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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 id = "l00001" name = "l00001" > < / a > < span class = "lineno" > 1< / span > < span class = "comment" > // Copyright 2010-2021 Google LLC< / span > < / div >
< div class = "line" > < a id = "l00002" 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 id = "l00003" 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 id = "l00004" 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 id = "l00005" name = "l00005" > < / a > < span class = "lineno" > 5< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00006" 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 id = "l00007" name = "l00007" > < / a > < span class = "lineno" > 7< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00008" 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 id = "l00009" 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 id = "l00010" 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 id = "l00011" 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 id = "l00012" name = "l00012" > < / a > < span class = "lineno" > 12< / span > < span class = "comment" > // limitations under the License.< / span > < / div >
< div class = "line" > < a id = "l00013" name = "l00013" > < / a > < span class = "lineno" > 13< / span > < / div >
< div class = "line" > < a id = "l00014" 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 id = "l00015" 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 id = "l00016" name = "l00016" > < / a > < span class = "lineno" > 16< / span > < / div >
< div class = "line" > < a id = "l00017" name = "l00017" > < / a > < span class = "lineno" > 17< / span > < span class = "preprocessor" > #include < queue> < / span > < / div >
< div class = "line" > < a id = "l00018" name = "l00018" > < / a > < span class = "lineno" > 18< / span > < span class = "preprocessor" > #include < vector> < / span > < / div >
< div class = "line" > < a id = "l00019" name = "l00019" > < / a > < span class = "lineno" > 19< / span > < / div >
< div class = "line" > < a id = "l00020" name = "l00020" > < / a > < span class = "lineno" > 20< / span > < span class = "preprocessor" > #include " < a class = "code" href = "adjustable__priority__queue-inl_8h.html" > ortools/base/adjustable_priority_queue-inl.h< / a > " < / span > < / div >
< div class = "line" > < a id = "l00021" name = "l00021" > < / a > < span class = "lineno" > 21< / span > < span class = "preprocessor" > #include " < a class = "code" href = "adjustable__priority__queue_8h.html" > ortools/base/adjustable_priority_queue.h< / a > " < / span > < / div >
< div class = "line" > < a id = "l00022" name = "l00022" > < / a > < span class = "lineno" > 22< / span > < span class = "preprocessor" > #include " < a class = "code" href = "integral__types_8h.html" > ortools/base/integral_types.h< / a > " < / span > < / div >
< div class = "line" > < a id = "l00023" name = "l00023" > < / a > < span class = "lineno" > 23< / span > < span class = "preprocessor" > #include " < a class = "code" href = "connected__components_8h.html" > ortools/graph/connected_components.h< / a > " < / span > < / div >
< div class = "line" > < a id = "l00024" name = "l00024" > < / a > < span class = "lineno" > 24< / span > < span class = "preprocessor" > #include " < a class = "code" href = "vector__or__function_8h.html" > ortools/util/vector_or_function.h< / a > " < / span > < / div >
< div class = "line" > < a id = "l00025" name = "l00025" > < / a > < span class = "lineno" > 25< / span > < / div >
< div class = "line" > < a id = "l00026" name = "l00026" > < / a > < span class = "lineno" > 26< / span > < span class = "keyword" > namespace < / span > < a class = "code hl_namespace" href = "namespaceoperations__research.html" > operations_research< / a > {< / div >
< div class = "line" > < a id = "l00027" name = "l00027" > < / a > < span class = "lineno" > 27< / span > < / div >
< div class = "line" > < a id = "l00028" 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 id = "l00029" 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 id = "l00030" 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 id = "l00031" 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 id = "l00032" 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 id = "l00033" 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 id = "l00034" 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 id = "l00035" name = "l00035" > < / a > < span class = "lineno" > 35< / span > < / div >
< div class = "line" > < a id = "l00036" 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 id = "l00037" 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 id = "l00038" name = "l00038" > < / a > < span class = "lineno" > 38< / span > < / div >
< div class = "line" > < a id = "l00039" 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 id = "l00040" 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 id = "l00041" name = "l00041" > < / a > < span class = "lineno" > 41< / span > < span class = "comment" > // arcs.< / span > < / div >
< div class = "line" > < a id = "l00042" name = "l00042" > < / a > < span class = "lineno" > 42< / span > < span class = "comment" > // Usage:< / span > < / div >
< div class = "line" > < a id = "l00043" name = "l00043" > < / a > < span class = "lineno" > 43< / span > < span class = "comment" > // ListGraph< int, int> graph(...);< / span > < / div >
< div class = "line" > < a id = "l00044" name = "l00044" > < / a > < span class = "lineno" > 44< / span > < span class = "comment" > // std::vector< int> sorted_arcs = ...;< / span > < / div >
< div class = "line" > < a id = "l00045" name = "l00045" > < / a > < span class = "lineno" > 45< / span > < span class = "comment" > // std::vector< int> mst = BuildKruskalMinimumSpanningTreeFromSortedArcs(< / span > < / div >
