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< a href = "minimum__spanning__tree_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 >
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< div class = "line" > < a name = "l00014" > < / a > < span class = "lineno" > 14< / span >   < span class = "preprocessor" > #ifndef OR_TOOLS_GRAPH_MINIMUM_SPANNING_TREE_H_< / span > < / div >
< div class = "line" > < a name = "l00015" > < / a > < span class = "lineno" > 15< / span >   < span class = "preprocessor" > #define OR_TOOLS_GRAPH_MINIMUM_SPANNING_TREE_H_< / span > < / div >
< div class = "line" > < a name = "l00016" > < / a > < span class = "lineno" > 16< / span >   < / div >
< div class = "line" > < a name = "l00017" > < / a > < span class = "lineno" > 17< / span >   < span class = "preprocessor" > #include < queue> < / span > < / div >
< div class = "line" > < a name = "l00018" > < / a > < span class = "lineno" > 18< / span >   < span class = "preprocessor" > #include < vector> < / span > < / div >
< div class = "line" > < a name = "l00019" > < / a > < span class = "lineno" > 19< / span >   < / div >
< div class = "line" > < a name = "l00020" > < / a > < span class = "lineno" > 20< / span >   < span class = "preprocessor" > #include " ortools/base/adjustable_priority_queue-inl.h" < / span > < / div >
< div class = "line" > < a name = "l00021" > < / a > < span class = "lineno" > 21< / span >   < span class = "preprocessor" > #include " ortools/base/adjustable_priority_queue.h" < / span > < / div >
< div class = "line" > < a name = "l00022" > < / a > < span class = "lineno" > 22< / span >   < span class = "preprocessor" > #include " ortools/base/integral_types.h" < / span > < / div >
< div class = "line" > < a name = "l00023" > < / a > < span class = "lineno" > 23< / span >   < span class = "preprocessor" > #include " < a class = "code" href = "connectivity_8h.html" > ortools/graph/connectivity.h< / a > " < / span > < / div >
< div class = "line" > < a name = "l00024" > < / a > < span class = "lineno" > 24< / span >   < span class = "preprocessor" > #include " ortools/util/vector_or_function.h" < / span > < / div >
< div class = "line" > < a name = "l00025" > < / a > < span class = "lineno" > 25< / span >   < / div >
< div class = "line" > < a name = "l00026" > < / a > < span class = "lineno" > 26< / span >   < span class = "keyword" > namespace < / span > < a class = "code" href = "namespaceoperations__research.html" > operations_research< / a > {< / div >
< div class = "line" > < a name = "l00027" > < / a > < span class = "lineno" > 27< / span >   < / div >
< div class = "line" > < a name = "l00028" > < / a > < span class = "lineno" > 28< / span >   < span class = "comment" > // Implementation of Kruskal' s mininumum spanning tree algorithm (c.f.< / span > < / div >
< div class = "line" > < a name = "l00029" > < / a > < span class = "lineno" > 29< / span >   < span class = "comment" > // https://en.wikipedia.org/wiki/Kruskal%27s_algorithm).< / span > < / div >
< div class = "line" > < a name = "l00030" > < / a > < span class = "lineno" > 30< / span >   < span class = "comment" > // Returns the index of the arcs appearing in the tree; will return a forest if< / span > < / div >
< div class = "line" > < a name = "l00031" > < / a > < span class = "lineno" > 31< / span >   < span class = "comment" > // the graph is disconnected. Nodes without any arcs will be ignored.< / span > < / div >
< div class = "line" > < a name = "l00032" > < / a > < span class = "lineno" > 32< / span >   < span class = "comment" > // Each arc of the graph is interpreted as an undirected arc.< / span > < / div >
< div class = "line" > < a name = "l00033" > < / a > < span class = "lineno" > 33< / span >   < span class = "comment" > // Complexity of the algorithm is O(E * log(E)) where E is the number of arcs< / span > < / div >
< div class = "line" > < a name = "l00034" > < / a > < span class = "lineno" > 34< / span >   < span class = "comment" > // in the graph. Memory usage is O(E * log(E)).< / 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 = "comment" > // TODO(user): Add a global Minimum Spanning Tree API automatically switching< / span > < / div >
