = "l00088" > < / a > < span class = "lineno" > 88< / span >   < span class = "keywordflow" > for< / span > (< span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > arc :< / div >
< div class = "line" > < a name = "l00089" > < / a > < span class = "lineno" > 89< / span >   graph.OutgoingOrOppositeIncomingArcsStartingFrom(< / div >
< div class = "line" > < a name = "l00090" > < / a > < span class = "lineno" > 90< / span >   node, active_arcs[node])) {< / div >
< div class = "line" > < a name = "l00091" > < / a > < span class = "lineno" > 91< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > edge = arc < 0 ? graph.OppositeArc(arc) : arc;< / div >
< div class = "line" > < a name = "l00092" > < / a > < span class = "lineno" > 92< / span >   < span class = "keywordflow" > if< / span > (unvisited_edges[edge]) {< / div >
< div class = "line" > < a name = "l00093" > < / a > < span class = "lineno" > 93< / span >   has_unvisited_edges = < span class = "keyword" > true< / span > ;< / div >
< div class = "line" > < a name = "l00094" > < / a > < span class = "lineno" > 94< / span >   active_arcs[node] = arc;< / div >
< div class = "line" > < a name = "l00095" > < / a > < span class = "lineno" > 95< / span >   tour_stack.push_back(graph.Head(arc));< / div >
< div class = "line" > < a name = "l00096" > < / a > < span class = "lineno" > 96< / span >   unvisited_edges[edge] = < span class = "keyword" > false< / span > ;< / div >
< div class = "line" > < a name = "l00097" > < / a > < span class = "lineno" > 97< / span >   < span class = "keywordflow" > break< / span > ;< / div >
< div class = "line" > < a name = "l00098" > < / a > < span class = "lineno" > 98< / span >   }< / div >
< div class = "line" > < a name = "l00099" > < / a > < span class = "lineno" > 99< / span >   }< / div >
< div class = "line" > < a name = "l00100" > < / a > < span class = "lineno" > 100< / span >   < span class = "keywordflow" > if< / span > (!has_unvisited_edges) {< / div >
< div class = "line" > < a name = "l00101" > < / a > < span class = "lineno" > 101< / span >   tour.push_back(node);< / div >
< div class = "line" > < a name = "l00102" > < / a > < span class = "lineno" > 102< / span >   tour_stack.pop_back();< / div >
< div class = "line" > < a name = "l00103" > < / a > < span class = "lineno" > 103< / span >   }< / div >
< div class = "line" > < a name = "l00104" > < / a > < span class = "lineno" > 104< / span >   }< / div >
< div class = "line" > < a name = "l00105" > < / a > < span class = "lineno" > 105< / span >   }< / div >
< div class = "line" > < a name = "l00106" > < / a > < span class = "lineno" > 106< / span >   < span class = "keywordflow" > return< / span > tour;< / div >
< div class = "line" > < a name = "l00107" > < / a > < span class = "lineno" > 107< / span >   }< / div >
< div class = "line" > < a name = "l00108" > < / a > < span class = "lineno" > 108< / span >   < / div >
< div class = "line" > < a name = "l00109" > < / a > < span class = "lineno" > 109< / span >   < span class = "comment" > // Builds an Eulerian tour/circuit/cycle starting and ending at node root on an< / span > < / div >
< div class = "line" > < a name = "l00110" > < / a > < span class = "lineno" > 110< / span >   < span class = "comment" > // undirected graph.< / span > < / div >
< div class = "line" > < a name = "l00111" > < / a > < span class = "lineno" > 111< / span >   < span class = "comment" > // This function works only on Reverse graphs< / span > < / div >
< div class = "line" > < a name = "l00112" > < / a > < span class = "lineno" > 112< / span >   < span class = "comment" > // (cf. ortools/graph/graph.h).< / span > < / div >
< div class = "line" > < a name = "l00113" > < / a > < span class = "lineno" > 113< / span >   < span class = "comment" > // Returns an empty tour if either root is invalid or if a tour cannot be built.< / span > < / div >
< div class = "line" > < a name = "l00114" > < / a > < span class = "lineno" > 114< / span >   < span class = "comment" > // As of 10/2015, assumes the graph is connected.< / span > < / div >
< div class = "line" > < a name = "l00115" > < / a > < span class = "lineno" > 115< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > NodeIndex, < span class = "keyword" > typename< / span > Graph> < / div >
< div class = "line" > < a name = "l00116" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#aa63055860fc53f8eed56d23d2571c180" > 116< / a > < / span >   std::vector< NodeIndex> < a class = "code" href = "namespaceoperations__research.html#aa63055860fc53f8eed56d23d2571c180" > BuildEulerianTourFromNode< / a > (< span class = "keyword" > const< / span > < a class = "code" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > & graph,< / div >
< div class = "line" > < a name = "l00117" > < / a > < span class = "lineno" > 117< / span >   < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > root) {< / div >
< div class = "line" > < a name = "l00118" > < / a > < span class = "lineno" > 118< / span >   std::vector< NodeIndex> tour;< / div >
< div class = "line" > < a name = "l00119" > < / a > < span class = "lineno" > 119< / span >   < span class = "keywordflow" > if< / span > (< a class = "code" href = "namespaceoperations__research.html#ab1cf773de0cae72d0c44efe5b8f4bb89" > IsEulerianGraph< / a > (graph)) {< / div >