< div class = "line" > < a id = "l00046" name = "l00046" > < / a > < span class = "lineno" > 46< / span > < span class = "comment" > // graph, sorted_arcs);< / span > < / div >
< div class = "line" > < a id = "l00047" name = "l00047" > < / a > < span class = "lineno" > 47< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00048" name = "l00048" > < / a > < span class = "lineno" > 48< / span > < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > Graph> < / div >
< div class = "line" > < a id = "l00049" name = "l00049" > < / a > < span class = "lineno" > 49< / span > std::vector< typename Graph::ArcIndex> < / div >
< div class = "line" > < a id = "l00050" name = "l00050" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#aefd088882d7ba8d27157eba391b02792" > 50< / a > < / span > < a class = "code hl_function" href = "namespaceoperations__research.html#aefd088882d7ba8d27157eba391b02792" > BuildKruskalMinimumSpanningTreeFromSortedArcs< / a > (< / div >
< div class = "line" > < a id = "l00051" name = "l00051" > < / a > < span class = "lineno" > 51< / span > < span class = "keyword" > const< / span > < a class = "code hl_typedef" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > & graph,< / div >
< div class = "line" > < a id = "l00052" 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 id = "l00053" name = "l00053" > < / a > < span class = "lineno" > 53< / span > < span class = "keyword" > using< / span > < a class = "code hl_typedef" href = "namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b" > ArcIndex< / a > = < span class = "keyword" > typename< / span > < a class = "code hl_typedef" href = "namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b" > Graph::ArcIndex< / a > ;< / div >
< div class = "line" > < a id = "l00054" name = "l00054" > < / a > < span class = "lineno" > 54< / span > < span class = "keyword" > using< / span > < a class = "code hl_typedef" href = "namespaceoperations__research.html#a7ae31ba4c3b4899478e53ca13df35dfc" > NodeIndex< / a > = < span class = "keyword" > typename< / span > < a class = "code hl_typedef" href = "namespaceoperations__research.html#a7ae31ba4c3b4899478e53ca13df35dfc" > Graph::NodeIndex< / a > ;< / div >
< div class = "line" > < a id = "l00055" 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 id = "l00056" name = "l00056" > < / a > < span class = "lineno" > 56< / span > < span class = "keywordtype" > int< / span > arc_index = 0;< / div >
< div class = "line" > < a id = "l00057" name = "l00057" > < / a > < span class = "lineno" > 57< / span > std::vector< ArcIndex> tree_arcs;< / div >
< div class = "line" > < a id = "l00058" name = "l00058" > < / a > < span class = "lineno" > 58< / span > < span class = "keywordflow" > if< / span > (graph.num_nodes() == 0) {< / div >
< div class = "line" > < a id = "l00059" name = "l00059" > < / a > < span class = "lineno" > 59< / span > < span class = "keywordflow" > return< / span > tree_arcs;< / div >
< div class = "line" > < a id = "l00060" name = "l00060" > < / a > < span class = "lineno" > 60< / span > }< / div >
< div class = "line" > < a id = "l00061" 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 id = "l00062" name = "l00062" > < / a > < span class = "lineno" > 62< / span > tree_arcs.reserve(expected_tree_size);< / div >
< div class = "line" > < a id = "l00063" name = "l00063" > < / a > < span class = "lineno" > 63< / span > < a class = "code hl_class" href = "class_dense_connected_components_finder.html" > DenseConnectedComponentsFinder< / a > components;< / div >
< div class = "line" > < a id = "l00064" name = "l00064" > < / a > < span class = "lineno" > 64< / span > components.< a class = "code hl_function" href = "class_dense_connected_components_finder.html#ad8e718920ab9683d39af650d714cffe1" > SetNumberOfNodes< / a > (graph.num_nodes());< / div >
< div class = "line" > < a id = "l00065" name = "l00065" > < / a > < span class = "lineno" > 65< / span > < span class = "keywordflow" > while< / span > (tree_arcs.size() != expected_tree_size & & arc_index < num_arcs) {< / div >
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< div class = "line" > < a id = "l00066" name = "l00066" > < / a > < span class = "lineno" > 66< / span > < span class = "keyword" > const< / span > < a class = "code hl_typedef" href = "namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b" > ArcIndex< / a > < a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > = sorted_arcs[arc_index];< / div >
< div class = "line" > < a id = "l00067" name = "l00067" > < / a > < span class = "lineno" > 67< / span > < span class = "keyword" > const< / span > < span class = "keyword" > auto< / span > < a class = "code hl_variable" href = "routing__flow_8cc.html#a64e7efc5529154ba56903e75f5300990" > tail< / a > = graph.Tail(< a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > );< / div >
< div class = "line" > < a id = "l00068" name = "l00068" > < / a > < span class = "lineno" > 68< / span > < span class = "keyword" > const< / span > < span class = "keyword" > auto< / span > < a class = "code hl_variable" href = "routing__flow_8cc.html#afca32f65388659a4b0956496169488b4" > head< / a > = graph.Head(< a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > );< / div >
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< div class = "line" > < a id = "l00069" name = "l00069" > < / a > < span class = "lineno" > 69< / span > < span class = "keywordflow" > if< / span > (!components.< a class = "code hl_function" href = "class_dense_connected_components_finder.html#a962b54327591b21cc0a9273f78906a8b" > Connected< / a > (< a class = "code hl_variable" href = "routing__flow_8cc.html#a64e7efc5529154ba56903e75f5300990" > tail< / a > , < a class = "code hl_variable" href = "routing__flow_8cc.html#afca32f65388659a4b0956496169488b4" > head< / a > )) {< / div >