< div class = "line" > < a name = "l00037" > < / a > < span class = "lineno" > 37< / span >   < span class = "comment" > // between Prim and Kruskal depending on problem size.< / span > < / div >
< div class = "line" > < a name = "l00038" > < / a > < span class = "lineno" > 38< / span >   < / div >
< div class = "line" > < a name = "l00039" > < / a > < span class = "lineno" > 39< / span >   < span class = "comment" > // Version taking sorted graph arcs. Allows somewhat incremental recomputation< / span > < / div >
< div class = "line" > < a name = "l00040" > < / a > < span class = "lineno" > 40< / span >   < span class = "comment" > // of minimum spanning trees as most of the processing time is spent sorting< / span > < / div >
< div class = "line" > < a name = "l00041" > < / a > < span class = "lineno" > 41< / span >   < span class = "comment" > // arcs.< / span > < / div >
< div class = "line" > < a name = "l00042" > < / a > < span class = "lineno" > 42< / span >   < span class = "comment" > // Usage:< / span > < / div >
< div class = "line" > < a name = "l00043" > < / a > < span class = "lineno" > 43< / span >   < span class = "comment" > // ListGraph< int, int> graph(...);< / span > < / div >
< div class = "line" > < a name = "l00044" > < / a > < span class = "lineno" > 44< / span >   < span class = "comment" > // std::vector< int> sorted_arcs = ...;< / span > < / div >
< div class = "line" > < a name = "l00045" > < / a > < span class = "lineno" > 45< / span >   < span class = "comment" > // std::vector< int> mst = BuildKruskalMinimumSpanningTreeFromSortedArcs(< / span > < / div >
< div class = "line" > < a name = "l00046" > < / a > < span class = "lineno" > 46< / span >   < span class = "comment" > // graph, sorted_arcs);< / span > < / div >
< div class = "line" > < a name = "l00047" > < / a > < span class = "lineno" > 47< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00048" > < / a > < span class = "lineno" > 48< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > Graph> < / div >
< div class = "line" > < a name = "l00049" > < / a > < span class = "lineno" > 49< / span >   std::vector< typename Graph::ArcIndex> < / div >
< div class = "line" > < a name = "l00050" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a00ab79ee21ffd8dece0996e37f9faa7a" > 50< / a > < / span >   < a class = "code" href = "namespaceoperations__research.html#a00ab79ee21ffd8dece0996e37f9faa7a" > BuildKruskalMinimumSpanningTreeFromSortedArcs< / a > (< / div >
< div class = "line" > < a name = "l00051" > < / a > < span class = "lineno" > 51< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > & graph,< / div >
< div class = "line" > < a name = "l00052" > < / a > < span class = "lineno" > 52< / span >   < span class = "keyword" > const< / span > std::vector< typename Graph::ArcIndex> & sorted_arcs) {< / div >
< div class = "line" > < a name = "l00053" > < / a > < span class = "lineno" > 53< / span >   < span class = "keyword" > using< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > = < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > Graph::ArcIndex< / a > ;< / div >
< div class = "line" > < a name = "l00054" > < / a > < span class = "lineno" > 54< / span >   < span class = "keyword" > using< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > = < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > Graph::NodeIndex< / a > ;< / div >
< div class = "line" > < a name = "l00055" > < / a > < span class = "lineno" > 55< / span >   < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > num_arcs = graph.num_arcs();< / div >
< div class = "line" > < a name = "l00056" > < / a > < span class = "lineno" > 56< / span >   < span class = "keywordtype" > int< / span > arc_index = 0;< / div >
< div class = "line" > < a name = "l00057" > < / a > < span class = "lineno" > 57< / span >   std::vector< ArcIndex> tree_arcs;< / div >
< div class = "line" > < a name = "l00058" > < / a > < span class = "lineno" > 58< / span >   < span class = "keywordflow" > if< / span > (graph.num_nodes() == 0) {< / div >
< div class = "line" > < a name = "l00059" > < / a > < span class = "lineno" > 59< / span >   < span class = "keywordflow" > return< / span > tree_arcs;< / div >
< div class = "line" > < a name = "l00060" > < / a > < span class = "lineno" > 60< / span >   }< / div >
