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< a href = "connectivity_8h.html" > Go to the documentation of this file.< / a > < div class = "fragment" > < div class = "line" > < a name = "l00001" > < / a > < span class = "lineno" > 1< / span >   < span class = "comment" > // Copyright 2010-2018 Google LLC< / span > < / div >
< div class = "line" > < a name = "l00002" > < / a > < span class = "lineno" > 2< / span >   < span class = "comment" > // Licensed under the Apache License, Version 2.0 (the " License" );< / span > < / div >
< div class = "line" > < a name = "l00003" > < / a > < span class = "lineno" > 3< / span >   < span class = "comment" > // you may not use this file except in compliance with the License.< / span > < / div >
< div class = "line" > < a name = "l00004" > < / a > < span class = "lineno" > 4< / span >   < span class = "comment" > // You may obtain a copy of the License at< / span > < / div >
< div class = "line" > < a name = "l00005" > < / a > < span class = "lineno" > 5< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00006" > < / a > < span class = "lineno" > 6< / span >   < span class = "comment" > // http://www.apache.org/licenses/LICENSE-2.0< / span > < / div >
< div class = "line" > < a name = "l00007" > < / a > < span class = "lineno" > 7< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00008" > < / a > < span class = "lineno" > 8< / span >   < span class = "comment" > // Unless required by applicable law or agreed to in writing, software< / span > < / div >
< div class = "line" > < a name = "l00009" > < / a > < span class = "lineno" > 9< / span >   < span class = "comment" > // distributed under the License is distributed on an " AS IS" BASIS,< / span > < / div >
< div class = "line" > < a name = "l00010" > < / a > < span class = "lineno" > 10< / span >   < span class = "comment" > // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.< / span > < / div >
< div class = "line" > < a name = "l00011" > < / a > < span class = "lineno" > 11< / span >   < span class = "comment" > // See the License for the specific language governing permissions and< / span > < / div >
< div class = "line" > < a name = "l00012" > < / a > < span class = "lineno" > 12< / span >   < span class = "comment" > // limitations under the License.< / span > < / div >
< div class = "line" > < a name = "l00013" > < / a > < span class = "lineno" > 13< / span >   < / div >
< div class = "line" > < a name = "l00014" > < / a > < span class = "lineno" > 14< / span >   < span class = "comment" > // Graph connectivity algorithm for undirected graphs.< / span > < / div >
< div class = "line" > < a name = "l00015" > < / a > < span class = "lineno" > 15< / span >   < span class = "comment" > // Memory consumption: O(n) where m is the number of arcs and n the number< / span > < / div >
< div class = "line" > < a name = "l00016" > < / a > < span class = "lineno" > 16< / span >   < span class = "comment" > // of nodes.< / span > < / div >
< div class = "line" > < a name = "l00017" > < / a > < span class = "lineno" > 17< / span >   < span class = "comment" > // TODO(user): add depth-first-search based connectivity for directed graphs.< / span > < / div >
< div class = "line" > < a name = "l00018" > < / a > < span class = "lineno" > 18< / span >   < span class = "comment" > // TODO(user): add depth-first-search based biconnectivity for directed graphs.< / 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" > #ifndef OR_TOOLS_GRAPH_CONNECTIVITY_H_< / span > < / div >
< div class = "line" > < a name = "l00021" > < / a > < span class = "lineno" > 21< / span >   < span class = "preprocessor" > #define OR_TOOLS_GRAPH_CONNECTIVITY_H_< / span > < / div >
< div class = "line" > < a name = "l00022" > < / a > < span class = "lineno" > 22< / span >   < / div >
< div class = "line" > < a name = "l00023" > < / a > < span class = "lineno" > 23< / span >   < span class = "preprocessor" > #include < vector> < / span > < / div >
< div class = "line" > < a name = "l00024" > < / a > < span class = "lineno" > 24< / span >   < / div >
< div class = "line" > < a name = "l00025" > < / a > < span class = "lineno" > 25< / span >   < span class = "preprocessor" > #include " ortools/base/integral_types.h" < / span > < / div >
< div class = "line" > < a name = "l00026" > < / a > < span class = "lineno" > 26< / span >   < span class = "preprocessor" > #include " ortools/base/logging.h" < / span > < / div >