< div class = "line" > < a id = "l00070" name = "l00070" > < / a > < span class = "lineno" > 70< / span > components.< a class = "code hl_function" href = "class_dense_connected_components_finder.html#a428ab6b7c944afe33bd86a6a1ae7e668" > AddEdge< / a > (< a class = "code hl_variable" href = "routing__flow_8cc.html#a64e7efc5529154ba56903e75f5300990" > tail< / a > , < a class = "code hl_variable" href = "routing__flow_8cc.html#afca32f65388659a4b0956496169488b4" > head< / a > );< / div >
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< div class = "line" > < a id = "l00071" name = "l00071" > < / a > < span class = "lineno" > 71< / span > tree_arcs.push_back(< a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > );< / div >
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< div class = "line" > < a id = "l00072" name = "l00072" > < / a > < span class = "lineno" > 72< / span > }< / div >
< div class = "line" > < a id = "l00073" name = "l00073" > < / a > < span class = "lineno" > 73< / span > ++arc_index;< / div >
< div class = "line" > < a id = "l00074" name = "l00074" > < / a > < span class = "lineno" > 74< / span > }< / div >
< div class = "line" > < a id = "l00075" name = "l00075" > < / a > < span class = "lineno" > 75< / span > < span class = "keywordflow" > return< / span > tree_arcs;< / div >
< div class = "line" > < a id = "l00076" name = "l00076" > < / a > < span class = "lineno" > 76< / span > }< / div >
< div class = "line" > < a id = "l00077" name = "l00077" > < / a > < span class = "lineno" > 77< / span > < / div >
< div class = "line" > < a id = "l00078" name = "l00078" > < / a > < span class = "lineno" > 78< / span > < span class = "comment" > // Version taking an arc comparator to sort graph arcs.< / span > < / div >
< div class = "line" > < a id = "l00079" name = "l00079" > < / a > < span class = "lineno" > 79< / span > < span class = "comment" > // Usage:< / span > < / div >
< div class = "line" > < a id = "l00080" name = "l00080" > < / a > < span class = "lineno" > 80< / span > < span class = "comment" > // ListGraph< int, int> graph(...);< / span > < / div >
< div class = "line" > < a id = "l00081" name = "l00081" > < / a > < span class = "lineno" > 81< / span > < span class = "comment" > // const auto arc_cost = [& graph](int arc) {< / span > < / div >
< div class = "line" > < a id = "l00082" name = "l00082" > < / a > < span class = "lineno" > 82< / span > < span class = "comment" > // return f(graph.Tail(arc), graph.Head(arc));< / span > < / div >
< div class = "line" > < a id = "l00083" name = "l00083" > < / a > < span class = "lineno" > 83< / span > < span class = "comment" > // };< / span > < / div >
< div class = "line" > < a id = "l00084" name = "l00084" > < / a > < span class = "lineno" > 84< / span > < span class = "comment" > // std::vector< int> mst = BuildKruskalMinimumSpanningTree(< / span > < / div >
< div class = "line" > < a id = "l00085" name = "l00085" > < / a > < span class = "lineno" > 85< / span > < span class = "comment" > // graph,< / span > < / div >
< div class = "line" > < a id = "l00086" name = "l00086" > < / a > < span class = "lineno" > 86< / span > < span class = "comment" > // [& arc_cost](int a, int b) { return arc_cost(a) < arc_cost(b); });< / span > < / div >
< div class = "line" > < a id = "l00087" name = "l00087" > < / a > < span class = "lineno" > 87< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00088" name = "l00088" > < / a > < span class = "lineno" > 88< / span > < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > Graph, < span class = "keyword" > typename< / span > ArcComparator> < / div >
< div class = "line" > < a id = "l00089" name = "l00089" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#aea7ea9ecb4c13ebf26b36a576c4fdc5f" > 89< / a > < / span > std::vector< typename Graph::ArcIndex> < a class = "code hl_function" href = "namespaceoperations__research.html#aea7ea9ecb4c13ebf26b36a576c4fdc5f" > BuildKruskalMinimumSpanningTree< / a > (< / div >
< div class = "line" > < a id = "l00090" name = "l00090" > < / a > < span class = "lineno" > 90< / span > < span class = "keyword" > const< / span > < a class = "code hl_typedef" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > & graph, < span class = "keyword" > const< / span > ArcComparator& arc_comparator) {< / div >
< div class = "line" > < a id = "l00091" name = "l00091" > < / a > < span class = "lineno" > 91< / span > < span class = "keyword" > using< / span > < a class = "code hl_typedef" href = "namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b" > ArcIndex< / a > = < span class = "keyword" > typename< / span > < a class = "code hl_typedef" href = "namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b" > Graph::ArcIndex< / a > ;< / div >
< div class = "line" > < a id = "l00092" name = "l00092" > < / a > < span class = "lineno" > 92< / span > std::vector< ArcIndex> sorted_arcs(graph.num_arcs());< / div >
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< div class = "line" > < a id = "l00093" name = "l00093" > < / a > < span class = "lineno" > 93< / span > < span class = "keywordflow" > for< / span > (< span class = "keyword" > const< / span > < a class = "code hl_typedef" href = "namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b" > ArcIndex< / a > < a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > : graph.AllForwardArcs()) {< / div >
< div class = "line" > < a id = "l00094" name = "l00094" > < / a > < span class = "lineno" > 94< / span > sorted_arcs[< a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > ] = < a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > ;< / div >
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< div class = "line" > < a id = "l00095" name = "l00095" > < / a > < span class = "lineno" > 95< / span > }< / div >
< div class = "line" > < a id = "l00096" name = "l00096" > < / a > < span class = "lineno" > 96< / span > std::sort(sorted_arcs.begin(), sorted_arcs.end(), arc_comparator);< / div >