< div class = "line" > < a name = "l00061" > < / a > < span class = "lineno" > 61< / span >   < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > expected_tree_size = graph.num_nodes() - 1;< / div >
< div class = "line" > < a name = "l00062" > < / a > < span class = "lineno" > 62< / span >   tree_arcs.reserve(expected_tree_size);< / div >
< div class = "line" > < a name = "l00063" > < / a > < span class = "lineno" > 63< / span >   < a class = "code" href = "classoperations__research_1_1ConnectedComponents.html" > ConnectedComponents< NodeIndex, ArcIndex> < / a > components;< / div >
< div class = "line" > < a name = "l00064" > < / a > < span class = "lineno" > 64< / span >   components.< a class = "code" href = "classoperations__research_1_1ConnectedComponents.html#a8247e505912b0c7d2309f3f9eaa74080" > Init< / a > (graph.num_nodes());< / div >
< div class = "line" > < a name = "l00065" > < / a > < span class = "lineno" > 65< / span >   < span class = "keywordflow" > while< / span > (tree_arcs.size() != expected_tree_size & & arc_index < num_arcs) {< / div >
< div class = "line" > < a name = "l00066" > < / a > < span class = "lineno" > 66< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > arc = sorted_arcs[arc_index];< / div >
< div class = "line" > < a name = "l00067" > < / a > < span class = "lineno" > 67< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > tail_class =< / div >
< div class = "line" > < a name = "l00068" > < / a > < span class = "lineno" > 68< / span >   components.< a class = "code" href = "classoperations__research_1_1ConnectedComponents.html#a874a54f45623ba735a5634b1ea9289ea" > GetClassRepresentative< / a > (graph.Tail(arc));< / div >
< div class = "line" > < a name = "l00069" > < / a > < span class = "lineno" > 69< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > head_class =< / div >
< div class = "line" > < a name = "l00070" > < / a > < span class = "lineno" > 70< / span >   components.< a class = "code" href = "classoperations__research_1_1ConnectedComponents.html#a874a54f45623ba735a5634b1ea9289ea" > GetClassRepresentative< / a > (graph.Head(arc));< / div >
< div class = "line" > < a name = "l00071" > < / a > < span class = "lineno" > 71< / span >   < span class = "keywordflow" > if< / span > (tail_class != head_class) {< / div >
< div class = "line" > < a name = "l00072" > < / a > < span class = "lineno" > 72< / span >   components.< a class = "code" href = "classoperations__research_1_1ConnectedComponents.html#a047f863116aabfa88d8eeeebda5de760" > MergeClasses< / a > (tail_class, head_class);< / div >
< div class = "line" > < a name = "l00073" > < / a > < span class = "lineno" > 73< / span >   tree_arcs.push_back(arc);< / div >
< div class = "line" > < a name = "l00074" > < / a > < span class = "lineno" > 74< / span >   }< / div >
< div class = "line" > < a name = "l00075" > < / a > < span class = "lineno" > 75< / span >   ++arc_index;< / div >
< div class = "line" > < a name = "l00076" > < / a > < span class = "lineno" > 76< / span >   }< / div >
< div class = "line" > < a name = "l00077" > < / a > < span class = "lineno" > 77< / span >   < span class = "keywordflow" > return< / span > tree_arcs;< / div >
< div class = "line" > < a name = "l00078" > < / a > < span class = "lineno" > 78< / span >   }< / div >
< div class = "line" > < a name = "l00079" > < / a > < span class = "lineno" > 79< / span >   < / div >
< div class = "line" > < a name = "l00080" > < / a > < span class = "lineno" > 80< / span >   < span class = "comment" > // Version taking an arc comparator to sort graph arcs.< / span > < / div >
< div class = "line" > < a name = "l00081" > < / a > < span class = "lineno" > 81< / span >   < span class = "comment" > // Usage:< / span > < / div >
< div class = "line" > < a name = "l00082" > < / a > < span class = "lineno" > 82< / span >   < span class = "comment" > // ListGraph< int, int> graph(...);< / span > < / div >
< div class = "line" > < a name = "l00083" > < / a > < span class = "lineno" > 83< / span >   < span class = "comment" > // const auto arc_cost = [& graph](int arc) {< / span > < / div >