< div class = "line" > < a name = "l00027" > < / a > < span class = "lineno" > 27< / span >   < span class = "preprocessor" > #include " ortools/base/macros.h" < / span > < / div >
< div class = "line" > < a name = "l00028" > < / a > < span class = "lineno" > 28< / span >   < / div >
< div class = "line" > < a name = "l00029" > < / a > < span class = "lineno" > 29< / span >   < span class = "keyword" > namespace < / span > < a class = "code" href = "namespaceoperations__research.html" > operations_research< / a > {< / div >
< div class = "line" > < a name = "l00030" > < / a > < span class = "lineno" > 30< / span >   < / div >
< div class = "line" > < a name = "l00031" > < / a > < span class = "lineno" > 31< / span >   < span class = "comment" > // Template class implementing a Union-Find algorithm with path compression for< / span > < / div >
< div class = "line" > < a name = "l00032" > < / a > < span class = "lineno" > 32< / span >   < span class = "comment" > // maintaining the connected components of a graph.< / span > < / div >
< div class = "line" > < a name = "l00033" > < / a > < span class = "lineno" > 33< / span >   < span class = "comment" > // See Cormen et al. 2nd Edition. MIT Press, 2001. ISBN 0-262-03293-7.< / span > < / div >
< div class = "line" > < a name = "l00034" > < / a > < span class = "lineno" > 34< / span >   < span class = "comment" > // Chapter 21: Data structures for Disjoint Sets, pp. 498-524.< / span > < / div >
< div class = "line" > < a name = "l00035" > < / a > < span class = "lineno" > 35< / span >   < span class = "comment" > // and Tarjan (1975). Efficiency of a Good But Not Linear Set< / span > < / div >
< div class = "line" > < a name = "l00036" > < / a > < span class = "lineno" > 36< / span >   < span class = "comment" > // Union Algorithm. Journal of the ACM 22(2):215-225< / span > < / div >
< div class = "line" > < a name = "l00037" > < / a > < span class = "lineno" > 37< / span >   < span class = "comment" > // It is implemented as a template so that the size of NodeIndex can be chosen< / span > < / div >
< div class = "line" > < a name = "l00038" > < / a > < span class = "lineno" > 38< / span >   < span class = "comment" > // depending on the size of the graphs considered.< / span > < / div >
< div class = "line" > < a name = "l00039" > < / a > < span class = "lineno" > 39< / span >   < span class = "comment" > // The main interest is that arcs do not need to be kept. Thus the memory< / span > < / div >
< div class = "line" > < a name = "l00040" > < / a > < span class = "lineno" > 40< / span >   < span class = "comment" > // complexity is O(n) where n is the number of nodes in the graph.< / span > < / div >
< div class = "line" > < a name = "l00041" > < / a > < span class = "lineno" > 41< / span >   < span class = "comment" > // The complexity of this algorithm is O(n . alpha(n)) where alpha(n) is< / span > < / div >
< div class = "line" > < a name = "l00042" > < / a > < span class = "lineno" > 42< / span >   < span class = "comment" > // the inverse Ackermann function. alpha(n) < = log(log(log(..log(log(n))..)< / span > < / div >
< div class = "line" > < a name = "l00043" > < / a > < span class = "lineno" > 43< / span >   < span class = "comment" > // In practice alpha(n) < = 5.< / span > < / div >
< div class = "line" > < a name = "l00044" > < / a > < span class = "lineno" > 44< / span >   < span class = "comment" > // See Tarjan and van Leeuwen (1984). Worst-case analysis of set union< / span > < / div >
< div class = "line" > < a name = "l00045" > < / a > < span class = "lineno" > 45< / span >   < span class = "comment" > // algorithms. Journal of the ACM 31(2):245-281.< / span > < / div >
< div class = "line" > < a name = "l00046" > < / a > < span class = "lineno" > 46< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00047" > < / a > < span class = "lineno" > 47< / span >   < span class = "comment" > // Usage example:< / span > < / div >
< div class = "line" > < a name = "l00048" > < / a > < span class = "lineno" > 48< / span >   < span class = "comment" > // ConnectedComponents< int, int> components;< / span > < / div >
< div class = "line" > < a name = "l00049" > < / a > < span class = "lineno" > 49< / span >   < span class = "comment" > // components.Init(num_nodes);< / span > < / div >