< div class = "line" > < a id = "l00097" name = "l00097" > < / a > < span class = "lineno" > 97< / span > < span class = "keywordflow" > return< / span > < a class = "code hl_function" href = "namespaceoperations__research.html#aefd088882d7ba8d27157eba391b02792" > BuildKruskalMinimumSpanningTreeFromSortedArcs< / a > (graph, sorted_arcs);< / div >
< div class = "line" > < a id = "l00098" name = "l00098" > < / a > < span class = "lineno" > 98< / span > }< / div >
< div class = "line" > < a id = "l00099" name = "l00099" > < / a > < span class = "lineno" > 99< / span > < / div >
< div class = "line" > < a id = "l00100" name = "l00100" > < / a > < span class = "lineno" > 100< / span > < span class = "comment" > // Implementation of Prim' s mininumum spanning tree algorithm (c.f.< / span > < / div >
< div class = "line" > < a id = "l00101" name = "l00101" > < / a > < span class = "lineno" > 101< / span > < span class = "comment" > // https://en.wikipedia.org/wiki/Prim' s_algorithm) on undirected connected< / span > < / div >
< div class = "line" > < a id = "l00102" name = "l00102" > < / a > < span class = "lineno" > 102< / span > < span class = "comment" > // graphs.< / span > < / div >
< div class = "line" > < a id = "l00103" name = "l00103" > < / a > < span class = "lineno" > 103< / span > < span class = "comment" > // Returns the index of the arcs appearing in the tree.< / span > < / div >
< div class = "line" > < a id = "l00104" name = "l00104" > < / a > < span class = "lineno" > 104< / 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 id = "l00105" name = "l00105" > < / a > < span class = "lineno" > 105< / 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 id = "l00106" name = "l00106" > < / a > < span class = "lineno" > 106< / span > < span class = "comment" > // taken by the graph.< / span > < / div >
< div class = "line" > < a id = "l00107" name = "l00107" > < / a > < span class = "lineno" > 107< / span > < span class = "comment" > // Usage:< / span > < / div >
< div class = "line" > < a id = "l00108" name = "l00108" > < / a > < span class = "lineno" > 108< / span > < span class = "comment" > // ListGraph< int, int> graph(...);< / span > < / div >
< div class = "line" > < a id = "l00109" name = "l00109" > < / a > < span class = "lineno" > 109< / span > < span class = "comment" > // const auto arc_cost = [& graph](int arc) -> int64_t {< / span > < / div >
< div class = "line" > < a id = "l00110" name = "l00110" > < / a > < span class = "lineno" > 110< / span > < span class = "comment" > // return f(graph.Tail(arc), graph.Head(arc));< / span > < / div >
< div class = "line" > < a id = "l00111" name = "l00111" > < / a > < span class = "lineno" > 111< / span > < span class = "comment" > // };< / span > < / div >
< div class = "line" > < a id = "l00112" name = "l00112" > < / a > < span class = "lineno" > 112< / span > < span class = "comment" > // std::vector< int> mst = BuildPrimMinimumSpanningTree(graph, arc_cost);< / span > < / div >
< div class = "line" > < a id = "l00113" name = "l00113" > < / a > < span class = "lineno" > 113< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00114" name = "l00114" > < / a > < span class = "lineno" > 114< / span > < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > Graph, < span class = "keyword" > typename< / span > ArcValue> < / div >
< div class = "line" > < a id = "l00115" name = "l00115" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#aa7f6b276e52d86253d0798bc37f4994e" > 115< / a > < / span > std::vector< typename Graph::ArcIndex> < a class = "code hl_function" href = "namespaceoperations__research.html#aa7f6b276e52d86253d0798bc37f4994e" > BuildPrimMinimumSpanningTree< / a > (< / div >
< div class = "line" > < a id = "l00116" name = "l00116" > < / a > < span class = "lineno" > 116< / span > < span class = "keyword" > const< / span > < a class = "code hl_typedef" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > & graph, < span class = "keyword" > const< / span > ArcValue& arc_value) {< / div >
< div class = "line" > < a id = "l00117" name = "l00117" > < / a > < span class = "lineno" > 117< / span > < span class = "keyword" > using< / span > < a class = "code hl_typedef" href = "namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b" > ArcIndex< / a > = < span class = "keyword" > typename< / span > < a class = "code hl_typedef" href = "namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b" > Graph::ArcIndex< / a > ;< / div >
< div class = "line" > < a id = "l00118" name = "l00118" > < / a > < span class = "lineno" > 118< / span > < span class = "keyword" > using< / span > < a class = "code hl_typedef" href = "namespaceoperations__research.html#a7ae31ba4c3b4899478e53ca13df35dfc" > NodeIndex< / a > = < span class = "keyword" > typename< / span > < a class = "code hl_typedef" href = "namespaceoperations__research.html#a7ae31ba4c3b4899478e53ca13df35dfc" > Graph::NodeIndex< / a > ;< / div >
< div class = "line" > < a id = "l00119" name = "l00119" > < / a > < span class = "lineno" > 119< / span > < span class = "keyword" > using< / span > ArcValueType = < span class = "keyword" > decltype< / span > (arc_value(0));< / div >
< div class = "line" > < a id = "l00120" name = "l00120" > < / a > < span class = "lineno" > 120< / span > std::vector< ArcIndex> tree_arcs;< / div >
< div class = "line" > < a id = "l00121" name = "l00121" > < / a > < span class = "lineno" > 121< / span > < span class = "keywordflow" > if< / span > (graph.num_nodes() == 0) {< / div >
< div class = "line" > < a id = "l00122" name = "l00122" > < / a > < span class = "lineno" > 122< / span > < span class = "keywordflow" > return< / span > tree_arcs;< / div >
< div class = "line" > < a id = "l00123" name = "l00123" > < / a > < span class = "lineno" > 123< / span > }< / div >