< div class = "line" > < a name = "l00084" > < / a > < span class = "lineno" > 84< / span >   < span class = "comment" > // return f(graph.Tail(arc), graph.Head(arc));< / span > < / div >
< div class = "line" > < a name = "l00085" > < / a > < span class = "lineno" > 85< / span >   < span class = "comment" > // };< / span > < / div >
< div class = "line" > < a name = "l00086" > < / a > < span class = "lineno" > 86< / span >   < span class = "comment" > // std::vector< int> mst = BuildKruskalMinimumSpanningTree(< / span > < / div >
< div class = "line" > < a name = "l00087" > < / a > < span class = "lineno" > 87< / span >   < span class = "comment" > // graph,< / span > < / div >
< div class = "line" > < a name = "l00088" > < / a > < span class = "lineno" > 88< / span >   < span class = "comment" > // [& arc_cost](int a, int b) { return arc_cost(a) < arc_cost(b); });< / span > < / div >
< div class = "line" > < a name = "l00089" > < / a > < span class = "lineno" > 89< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00090" > < / a > < span class = "lineno" > 90< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > Graph, < span class = "keyword" > typename< / span > ArcComparator> < / div >
< div class = "line" > < a name = "l00091" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#aa565a47a059ef32ef1aec39768e4ec98" > 91< / a > < / span >   std::vector< typename Graph::ArcIndex> < a class = "code" href = "namespaceoperations__research.html#aa565a47a059ef32ef1aec39768e4ec98" > BuildKruskalMinimumSpanningTree< / a > (< / div >
< div class = "line" > < a name = "l00092" > < / a > < span class = "lineno" > 92< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > & graph, < span class = "keyword" > const< / span > ArcComparator& arc_comparator) {< / div >
< div class = "line" > < a name = "l00093" > < / a > < span class = "lineno" > 93< / span >   < span class = "keyword" > using< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > = < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > Graph::ArcIndex< / a > ;< / div >
< div class = "line" > < a name = "l00094" > < / a > < span class = "lineno" > 94< / span >   std::vector< ArcIndex> sorted_arcs(graph.num_arcs());< / div >
< div class = "line" > < a name = "l00095" > < / a > < span class = "lineno" > 95< / span >   < span class = "keywordflow" > for< / span > (< span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > arc : graph.AllForwardArcs()) {< / div >
< div class = "line" > < a name = "l00096" > < / a > < span class = "lineno" > 96< / span >   sorted_arcs[arc] = arc;< / div >
< div class = "line" > < a name = "l00097" > < / a > < span class = "lineno" > 97< / span >   }< / div >
< div class = "line" > < a name = "l00098" > < / a > < span class = "lineno" > 98< / span >   std::sort(sorted_arcs.begin(), sorted_arcs.end(), arc_comparator);< / div >
< div class = "line" > < a name = "l00099" > < / a > < span class = "lineno" > 99< / span >   < span class = "keywordflow" > return< / span > < a class = "code" href = "namespaceoperations__research.html#a00ab79ee21ffd8dece0996e37f9faa7a" > BuildKruskalMinimumSpanningTreeFromSortedArcs< / a > (graph, sorted_arcs);< / div >
< div class = "line" > < a name = "l00100" > < / a > < span class = "lineno" > 100< / span >   }< / div >
< div class = "line" > < a name = "l00101" > < / a > < span class = "lineno" > 101< / span >   < / div >
< div class = "line" > < a name = "l00102" > < / a > < span class = "lineno" > 102< / span >   < span class = "comment" > // Implementation of Prim' s mininumum spanning tree algorithm (c.f.< / span > < / div >
< div class = "line" > < a name = "l00103" > < / a > < span class = "lineno" > 103< / span >   < span class = "comment" > // https://en.wikipedia.org/wiki/Prim' s_algorithm) on undirected connected< / span > < / div >
< div class = "line" > < a name = "l00104" > < / a > < span class = "lineno" > 104< / span >   < span class = "comment" > // graphs.< / span > < / div >
< div class = "line" > < a name = "l00105" > < / a > < span class = "lineno" > 105< / span >   < span class = "comment" > // Returns the index of the arcs appearing in the tree.< / span > < / div >
< div class = "line" > < a name = "l00106" > < / a > < span class = "lineno" > 106< / span >   < span class = "comment" > // Complexity of the algorithm is O(E * log(V)) where E is the number of arcs< / span > < / div >