< div class = "line" > < a name = "l00050" > < / a > < span class = "lineno" > 50< / span >   < span class = "comment" > // for (int arc = 0; arc < num_arcs; ++arc) {< / span > < / div >
< div class = "line" > < a name = "l00051" > < / a > < span class = "lineno" > 51< / span >   < span class = "comment" > // components.AddArc(tail[arc], head[arc]);< / span > < / div >
< div class = "line" > < a name = "l00052" > < / a > < span class = "lineno" > 52< / span >   < span class = "comment" > // }< / span > < / div >
< div class = "line" > < a name = "l00053" > < / a > < span class = "lineno" > 53< / span >   < span class = "comment" > // int num_connected_components = components.GetNumberOfConnectedComponents();< / span > < / div >
< div class = "line" > < a name = "l00054" > < / a > < span class = "lineno" > 54< / span >   < span class = "comment" > // if (num_connected_components == 1) {< / span > < / div >
< div class = "line" > < a name = "l00055" > < / a > < span class = "lineno" > 55< / span >   < span class = "comment" > // // Graph is completely connected.< / span > < / div >
< div class = "line" > < a name = "l00056" > < / a > < span class = "lineno" > 56< / span >   < span class = "comment" > // }< / span > < / div >
< div class = "line" > < a name = "l00057" > < / a > < span class = "lineno" > 57< / span >   < span class = "comment" > // // Group the nodes in the same connected component together.< / span > < / div >
< div class = "line" > < a name = "l00058" > < / a > < span class = "lineno" > 58< / span >   < span class = "comment" > // // group[class_number][i] contains the i-th node in group class_number.< / span > < / div >
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< div class = "line" > < a name = "l00059" > < / a > < span class = "lineno" > 59< / span >   < span class = "comment" > // hash_map< int, vector< int> > group(num_connected_components);< / span > < / div >
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< div class = "line" > < a name = "l00060" > < / a > < span class = "lineno" > 60< / span >   < span class = "comment" > // for (int node = 0; node < num_nodes; ++node) {< / span > < / div >
< div class = "line" > < a name = "l00061" > < / a > < span class = "lineno" > 61< / span >   < span class = "comment" > // group[components.GetClassRepresentative(node)].push_back(node);< / span > < / div >
< div class = "line" > < a name = "l00062" > < / a > < span class = "lineno" > 62< / span >   < span class = "comment" > // }< / span > < / div >
< div class = "line" > < a name = "l00063" > < / a > < span class = "lineno" > 63< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00064" > < / a > < span class = "lineno" > 64< / span >   < span class = "comment" > // Keywords: graph, connected components.< / span > < / div >
< div class = "line" > < a name = "l00065" > < / a > < span class = "lineno" > 65< / span >   < / div >
< div class = "line" > < a name = "l00066" > < / a > < span class = "lineno" > 66< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > NodeIndex, < span class = "keyword" > typename< / span > ArcIndex> < / div >
< div class = "line" > < a name = "l00067" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1ConnectedComponents.html" > 67< / a > < / span >   < span class = "keyword" > class < / span > < a class = "code" href = "classoperations__research_1_1ConnectedComponents.html" > ConnectedComponents< / a > {< / div >
< div class = "line" > < a name = "l00068" > < / a > < span class = "lineno" > 68< / span >   < span class = "keyword" > public< / span > :< / div >
< div class = "line" > < a name = "l00069" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1ConnectedComponents.html#a04bf0bd47cf349309302338120f12465" > 69< / a > < / span >   < a class = "code" href = "classoperations__research_1_1ConnectedComponents.html#a04bf0bd47cf349309302338120f12465" > ConnectedComponents< / a > () : num_nodes_(0), class_(), class_size_() {}< / div >
< div class = "line" > < a name = "l00070" > < / a > < span class = "lineno" > 70< / span >   < / div >
< div class = "line" > < a name = "l00071" > < / a > < span class = "lineno" > 71< / span >   < span class = "comment" > // Reserves memory for num_nodes and resets the data structures.< / span > < / div >
< div class = "line" > < a name = "l00072" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1ConnectedComponents.html#a8247e505912b0c7d2309f3f9eaa74080" > 72< / a > < / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1ConnectedComponents.html#a8247e505912b0c7d2309f3f9eaa74080" > Init< / a > (< a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > num_nodes) {< / div >