< div class = "line" > < a id = "l00124" name = "l00124" > < / a > < span class = "lineno" > 124< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > expected_tree_size = graph.num_nodes() - 1;< / div >
< div class = "line" > < a id = "l00125" name = "l00125" > < / a > < span class = "lineno" > 125< / span > tree_arcs.reserve(expected_tree_size);< / div >
< div class = "line" > < a id = "l00126" name = "l00126" > < / a > < span class = "lineno" > 126< / span > std::vector< ArcIndex> node_neighbor(graph.num_nodes(), Graph::kNilArc);< / div >
< div class = "line" > < a id = "l00127" name = "l00127" > < / a > < span class = "lineno" > 127< / span > std::vector< bool> node_active(graph.num_nodes(), < span class = "keyword" > true< / span > );< / div >
< div class = "line" > < a id = "l00128" name = "l00128" > < / a > < span class = "lineno" > 128< / span > < / div >
< div class = "line" > < a id = "l00129" name = "l00129" > < / a > < span class = "lineno" > 129< / span > < span class = "comment" > // This struct represents entries in the adjustable priority queue which< / span > < / div >
< div class = "line" > < a id = "l00130" name = "l00130" > < / a > < span class = "lineno" > 130< / span > < span class = "comment" > // maintains active nodes (not added to the tree yet) in decreasing insertion< / span > < / div >
< div class = "line" > < a id = "l00131" name = "l00131" > < / a > < span class = "lineno" > 131< / span > < span class = "comment" > // cost order. AdjustablePriorityQueue requires the existence of the< / span > < / div >
< div class = "line" > < a id = "l00132" name = "l00132" > < / a > < span class = "lineno" > 132< / span > < span class = "comment" > // SetHeapIndex and GetHeapIndex methods.< / span > < / div >
< div class = "line" > < a id = "l00133" name = "l00133" > < / a > < span class = "lineno" > 133< / span > < span class = "keyword" > struct < / span > Entry {< / div >
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< div class = "line" > < a id = "l00134" name = "l00134" > < / a > < span class = "lineno" > 134< / span > < span class = "keywordtype" > void< / span > SetHeapIndex(< span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0" > index< / a > ) { heap_index = < a class = "code hl_variable" href = "local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0" > index< / a > ; }< / div >
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< div class = "line" > < a id = "l00135" name = "l00135" > < / a > < span class = "lineno" > 135< / span > < span class = "keywordtype" > int< / span > GetHeapIndex()< span class = "keyword" > const < / span > { < span class = "keywordflow" > return< / span > heap_index; }< / div >
< div class = "line" > < a id = "l00136" name = "l00136" > < / a > < span class = "lineno" > 136< / span > < span class = "keywordtype" > bool< / span > operator< (< span class = "keyword" > const< / span > Entry& other)< span class = "keyword" > const < / span > { < span class = "keywordflow" > return< / span > < a class = "code hl_variable" href = "demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514" > value< / a > > other.value; }< / div >
< div class = "line" > < a id = "l00137" name = "l00137" > < / a > < span class = "lineno" > 137< / span > < / div >
< div class = "line" > < a id = "l00138" name = "l00138" > < / a > < span class = "lineno" > 138< / span > < a class = "code hl_typedef" href = "namespaceoperations__research.html#a7ae31ba4c3b4899478e53ca13df35dfc" > NodeIndex< / a > node;< / div >
< div class = "line" > < a id = "l00139" name = "l00139" > < / a > < span class = "lineno" > 139< / span > ArcValueType < a class = "code hl_variable" href = "demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514" > value< / a > ;< / div >
< div class = "line" > < a id = "l00140" name = "l00140" > < / a > < span class = "lineno" > 140< / span > < span class = "keywordtype" > int< / span > heap_index;< / div >
< div class = "line" > < a id = "l00141" name = "l00141" > < / a > < span class = "lineno" > 141< / span > };< / div >
< div class = "line" > < a id = "l00142" name = "l00142" > < / a > < span class = "lineno" > 142< / span > < / div >
< div class = "line" > < a id = "l00143" name = "l00143" > < / a > < span class = "lineno" > 143< / span > < a class = "code hl_class" href = "class_adjustable_priority_queue.html" > AdjustablePriorityQueue< Entry> < / a > pq;< / div >
< div class = "line" > < a id = "l00144" name = "l00144" > < / a > < span class = "lineno" > 144< / span > std::vector< Entry> entries;< / div >
< div class = "line" > < a id = "l00145" name = "l00145" > < / a > < span class = "lineno" > 145< / span > std::vector< bool> touched_entry(graph.num_nodes(), < span class = "keyword" > false< / span > );< / div >
< div class = "line" > < a id = "l00146" name = "l00146" > < / a > < span class = "lineno" > 146< / span > < span class = "keywordflow" > for< / span > (< a class = "code hl_typedef" href = "namespaceoperations__research.html#a7ae31ba4c3b4899478e53ca13df35dfc" > NodeIndex< / a > node : graph.AllNodes()) {< / div >
< div class = "line" > < a id = "l00147" name = "l00147" > < / a > < span class = "lineno" > 147< / span > entries.push_back({node, < a class = "code hl_variable" href = "alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f" > std::numeric_limits< ArcValueType> ::max< / a > (), -1});< / div >
< div class = "line" > < a id = "l00148" name = "l00148" > < / a > < span class = "lineno" > 148< / span > }< / div >
< div class = "line" > < a id = "l00149" name = "l00149" > < / a > < span class = "lineno" > 149< / span > entries[0].value = 0;< / div >
< div class = "line" > < a id = "l00150" name = "l00150" > < / a > < span class = "lineno" > 150< / span > pq.< a class = "code hl_function" href = "class_adjustable_priority_queue.html#ac312fa979ea8afd5deabd6b581b3bb1f" > Add< / a > (& entries[0]);< / div >