< div class = "line" > < a name = "l00120" > < / a > < span class = "lineno" > 120< / span >   tour = < a class = "code" href = "namespaceoperations__research.html#a743d8c9d6f64531bdeb7bbf18023e9d4" > BuildEulerianPathFromNode< / a > (graph, root);< / div >
< div class = "line" > < a name = "l00121" > < / a > < span class = "lineno" > 121< / span >   }< / div >
< div class = "line" > < a name = "l00122" > < / a > < span class = "lineno" > 122< / span >   < span class = "keywordflow" > return< / span > tour;< / div >
< div class = "line" > < a name = "l00123" > < / a > < span class = "lineno" > 123< / span >   }< / div >
< div class = "line" > < a name = "l00124" > < / a > < span class = "lineno" > 124< / span >   < / div >
< div class = "line" > < a name = "l00125" > < / a > < span class = "lineno" > 125< / span >   < span class = "comment" > // Same as above but without specifying a start/end root node (node 0 is taken< / span > < / div >
< div class = "line" > < a name = "l00126" > < / a > < span class = "lineno" > 126< / span >   < span class = "comment" > // as default root).< / span > < / div >
< div class = "line" > < a name = "l00127" > < / a > < span class = "lineno" > 127< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > Graph> < / div >
< div class = "line" > < a name = "l00128" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a034666fe63ca105b735272974006362a" > 128< / a > < / span >   std::vector< typename Graph::NodeIndex> < a class = "code" href = "namespaceoperations__research.html#a034666fe63ca105b735272974006362a" > BuildEulerianTour< / a > (< span class = "keyword" > const< / span > < a class = "code" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > & graph) {< / div >
< div class = "line" > < a name = "l00129" > < / a > < span class = "lineno" > 129< / span >   < span class = "keywordflow" > return< / span > < a class = "code" href = "namespaceoperations__research.html#aa63055860fc53f8eed56d23d2571c180" > BuildEulerianTourFromNode< / a > (graph, 0);< / div >
< div class = "line" > < a name = "l00130" > < / a > < span class = "lineno" > 130< / span >   }< / div >
< div class = "line" > < a name = "l00131" > < / a > < span class = "lineno" > 131< / span >   < / div >
< div class = "line" > < a name = "l00132" > < / a > < span class = "lineno" > 132< / span >   < span class = "comment" > // Builds an Eulerian path/trail on an undirected graph.< / span > < / div >
< div class = "line" > < a name = "l00133" > < / a > < span class = "lineno" > 133< / span >   < span class = "comment" > // This function works only on Reverse graphs< / span > < / div >
< div class = "line" > < a name = "l00134" > < / a > < span class = "lineno" > 134< / span >   < span class = "comment" > // (cf. ortools/graph/graph.h).< / span > < / div >
< div class = "line" > < a name = "l00135" > < / a > < span class = "lineno" > 135< / span >   < span class = "comment" > // Returns an empty tour if a tour cannot be built.< / span > < / div >
< div class = "line" > < a name = "l00136" > < / a > < span class = "lineno" > 136< / span >   < span class = "comment" > // As of 10/2015, assumes the graph is connected.< / span > < / div >
< div class = "line" > < a name = "l00137" > < / a > < span class = "lineno" > 137< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > Graph> < / div >
< div class = "line" > < a name = "l00138" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a49b170b2d03863c465331e67b21f0c33" > 138< / a > < / span >   std::vector< typename Graph::NodeIndex> < a class = "code" href = "namespaceoperations__research.html#a49b170b2d03863c465331e67b21f0c33" > BuildEulerianPath< / a > (< span class = "keyword" > const< / span > < a class = "code" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > & graph) {< / div >
< div class = "line" > < a name = "l00139" > < / a > < span class = "lineno" > 139< / span >   < span class = "keyword" > typedef< / span > < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > Graph::NodeIndex< / a > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > ;< / div >
< div class = "line" > < a name = "l00140" > < / a > < span class = "lineno" > 140< / span >   std::vector< NodeIndex> path;< / div >
< div class = "line" > < a name = "l00141" > < / a > < span class = "lineno" > 141< / span >   std::vector< NodeIndex> roots;< / div >
< div class = "line" > < a name = "l00142" > < / a > < span class = "lineno" > 142< / span >   < span class = "keywordflow" > if< / span > (< a class = "code" href = "namespaceoperations__research.html#a6b312dd19c90b2af099e6f159869f7ee" > IsSemiEulerianGraph< / a > (graph, & roots)) {< / div >
< div class = "line" > < a name = "l00143" > < / a > < span class = "lineno" > 143< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > root = roots.empty() ? 0 : roots.back();< / div >
< div class = "line" > < a name = "l00144" > < / a > < span class = "lineno" > 144< / span >   path = < a class = "code" href = "namespaceoperations__research.html#a743d8c9d6f64531bdeb7bbf18023e9d4" > BuildEulerianPathFromNode< / a > (graph, root);< / div >
< div class = "line" > < a name = "l00145" > < / a > < span class = "lineno" > 145< / span >   }< / div >