< div class = "line" > < a name = "l00073" > < / a > < span class = "lineno" > 73< / span >   CHECK_GE(num_nodes, 0);< / div >
< div class = "line" > < a name = "l00074" > < / a > < span class = "lineno" > 74< / span >   num_nodes_ = num_nodes;< / div >
< div class = "line" > < a name = "l00075" > < / a > < span class = "lineno" > 75< / span >   class_.resize(num_nodes_);< / div >
< div class = "line" > < a name = "l00076" > < / a > < span class = "lineno" > 76< / span >   class_size_.assign(num_nodes_, 1);< / div >
< div class = "line" > < a name = "l00077" > < / a > < span class = "lineno" > 77< / span >   < span class = "keywordflow" > for< / span > (< a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > node = 0; node < num_nodes_; ++node) {< / div >
< div class = "line" > < a name = "l00078" > < / a > < span class = "lineno" > 78< / span >   class_[node] = node;< / 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 >   }< / div >
< div class = "line" > < a name = "l00081" > < / a > < span class = "lineno" > 81< / span >   < / div >
< div class = "line" > < a name = "l00082" > < / a > < span class = "lineno" > 82< / span >   < span class = "comment" > // Adds the information that NodeIndex tail and NodeIndex head are connected.< / span > < / div >
< div class = "line" > < a name = "l00083" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1ConnectedComponents.html#a07ef59a345df6bddab386c943af4238c" > 83< / a > < / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1ConnectedComponents.html#a07ef59a345df6bddab386c943af4238c" > AddArc< / a > (< a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > tail, < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > head) {< / div >
< div class = "line" > < a name = "l00084" > < / a > < span class = "lineno" > 84< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > tail_class = < a class = "code" href = "classoperations__research_1_1ConnectedComponents.html#aeaa04a98ce83a11cc8260f15b7ceb6ce" > CompressPath< / a > (tail);< / div >
< div class = "line" > < a name = "l00085" > < / a > < span class = "lineno" > 85< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > head_class = < a class = "code" href = "classoperations__research_1_1ConnectedComponents.html#aeaa04a98ce83a11cc8260f15b7ceb6ce" > CompressPath< / a > (head);< / div >
< div class = "line" > < a name = "l00086" > < / a > < span class = "lineno" > 86< / span >   < span class = "keywordflow" > if< / span > (tail_class != head_class) {< / div >
< div class = "line" > < a name = "l00087" > < / a > < span class = "lineno" > 87< / span >   < a class = "code" href = "classoperations__research_1_1ConnectedComponents.html#a047f863116aabfa88d8eeeebda5de760" > MergeClasses< / a > (tail_class, head_class);< / div >
< div class = "line" > < a name = "l00088" > < / a > < span class = "lineno" > 88< / span >   }< / div >
< div class = "line" > < a name = "l00089" > < / a > < span class = "lineno" > 89< / span >   }< / div >
< div class = "line" > < a name = "l00090" > < / a > < span class = "lineno" > 90< / span >   < / div >
< div class = "line" > < a name = "l00091" > < / a > < span class = "lineno" > 91< / span >   < span class = "comment" > // Adds a complete StarGraph to the object. Note that Depth-First Search< / span > < / div >
< div class = "line" > < a name = "l00092" > < / a > < span class = "lineno" > 92< / span >   < span class = "comment" > // is a better algorithm for finding connected components on graphs.< / span > < / div >
< div class = "line" > < a name = "l00093" > < / a > < span class = "lineno" > 93< / span >   < span class = "comment" > // TODO(user): implement Depth-First Search-based connected components finder.< / span > < / div >
< div class = "line" > < a name = "l00094" > < / a > < span class = "lineno" > 94< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > Graph> < / div >
< div class = "line" > < a name = "l00095" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1ConnectedComponents.html#a0f653082d74e1d7e9d8e97be437ba036" > 95< / a > < / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1ConnectedComponents.html#a0f653082d74e1d7e9d8e97be437ba036" > AddGraph< / a > (< span class = "keyword" > const< / span > < a class = "code" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > & graph) {< / div >