< div class = "line" > < a id = "l00151" name = "l00151" > < / a > < span class = "lineno" > 151< / span > < span class = "keywordflow" > while< / span > (!pq.< a class = "code hl_function" href = "class_adjustable_priority_queue.html#a8e12342fc420701fbffd97025421575a" > IsEmpty< / a > () & & tree_arcs.size() != expected_tree_size) {< / div >
< div class = "line" > < a id = "l00152" name = "l00152" > < / a > < span class = "lineno" > 152< / span > < span class = "keyword" > const< / span > Entry* best = pq.< a class = "code hl_function" href = "class_adjustable_priority_queue.html#a503e1bfef34fc7acf03340ddd74b5872" > Top< / a > ();< / div >
< div class = "line" > < a id = "l00153" name = "l00153" > < / a > < span class = "lineno" > 153< / span > < span class = "keyword" > const< / span > < a class = "code hl_typedef" href = "namespaceoperations__research.html#a7ae31ba4c3b4899478e53ca13df35dfc" > NodeIndex< / a > node = best-> node;< / div >
< div class = "line" > < a id = "l00154" name = "l00154" > < / a > < span class = "lineno" > 154< / span > pq.< a class = "code hl_function" href = "class_adjustable_priority_queue.html#a701a584ce72cccbcce9cb0656b6c898b" > Pop< / a > ();< / div >
< div class = "line" > < a id = "l00155" name = "l00155" > < / a > < span class = "lineno" > 155< / span > node_active[node] = < span class = "keyword" > false< / span > ;< / div >
< div class = "line" > < a id = "l00156" name = "l00156" > < / a > < span class = "lineno" > 156< / span > < span class = "keywordflow" > if< / span > (node_neighbor[node] != Graph::kNilArc) {< / div >
< div class = "line" > < a id = "l00157" name = "l00157" > < / a > < span class = "lineno" > 157< / span > tree_arcs.push_back(node_neighbor[node]);< / div >
< div class = "line" > < a id = "l00158" name = "l00158" > < / a > < span class = "lineno" > 158< / span > }< / div >
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< div class = "line" > < a id = "l00159" name = "l00159" > < / a > < span class = "lineno" > 159< / span > < span class = "keywordflow" > for< / span > (< span class = "keyword" > const< / span > < a class = "code hl_typedef" href = "namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b" > ArcIndex< / a > < a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > : graph.OutgoingArcs(node)) {< / div >
< div class = "line" > < a id = "l00160" name = "l00160" > < / a > < span class = "lineno" > 160< / span > < span class = "keyword" > const< / span > < a class = "code hl_typedef" href = "namespaceoperations__research.html#a7ae31ba4c3b4899478e53ca13df35dfc" > NodeIndex< / a > neighbor = graph.Head(< a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > );< / div >
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< div class = "line" > < a id = "l00161" name = "l00161" > < / a > < span class = "lineno" > 161< / span > < span class = "keywordflow" > if< / span > (node_active[neighbor]) {< / div >
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< div class = "line" > < a id = "l00162" name = "l00162" > < / a > < span class = "lineno" > 162< / span > < span class = "keyword" > const< / span > ArcValueType < a class = "code hl_variable" href = "demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514" > value< / a > = arc_value(< a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > );< / div >
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< div class = "line" > < a id = "l00163" name = "l00163" > < / a > < span class = "lineno" > 163< / span > Entry& entry = entries[neighbor];< / div >
< div class = "line" > < a id = "l00164" name = "l00164" > < / a > < span class = "lineno" > 164< / span > < span class = "keywordflow" > if< / span > (< a class = "code hl_variable" href = "demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514" > value< / a > < entry.value || !touched_entry[neighbor]) {< / div >
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< div class = "line" > < a id = "l00165" name = "l00165" > < / a > < span class = "lineno" > 165< / span > node_neighbor[neighbor] = < a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > ;< / div >
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< div class = "line" > < a id = "l00166" name = "l00166" > < / a > < span class = "lineno" > 166< / span > entry.value = < a class = "code hl_variable" href = "demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514" > value< / a > ;< / div >
< div class = "line" > < a id = "l00167" name = "l00167" > < / a > < span class = "lineno" > 167< / span > touched_entry[neighbor] = < span class = "keyword" > true< / span > ;< / div >
< div class = "line" > < a id = "l00168" name = "l00168" > < / a > < span class = "lineno" > 168< / span > < span class = "keywordflow" > if< / span > (pq.< a class = "code hl_function" href = "class_adjustable_priority_queue.html#a7d1005d75f40525f91a2acb84348bc3c" > Contains< / a > (& entry)) {< / div >
< div class = "line" > < a id = "l00169" name = "l00169" > < / a > < span class = "lineno" > 169< / span > pq.< a class = "code hl_function" href = "class_adjustable_priority_queue.html#a506169056c5f470fabdf77aa1934a5a3" > NoteChangedPriority< / a > (& entry);< / div >
< div class = "line" > < a id = "l00170" name = "l00170" > < / a > < span class = "lineno" > 170< / span > } < span class = "keywordflow" > else< / span > {< / div >
< div class = "line" > < a id = "l00171" name = "l00171" > < / a > < span class = "lineno" > 171< / span > pq.< a class = "code hl_function" href = "class_adjustable_priority_queue.html#ac312fa979ea8afd5deabd6b581b3bb1f" > Add< / a > (& entry);< / div >
< div class = "line" > < a id = "l00172" name = "l00172" > < / a > < span class = "lineno" > 172< / span > }< / div >
< div class = "line" > < a id = "l00173" name = "l00173" > < / a > < span class = "lineno" > 173< / span > }< / div >