< div class = "line" > < a name = "l00107" > < / a > < span class = "lineno" > 107< / span >   < span class = "comment" > // in the graph, V is the number of vertices. Memory usage is O(V) + memory< / span > < / div >
< div class = "line" > < a name = "l00108" > < / a > < span class = "lineno" > 108< / span >   < span class = "comment" > // taken by the graph.< / span > < / div >
< div class = "line" > < a name = "l00109" > < / a > < span class = "lineno" > 109< / span >   < span class = "comment" > // Usage:< / span > < / div >
< div class = "line" > < a name = "l00110" > < / a > < span class = "lineno" > 110< / span >   < span class = "comment" > // ListGraph< int, int> graph(...);< / span > < / div >
< div class = "line" > < a name = "l00111" > < / a > < span class = "lineno" > 111< / span >   < span class = "comment" > // const auto arc_cost = [& graph](int arc) -> int64 {< / span > < / div >
< div class = "line" > < a name = "l00112" > < / a > < span class = "lineno" > 112< / span >   < span class = "comment" > // return f(graph.Tail(arc), graph.Head(arc));< / span > < / div >
< div class = "line" > < a name = "l00113" > < / a > < span class = "lineno" > 113< / span >   < span class = "comment" > // };< / span > < / div >
< div class = "line" > < a name = "l00114" > < / a > < span class = "lineno" > 114< / span >   < span class = "comment" > // std::vector< int> mst = BuildPrimMinimumSpanningTree(graph, arc_cost);< / span > < / div >
< div class = "line" > < a name = "l00115" > < / a > < span class = "lineno" > 115< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00116" > < / a > < span class = "lineno" > 116< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > Graph, < span class = "keyword" > typename< / span > ArcValue> < / div >
< div class = "line" > < a name = "l00117" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a33a2f4c26fd60cd0fa98257b571c974f" > 117< / a > < / span >   std::vector< typename Graph::ArcIndex> < a class = "code" href = "namespaceoperations__research.html#a33a2f4c26fd60cd0fa98257b571c974f" > BuildPrimMinimumSpanningTree< / a > (< / div >
< div class = "line" > < a name = "l00118" > < / a > < span class = "lineno" > 118< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > & graph, < span class = "keyword" > const< / span > ArcValue& arc_value) {< / div >
< div class = "line" > < a name = "l00119" > < / a > < span class = "lineno" > 119< / span >   < span class = "keyword" > using< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > = < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > Graph::ArcIndex< / a > ;< / div >
< div class = "line" > < a name = "l00120" > < / a > < span class = "lineno" > 120< / span >   < span class = "keyword" > using< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > = < span class = "keyword" > typename< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > Graph::NodeIndex< / a > ;< / div >
< div class = "line" > < a name = "l00121" > < / a > < span class = "lineno" > 121< / span >   < span class = "keyword" > using< / span > ArcValueType = decltype(arc_value(0));< / div >
< div class = "line" > < a name = "l00122" > < / a > < span class = "lineno" > 122< / span >   std::vector< ArcIndex> tree_arcs;< / div >
< div class = "line" > < a name = "l00123" > < / a > < span class = "lineno" > 123< / span >   < span class = "keywordflow" > if< / span > (graph.num_nodes() == 0) {< / div >
< div class = "line" > < a name = "l00124" > < / a > < span class = "lineno" > 124< / span >   < span class = "keywordflow" > return< / span > tree_arcs;< / div >
< div class = "line" > < a name = "l00125" > < / a > < span class = "lineno" > 125< / span >   }< / div >
< div class = "line" > < a name = "l00126" > < / a > < span class = "lineno" > 126< / span >   < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > expected_tree_size = graph.num_nodes() - 1;< / div >
< div class = "line" > < a name = "l00127" > < / a > < span class = "lineno" > 127< / span >   tree_arcs.reserve(expected_tree_size);< / div >
< div class = "line" > < a name = "l00128" > < / a > < span class = "lineno" > 128< / span >   std::vector< ArcIndex> node_neighbor(graph.num_nodes(), Graph::kNilArc);< / div >