< div class = "line" > < a name = "l00096" > < / a > < span class = "lineno" > 96< / span >   < a class = "code" href = "classoperations__research_1_1ConnectedComponents.html#a8247e505912b0c7d2309f3f9eaa74080" > Init< / a > (graph.num_nodes());< / div >
< div class = "line" > < a name = "l00097" > < / a > < span class = "lineno" > 97< / span >   < span class = "keywordflow" > for< / span > (< a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > tail = 0; tail < graph.num_nodes(); ++tail) {< / div >
< div class = "line" > < a name = "l00098" > < / a > < span class = "lineno" > 98< / span >   < span class = "keywordflow" > for< / span > (< span class = "keyword" > typename< / span > Graph::OutgoingArcIterator it(graph, tail); it.Ok();< / div >
< div class = "line" > < a name = "l00099" > < / a > < span class = "lineno" > 99< / span >   it.Next()) {< / div >
< div class = "line" > < a name = "l00100" > < / a > < span class = "lineno" > 100< / span >   < a class = "code" href = "classoperations__research_1_1ConnectedComponents.html#a07ef59a345df6bddab386c943af4238c" > AddArc< / a > (tail, graph.Head(it.Index()));< / 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 >   }< / div >
< div class = "line" > < a name = "l00103" > < / a > < span class = "lineno" > 103< / span >   }< / div >
< div class = "line" > < a name = "l00104" > < / a > < span class = "lineno" > 104< / span >   < / div >
< div class = "line" > < a name = "l00105" > < / a > < span class = "lineno" > 105< / span >   < span class = "comment" > // Compresses the path for node.< / span > < / div >
< div class = "line" > < a name = "l00106" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1ConnectedComponents.html#aeaa04a98ce83a11cc8260f15b7ceb6ce" > 106< / a > < / span >   < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > < a class = "code" href = "classoperations__research_1_1ConnectedComponents.html#aeaa04a98ce83a11cc8260f15b7ceb6ce" > CompressPath< / a > (< a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > node) {< / div >
< div class = "line" > < a name = "l00107" > < / a > < span class = "lineno" > 107< / span >   CheckNodeBounds(node);< / div >
< div class = "line" > < a name = "l00108" > < / a > < span class = "lineno" > 108< / span >   < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > parent = node;< / div >
< div class = "line" > < a name = "l00109" > < / a > < span class = "lineno" > 109< / span >   < span class = "keywordflow" > while< / span > (parent != class_[parent]) {< / div >
< div class = "line" > < a name = "l00110" > < / a > < span class = "lineno" > 110< / span >   CheckNodeBounds(class_[parent]);< / div >
< div class = "line" > < a name = "l00111" > < / a > < span class = "lineno" > 111< / span >   CheckNodeBounds(class_[class_[parent]]);< / div >
< div class = "line" > < a name = "l00112" > < / a > < span class = "lineno" > 112< / span >   parent = class_[parent];< / div >
< div class = "line" > < a name = "l00113" > < / a > < span class = "lineno" > 113< / span >   }< / div >
< div class = "line" > < a name = "l00114" > < / a > < span class = "lineno" > 114< / span >   < span class = "keywordflow" > while< / span > (node != class_[node]) {< / div >
< div class = "line" > < a name = "l00115" > < / a > < span class = "lineno" > 115< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > old_parent = class_[node];< / div >
< div class = "line" > < a name = "l00116" > < / a > < span class = "lineno" > 116< / span >   class_[node] = parent;< / div >
< div class = "line" > < a name = "l00117" > < / a > < span class = "lineno" > 117< / span >   node = old_parent;< / div >
< div class = "line" > < a name = "l00118" > < / a > < span class = "lineno" > 118< / span >   }< / div >
< div class = "line" > < a name = "l00119" > < / a > < span class = "lineno" > 119< / span >   < span class = "keywordflow" > return< / span > parent;< / div >
< div class = "line" > < a name = "l00120" > < / a > < span class = "lineno" > 120< / span >   }< / div >
< div class = "line" > < a name = "l00121" > < / a > < span class = "lineno" > 121< / span >   < / div >
< div class = "line" > < a name = "l00122" > < / a > < span class = "lineno" > 122< / span >   < span class = "comment" > // Returns the equivalence class representative for node.< / span > < / div >