< div class = "line" > < a id = "l00174" name = "l00174" > < / a > < span class = "lineno" > 174< / span > }< / div >
< div class = "line" > < a id = "l00175" name = "l00175" > < / a > < span class = "lineno" > 175< / span > }< / div >
< div class = "line" > < a id = "l00176" name = "l00176" > < / a > < span class = "lineno" > 176< / span > }< / div >
< div class = "line" > < a id = "l00177" name = "l00177" > < / a > < span class = "lineno" > 177< / span > < span class = "keywordflow" > return< / span > tree_arcs;< / div >
< div class = "line" > < a id = "l00178" name = "l00178" > < / a > < span class = "lineno" > 178< / span > }< / div >
< div class = "line" > < a id = "l00179" name = "l00179" > < / a > < span class = "lineno" > 179< / span > < / div >
< div class = "line" > < a id = "l00180" name = "l00180" > < / a > < span class = "lineno" > 180< / span > } < span class = "comment" > // namespace operations_research< / span > < / div >
< div class = "line" > < a id = "l00181" name = "l00181" > < / a > < span class = "lineno" > 181< / span > < span class = "preprocessor" > #endif < / span > < span class = "comment" > // OR_TOOLS_GRAPH_MINIMUM_SPANNING_TREE_H_< / span > < / div >
< div class = "ttc" id = "aadjustable__priority__queue-inl_8h_html" > < div class = "ttname" > < a href = "adjustable__priority__queue-inl_8h.html" > adjustable_priority_queue-inl.h< / a > < / div > < / div >
< div class = "ttc" id = "aadjustable__priority__queue_8h_html" > < div class = "ttname" > < a href = "adjustable__priority__queue_8h.html" > adjustable_priority_queue.h< / a > < / div > < / div >
< div class = "ttc" id = "aalldiff__cst_8cc_html_a26e6db9bcc64b584051ecc28171ed11f" > < div class = "ttname" > < a href = "alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f" > max< / a > < / div > < div class = "ttdeci" > int64_t max< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "alldiff__cst_8cc_source.html#l00140" > alldiff_cst.cc:140< / a > < / div > < / div >
< div class = "ttc" id = "aclass_adjustable_priority_queue_html" > < div class = "ttname" > < a href = "class_adjustable_priority_queue.html" > AdjustablePriorityQueue< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "adjustable__priority__queue_8h_source.html#l00038" > adjustable_priority_queue.h:38< / a > < / div > < / div >
< div class = "ttc" id = "aclass_adjustable_priority_queue_html_a503e1bfef34fc7acf03340ddd74b5872" > < div class = "ttname" > < a href = "class_adjustable_priority_queue.html#a503e1bfef34fc7acf03340ddd74b5872" > AdjustablePriorityQueue::Top< / a > < / div > < div class = "ttdeci" > T * Top()< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "adjustable__priority__queue_8h_source.html#l00087" > adjustable_priority_queue.h:87< / a > < / div > < / div >
< div class = "ttc" id = "aclass_adjustable_priority_queue_html_a506169056c5f470fabdf77aa1934a5a3" > < div class = "ttname" > < a href = "class_adjustable_priority_queue.html#a506169056c5f470fabdf77aa1934a5a3" > AdjustablePriorityQueue::NoteChangedPriority< / a > < / div > < div class = "ttdeci" > void NoteChangedPriority(T *val)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "adjustable__priority__queue_8h_source.html#l00074" > adjustable_priority_queue.h:74< / a > < / div > < / div >
< div class = "ttc" id = "aclass_adjustable_priority_queue_html_a701a584ce72cccbcce9cb0656b6c898b" > < div class = "ttname" > < a href = "class_adjustable_priority_queue.html#a701a584ce72cccbcce9cb0656b6c898b" > AdjustablePriorityQueue::Pop< / a > < / div > < div class = "ttdeci" > void Pop()< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "adjustable__priority__queue_8h_source.html#l00117" > adjustable_priority_queue.h:117< / a > < / div > < / div >
< div class = "ttc" id = "aclass_adjustable_priority_queue_html_a7d1005d75f40525f91a2acb84348bc3c" > < div class = "ttname" > < a href = "class_adjustable_priority_queue.html#a7d1005d75f40525f91a2acb84348bc3c" > AdjustablePriorityQueue::Contains< / a > < / div > < div class = "ttdeci" > bool Contains(const T *val) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "adjustable__priority__queue_8h_source.html#l00069" > adjustable_priority_queue.h:69< / a > < / div > < / div >
< div class = "ttc" id = "aclass_adjustable_priority_queue_html_a8e12342fc420701fbffd97025421575a" > < div class = "ttname" > < a href = "class_adjustable_priority_queue.html#a8e12342fc420701fbffd97025421575a" > AdjustablePriorityQueue::IsEmpty< / a > < / div > < div class = "ttdeci" > bool IsEmpty() const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "adjustable__priority__queue_8h_source.html#l00127" > adjustable_priority_queue.h:127< / a > < / div > < / div >
< div class = "ttc" id = "aclass_adjustable_priority_queue_html_ac312fa979ea8afd5deabd6b581b3bb1f" > < div class = "ttname" > < a href = "class_adjustable_priority_queue.html#ac312fa979ea8afd5deabd6b581b3bb1f" > AdjustablePriorityQueue::Add< / a > < / div > < div class = "ttdeci" > void Add(T *val)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "adjustable__priority__queue_8h_source.html#l00049" > adjustable_priority_queue.h:49< / a > < / div > < / div >
< div class = "ttc" id = "aclass_dense_connected_components_finder_html" > < div class = "ttname" > < a href = "class_dense_connected_components_finder.html" > DenseConnectedComponentsFinder< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "connected__components_8h_source.html#l00081" > connected_components.h:81< / a > < / div > < / div >
< div class = "ttc" id = "aclass_dense_connected_components_finder_html_a428ab6b7c944afe33bd86a6a1ae7e668" > < div class = "ttname" > < a href = "class_dense_connected_components_finder.html#a428ab6b7c944afe33bd86a6a1ae7e668" > DenseConnectedComponentsFinder::AddEdge< / a > < / div > < div class = "ttdeci" > bool AddEdge(int node1, int node2)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "connected__components_8cc_source.html#l00096" > connected_components.cc:96< / a > < / div > < / div >