< div class = "line" > < a name = "l00146" > < / a > < span class = "lineno" > 146< / span >   < span class = "keywordflow" > return< / span > path;< / div >
< div class = "line" > < a name = "l00147" > < / a > < span class = "lineno" > 147< / span >   }< / div >
< div class = "line" > < a name = "l00148" > < / a > < span class = "lineno" > 148< / span >   } < span class = "comment" > // namespace operations_research< / span > < / div >
< div class = "line" > < a name = "l00149" > < / a > < span class = "lineno" > 149< / span >   < / div >
< div class = "line" > < a name = "l00150" > < / a > < span class = "lineno" > 150< / span >   < span class = "preprocessor" > #endif // OR_TOOLS_GRAPH_EULERIAN_PATH_H_< / span > < / div >
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< / div > <!-- fragment --> < / div > <!-- contents -->
2019-11-14 13:52:51 -08:00
< div class = "ttc" id = "anamespaceoperations__research_html_a034666fe63ca105b735272974006362a" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a034666fe63ca105b735272974006362a" > operations_research::BuildEulerianTour< / a > < / div > < div class = "ttdeci" > std::vector< typename Graph::NodeIndex > BuildEulerianTour(const Graph & graph)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "eulerian__path_8h_source.html#l00128" > eulerian_path.h:128< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_ab1cf773de0cae72d0c44efe5b8f4bb89" > < div class = "ttname" > < a href = "namespaceoperations__research.html#ab1cf773de0cae72d0c44efe5b8f4bb89" > operations_research::IsEulerianGraph< / a > < / div > < div class = "ttdeci" > bool IsEulerianGraph(const Graph & graph)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "eulerian__path_8h_source.html#l00040" > eulerian_path.h:40< / a > < / div > < / div >
2020-04-23 15:34:43 +02:00
< div class = "ttc" id = "anamespaceutil_html_a2f76166dbe0c4055a1f256235ad00478" > < div class = "ttname" > < a href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > util::Graph< / a > < / div > < div class = "ttdeci" > ListGraph Graph< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "graph_8h_source.html#l02354" > graph.h:2354< / a > < / div > < / div >
2019-11-14 13:52:51 -08:00
< div class = "ttc" id = "anamespaceoperations__research_html" > < div class = "ttname" > < a href = "namespaceoperations__research.html" > operations_research< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "christofides_8h_source.html#l00033" > christofides.h:33< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_a6b312dd19c90b2af099e6f159869f7ee" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a6b312dd19c90b2af099e6f159869f7ee" > operations_research::IsSemiEulerianGraph< / a > < / div > < div class = "ttdeci" > bool IsSemiEulerianGraph(const Graph & graph, std::vector< NodeIndex > *odd_nodes)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "eulerian__path_8h_source.html#l00055" > eulerian_path.h:55< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_ad90a9fc7d16bb2c98a088a4162bbbc9d" > < div class = "ttname" > < a href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > operations_research::ArcIndex< / a > < / div > < div class = "ttdeci" > int32 ArcIndex< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "ebert__graph_8h_source.html#l00201" > ebert_graph.h:201< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_aa63055860fc53f8eed56d23d2571c180" > < div class = "ttname" > < a href = "namespaceoperations__research.html#aa63055860fc53f8eed56d23d2571c180" > operations_research::BuildEulerianTourFromNode< / a > < / div > < div class = "ttdeci" > std::vector< NodeIndex > BuildEulerianTourFromNode(const Graph & graph, NodeIndex root)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "eulerian__path_8h_source.html#l00116" > eulerian_path.h:116< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_a272bcc4d6ee0e87a7fc430a5cb13c582" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > operations_research::NodeIndex< / a > < / div > < div class = "ttdeci" > int32 NodeIndex< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "ebert__graph_8h_source.html#l00192" > ebert_graph.h:192< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_a743d8c9d6f64531bdeb7bbf18023e9d4" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a743d8c9d6f64531bdeb7bbf18023e9d4" > operations_research::BuildEulerianPathFromNode< / a > < / div > < div class = "ttdeci" > std::vector< NodeIndex > BuildEulerianPathFromNode(const Graph & graph, NodeIndex root)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "eulerian__path_8h_source.html#l00074" > eulerian_path.h:74< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_a49b170b2d03863c465331e67b21f0c33" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a49b170b2d03863c465331e67b21f0c33" > operations_research::BuildEulerianPath< / a > < / div > < div class = "ttdeci" > std::vector< typename Graph::NodeIndex > BuildEulerianPath(const Graph & graph)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "eulerian__path_8h_source.html#l00138" > eulerian_path.h:138< / a > < / div > < / div >
2019-08-07 18:01:08 -07:00
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2019-06-13 15:36:14 +02:00
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