< div class = "line" > < a name = "l00129" > < / a > < span class = "lineno" > 129< / span >   std::vector< bool> node_active(graph.num_nodes(), < span class = "keyword" > true< / span > );< / 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 >   < span class = "comment" > // This struct represents entries in the adjustable priority queue which< / span > < / div >
< div class = "line" > < a name = "l00132" > < / a > < span class = "lineno" > 132< / span >   < span class = "comment" > // maintains active nodes (not added to the tree yet) in decreasing insertion< / span > < / div >
< div class = "line" > < a name = "l00133" > < / a > < span class = "lineno" > 133< / span >   < span class = "comment" > // cost order. AdjustablePriorityQueue requires the existence of the< / span > < / div >
< div class = "line" > < a name = "l00134" > < / a > < span class = "lineno" > 134< / span >   < span class = "comment" > // SetHeapIndex and GetHeapIndex methods.< / span > < / div >
< div class = "line" > < a name = "l00135" > < / a > < span class = "lineno" > 135< / span >   < span class = "keyword" > struct < / span > Entry {< / div >
< div class = "line" > < a name = "l00136" > < / a > < span class = "lineno" > 136< / span >   < span class = "keywordtype" > void< / span > SetHeapIndex(< span class = "keywordtype" > int< / span > index) { heap_index = index; }< / div >
< div class = "line" > < a name = "l00137" > < / a > < span class = "lineno" > 137< / span >   < span class = "keywordtype" > int< / span > GetHeapIndex()< span class = "keyword" > const < / span > { < span class = "keywordflow" > return< / span > heap_index; }< / div >
< div class = "line" > < a name = "l00138" > < / a > < span class = "lineno" > 138< / span >   < span class = "keywordtype" > bool< / span > operator< (< span class = "keyword" > const< / span > Entry& other)< span class = "keyword" > const < / span > { < span class = "keywordflow" > return< / span > value > other.value; }< / div >
< div class = "line" > < a name = "l00139" > < / a > < span class = "lineno" > 139< / span >   < / div >
< div class = "line" > < a name = "l00140" > < / a > < span class = "lineno" > 140< / span >   < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > node;< / div >
< div class = "line" > < a name = "l00141" > < / a > < span class = "lineno" > 141< / span >   ArcValueType value;< / div >
< div class = "line" > < a name = "l00142" > < / a > < span class = "lineno" > 142< / span >   < span class = "keywordtype" > int< / span > heap_index;< / div >
< div class = "line" > < a name = "l00143" > < / a > < span class = "lineno" > 143< / span >   };< / div >
< div class = "line" > < a name = "l00144" > < / a > < span class = "lineno" > 144< / span >   < / div >
< div class = "line" > < a name = "l00145" > < / a > < span class = "lineno" > 145< / span >   AdjustablePriorityQueue< Entry> pq;< / div >
< div class = "line" > < a name = "l00146" > < / a > < span class = "lineno" > 146< / span >   std::vector< Entry> entries;< / div >
< div class = "line" > < a name = "l00147" > < / a > < span class = "lineno" > 147< / span >   std::vector< bool> touched_entry(graph.num_nodes(), < span class = "keyword" > false< / span > );< / div >
< div class = "line" > < a name = "l00148" > < / a > < span class = "lineno" > 148< / span >   < span class = "keywordflow" > for< / span > (< a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > node : graph.AllNodes()) {< / div >
< div class = "line" > < a name = "l00149" > < / a > < span class = "lineno" > 149< / span >   entries.push_back({node, std::numeric_limits< ArcValueType> ::max(), -1});< / div >
< div class = "line" > < a name = "l00150" > < / a > < span class = "lineno" > 150< / span >   }< / div >
< div class = "line" > < a name = "l00151" > < / a > < span class = "lineno" > 151< / span >   entries[0].value = 0;< / div >
< div class = "line" > < a name = "l00152" > < / a > < span class = "lineno" > 152< / span >   pq.Add(& entries[0]);< / div >
< div class = "line" > < a name = "l00153" > < / a > < span class = "lineno" > 153< / span >   < span class = "keywordflow" > while< / span > (!pq.IsEmpty() & & tree_arcs.size() != expected_tree_size) {< / div >