< div class = "ttc" id = "aclass_dense_connected_components_finder_html_a962b54327591b21cc0a9273f78906a8b" > < div class = "ttname" > < a href = "class_dense_connected_components_finder.html#a962b54327591b21cc0a9273f78906a8b" > DenseConnectedComponentsFinder::Connected< / a > < / div > < div class = "ttdeci" > bool Connected(int node1, int node2)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "connected__components_8cc_source.html#l00134" > connected_components.cc:134< / a > < / div > < / div >
< div class = "ttc" id = "aclass_dense_connected_components_finder_html_ad8e718920ab9683d39af650d714cffe1" > < div class = "ttname" > < a href = "class_dense_connected_components_finder.html#ad8e718920ab9683d39af650d714cffe1" > DenseConnectedComponentsFinder::SetNumberOfNodes< / a > < / div > < div class = "ttdeci" > void SetNumberOfNodes(int num_nodes)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "connected__components_8cc_source.html#l00036" > connected_components.cc:36< / a > < / div > < / div >
< div class = "ttc" id = "aconnected__components_8h_html" > < div class = "ttname" > < a href = "connected__components_8h.html" > connected_components.h< / a > < / div > < / div >
< div class = "ttc" id = "ademon__profiler_8cc_html_ac072af30c4ffbc834bb4c681f6ecb514" > < div class = "ttname" > < a href = "demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514" > value< / a > < / div > < div class = "ttdeci" > int64_t value< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "demon__profiler_8cc_source.html#l00044" > demon_profiler.cc:44< / a > < / div > < / div >
< div class = "ttc" id = "aintegral__types_8h_html" > < div class = "ttname" > < a href = "integral__types_8h.html" > integral_types.h< / a > < / div > < / div >
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< div class = "ttc" id = "alocal__search_8cc_html_a30b5726116ac85ea64777e5d6e333894" > < div class = "ttname" > < a href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > < / div > < div class = "ttdeci" > int arc< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "local__search_8cc_source.html#l02751" > local_search.cc:2751< / a > < / div > < / div >
< div class = "ttc" id = "alocal__search_8cc_html_a750b5d744c39a06bfb13e6eb010e35d0" > < div class = "ttname" > < a href = "local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0" > index< / a > < / div > < div class = "ttdeci" > int index< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "local__search_8cc_source.html#l02750" > local_search.cc:2750< / a > < / div > < / div >
2022-01-17 21:42:14 +01:00
< div class = "ttc" id = "anamespaceoperations__research_html" > < div class = "ttname" > < a href = "namespaceoperations__research.html" > operations_research< / a > < / div > < div class = "ttdoc" > Collection of objects used to extend the Constraint Solver library.< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "dense__doubly__linked__list_8h_source.html#l00021" > dense_doubly_linked_list.h:21< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_a7ae31ba4c3b4899478e53ca13df35dfc" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a7ae31ba4c3b4899478e53ca13df35dfc" > operations_research::NodeIndex< / a > < / div > < div class = "ttdeci" > int32_t NodeIndex< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "ebert__graph_8h_source.html#l00201" > ebert_graph.h:193< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_aa7f6b276e52d86253d0798bc37f4994e" > < div class = "ttname" > < a href = "namespaceoperations__research.html#aa7f6b276e52d86253d0798bc37f4994e" > 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#l00115" > minimum_spanning_tree.h:115< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_aea7ea9ecb4c13ebf26b36a576c4fdc5f" > < div class = "ttname" > < a href = "namespaceoperations__research.html#aea7ea9ecb4c13ebf26b36a576c4fdc5f" > 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#l00089" > minimum_spanning_tree.h:89< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_aecf320bda6e95d1edaf3a546673e3e6b" > < div class = "ttname" > < a href = "namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b" > operations_research::ArcIndex< / a > < / div > < div class = "ttdeci" > int32_t ArcIndex< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "ebert__graph_8h_source.html#l00202" > ebert_graph.h:202< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_aefd088882d7ba8d27157eba391b02792" > < div class = "ttname" > < a href = "namespaceoperations__research.html#aefd088882d7ba8d27157eba391b02792" > 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 = "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#l02362" > graph.h:2362< / a > < / div > < / div >
< div class = "ttc" id = "arouting__flow_8cc_html_a64e7efc5529154ba56903e75f5300990" > < div class = "ttname" > < a href = "routing__flow_8cc.html#a64e7efc5529154ba56903e75f5300990" > tail< / a > < / div > < div class = "ttdeci" > int64_t tail< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "routing__flow_8cc_source.html#l00149" > routing_flow.cc:149< / a > < / div > < / div >
< div class = "ttc" id = "arouting__flow_8cc_html_afca32f65388659a4b0956496169488b4" > < div class = "ttname" > < a href = "routing__flow_8cc.html#afca32f65388659a4b0956496169488b4" > head< / a > < / div > < div class = "ttdeci" > int64_t head< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "routing__flow_8cc_source.html#l00150" > routing_flow.cc:150< / a > < / div > < / div >
< div class = "ttc" id = "avector__or__function_8h_html" > < div class = "ttname" > < a href = "vector__or__function_8h.html" > vector_or_function.h< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
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2020-09-02 09:42:51 +02:00
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