< div class = "line" > < a name = "l00154" > < / a > < span class = "lineno" > 154< / span >   < span class = "keyword" > const< / span > Entry* best = pq.Top();< / div >
< div class = "line" > < a name = "l00155" > < / a > < span class = "lineno" > 155< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > node = best-> node;< / div >
< div class = "line" > < a name = "l00156" > < / a > < span class = "lineno" > 156< / span >   pq.Pop();< / div >
< div class = "line" > < a name = "l00157" > < / a > < span class = "lineno" > 157< / span >   node_active[node] = < span class = "keyword" > false< / span > ;< / div >
< div class = "line" > < a name = "l00158" > < / a > < span class = "lineno" > 158< / span >   < span class = "keywordflow" > if< / span > (node_neighbor[node] != Graph::kNilArc) {< / div >
< div class = "line" > < a name = "l00159" > < / a > < span class = "lineno" > 159< / span >   tree_arcs.push_back(node_neighbor[node]);< / div >
< div class = "line" > < a name = "l00160" > < / a > < span class = "lineno" > 160< / span >   }< / div >
< div class = "line" > < a name = "l00161" > < / a > < span class = "lineno" > 161< / span >   < span class = "keywordflow" > for< / span > (< span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#ad90a9fc7d16bb2c98a088a4162bbbc9d" > ArcIndex< / a > arc : graph.OutgoingArcs(node)) {< / div >
< div class = "line" > < a name = "l00162" > < / a > < span class = "lineno" > 162< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > neighbor = graph.Head(arc);< / div >
< div class = "line" > < a name = "l00163" > < / a > < span class = "lineno" > 163< / span >   < span class = "keywordflow" > if< / span > (node_active[neighbor]) {< / div >
< div class = "line" > < a name = "l00164" > < / a > < span class = "lineno" > 164< / span >   < span class = "keyword" > const< / span > ArcValueType value = arc_value(arc);< / div >
< div class = "line" > < a name = "l00165" > < / a > < span class = "lineno" > 165< / span >   Entry& entry = entries[neighbor];< / div >
< div class = "line" > < a name = "l00166" > < / a > < span class = "lineno" > 166< / span >   < span class = "keywordflow" > if< / span > (value < entry.value || !touched_entry[neighbor]) {< / div >
< div class = "line" > < a name = "l00167" > < / a > < span class = "lineno" > 167< / span >   node_neighbor[neighbor] = arc;< / div >
< div class = "line" > < a name = "l00168" > < / a > < span class = "lineno" > 168< / span >   entry.value = value;< / div >
< div class = "line" > < a name = "l00169" > < / a > < span class = "lineno" > 169< / span >   touched_entry[neighbor] = < span class = "keyword" > true< / span > ;< / div >
< div class = "line" > < a name = "l00170" > < / a > < span class = "lineno" > 170< / span >   < span class = "keywordflow" > if< / span > (pq.Contains(& entry)) {< / div >
< div class = "line" > < a name = "l00171" > < / a > < span class = "lineno" > 171< / span >   pq.NoteChangedPriority(& entry);< / div >
< div class = "line" > < a name = "l00172" > < / a > < span class = "lineno" > 172< / span >   } < span class = "keywordflow" > else< / span > {< / div >
< div class = "line" > < a name = "l00173" > < / a > < span class = "lineno" > 173< / span >   pq.Add(& entry);< / div >
< div class = "line" > < a name = "l00174" > < / a > < span class = "lineno" > 174< / span >   }< / div >
< div class = "line" > < a name = "l00175" > < / a > < span class = "lineno" > 175< / span >   }< / div >
< div class = "line" > < a name = "l00176" > < / a > < span class = "lineno" > 176< / span >   }< / div >
< div class = "line" > < a name = "l00177" > < / a > < span class = "lineno" > 177< / span >   }< / div >
< div class = "line" > < a name = "l00178" > < / a > < span class = "lineno" > 178< / span >   }< / div >
< div class = "line" > < a name = "l00179" > < / a > < span class = "lineno" > 179< / span >   < span class = "keywordflow" > return< / span > tree_arcs;< / div >
< div class = "line" > < a name = "l00180" > < / a > < span class = "lineno" > 180< / span >   }< / div >
< div class = "line" > < a name = "l00181" > < / a > < span class = "lineno" > 181< / span >   < / div >
< div class = "line" > < a name = "l00182" > < / a > < span class = "lineno" > 182< / span >   } < span class = "comment" > // namespace operations_research< / span > < / div >
< div class = "line" > < a name = "l00183" > < / a > < span class = "lineno" > 183< / span >   < span class = "preprocessor" > #endif // OR_TOOLS_GRAPH_MINIMUM_SPANNING_TREE_H_< / span > < / div >
2019-06-13 15:36:14 +02:00
< / div > <!-- fragment --> < / div > <!-- contents -->
2019-11-14 13:52:51 -08:00
< div class = "ttc" id = "anamespaceoperations__research_html_a00ab79ee21ffd8dece0996e37f9faa7a" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a00ab79ee21ffd8dece0996e37f9faa7a" > operations_research::BuildKruskalMinimumSpanningTreeFromSortedArcs< / a > < / div > < div class = "ttdeci" > std::vector< typename Graph::ArcIndex > BuildKruskalMinimumSpanningTreeFromSortedArcs(const Graph & graph, const std::vector< typename Graph::ArcIndex > & sorted_arcs)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "minimum__spanning__tree_8h_source.html#l00050" > minimum_spanning_tree.h:50< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_aa565a47a059ef32ef1aec39768e4ec98" > < div class = "ttname" > < a href = "namespaceoperations__research.html#aa565a47a059ef32ef1aec39768e4ec98" > operations_research::BuildKruskalMinimumSpanningTree< / a > < / div > < div class = "ttdeci" > std::vector< typename Graph::ArcIndex > BuildKruskalMinimumSpanningTree(const Graph & graph, const ArcComparator & arc_comparator)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "minimum__spanning__tree_8h_source.html#l00091" > minimum_spanning_tree.h:91< / 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 = "aclassoperations__research_1_1ConnectedComponents_html_a874a54f45623ba735a5634b1ea9289ea" > < div class = "ttname" > < a href = "classoperations__research_1_1ConnectedComponents.html#a874a54f45623ba735a5634b1ea9289ea" > operations_research::ConnectedComponents::GetClassRepresentative< / a > < / div > < div class = "ttdeci" > NodeIndex GetClassRepresentative(NodeIndex node)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "connectivity_8h_source.html#l00123" > connectivity.h:123< / a > < / div > < / div >
< div class = "ttc" id = "aconnectivity_8h_html" > < div class = "ttname" > < a href = "connectivity_8h.html" > connectivity.h< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_a33a2f4c26fd60cd0fa98257b571c974f" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a33a2f4c26fd60cd0fa98257b571c974f" > operations_research::BuildPrimMinimumSpanningTree< / a > < / div > < div class = "ttdeci" > std::vector< typename Graph::ArcIndex > BuildPrimMinimumSpanningTree(const Graph & graph, const ArcValue & arc_value)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "minimum__spanning__tree_8h_source.html#l00117" > minimum_spanning_tree.h:117< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1ConnectedComponents_html_a8247e505912b0c7d2309f3f9eaa74080" > < div class = "ttname" > < a href = "classoperations__research_1_1ConnectedComponents.html#a8247e505912b0c7d2309f3f9eaa74080" > operations_research::ConnectedComponents::Init< / a > < / div > < div class = "ttdeci" > void Init(NodeIndex num_nodes)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "connectivity_8h_source.html#l00072" > connectivity.h:72< / 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 = "aclassoperations__research_1_1ConnectedComponents_html_a047f863116aabfa88d8eeeebda5de760" > < div class = "ttname" > < a href = "classoperations__research_1_1ConnectedComponents.html#a047f863116aabfa88d8eeeebda5de760" > operations_research::ConnectedComponents::MergeClasses< / a > < / div > < div class = "ttdeci" > void MergeClasses(NodeIndex node1, NodeIndex node2)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "connectivity_8h_source.html#l00138" > connectivity.h:138< / 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 = "aclassoperations__research_1_1ConnectedComponents_html" > < div class = "ttname" > < a href = "classoperations__research_1_1ConnectedComponents.html" > operations_research::ConnectedComponents< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "connectivity_8h_source.html#l00067" > connectivity.h:67< / a > < / div > < / div >
2019-08-07 18:01:08 -07:00
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