< div class = "line" > < a name = "l00123" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1ConnectedComponents.html#a874a54f45623ba735a5634b1ea9289ea" > 123< / a > < / span >   < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > < a class = "code" href = "classoperations__research_1_1ConnectedComponents.html#a874a54f45623ba735a5634b1ea9289ea" > GetClassRepresentative< / a > (< a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > node) {< / div >
< div class = "line" > < a name = "l00124" > < / a > < span class = "lineno" > 124< / span >   < span class = "keywordflow" > return< / span > < a class = "code" href = "classoperations__research_1_1ConnectedComponents.html#aeaa04a98ce83a11cc8260f15b7ceb6ce" > CompressPath< / a > (node);< / 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 >   < / div >
< div class = "line" > < a name = "l00127" > < / a > < span class = "lineno" > 127< / span >   < span class = "comment" > // Returns the number of connected components. Allocates num_nodes_ bits for< / span > < / div >
< div class = "line" > < a name = "l00128" > < / a > < span class = "lineno" > 128< / span >   < span class = "comment" > // the computation.< / span > < / div >
< div class = "line" > < a name = "l00129" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1ConnectedComponents.html#ad93186658fbb95624b55f85af74f8ea5" > 129< / a > < / span >   < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > < a class = "code" href = "classoperations__research_1_1ConnectedComponents.html#ad93186658fbb95624b55f85af74f8ea5" > GetNumberOfConnectedComponents< / a > () {< / div >
< div class = "line" > < a name = "l00130" > < / a > < span class = "lineno" > 130< / span >   < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > number = 0;< / div >
< div class = "line" > < a name = "l00131" > < / a > < span class = "lineno" > 131< / span >   < span class = "keywordflow" > for< / span > (< a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > node = 0; node < num_nodes_; ++node) {< / div >
< div class = "line" > < a name = "l00132" > < / a > < span class = "lineno" > 132< / span >   < span class = "keywordflow" > if< / span > (class_[node] == node) ++number;< / div >
< div class = "line" > < a name = "l00133" > < / a > < span class = "lineno" > 133< / span >   }< / div >
< div class = "line" > < a name = "l00134" > < / a > < span class = "lineno" > 134< / span >   < span class = "keywordflow" > return< / span > number;< / div >
< div class = "line" > < a name = "l00135" > < / a > < span class = "lineno" > 135< / span >   }< / div >
< div class = "line" > < a name = "l00136" > < / a > < span class = "lineno" > 136< / span >   < / div >
< div class = "line" > < a name = "l00137" > < / a > < span class = "lineno" > 137< / span >   < span class = "comment" > // Merges the equivalence classes of node1 and node2.< / span > < / div >
< div class = "line" > < a name = "l00138" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1ConnectedComponents.html#a047f863116aabfa88d8eeeebda5de760" > 138< / a > < / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1ConnectedComponents.html#a047f863116aabfa88d8eeeebda5de760" > MergeClasses< / a > (< a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > node1, < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > node2) {< / div >
< div class = "line" > < a name = "l00139" > < / a > < span class = "lineno" > 139< / span >   < span class = "comment" > // It' s faster (~10%) to swap the two values and have a single piece of< / span > < / div >
< div class = "line" > < a name = "l00140" > < / a > < span class = "lineno" > 140< / span >   < span class = "comment" > // code for merging the classes.< / span > < / div >
< div class = "line" > < a name = "l00141" > < / a > < span class = "lineno" > 141< / span >   CheckNodeBounds(node1);< / div >
< div class = "line" > < a name = "l00142" > < / a > < span class = "lineno" > 142< / span >   CheckNodeBounds(node2);< / div >
< div class = "line" > < a name = "l00143" > < / a > < span class = "lineno" > 143< / span >   < span class = "keywordflow" > if< / span > (class_size_[node1] < class_size_[node2]) {< / div >
< div class = "line" > < a name = "l00144" > < / a > < span class = "lineno" > 144< / span >   std::swap(node1, node2);< / div >
< div class = "line" > < a name = "l00145" > < / a > < span class = "lineno" > 145< / span >   }< / div >
< div class = "line" > < a name = "l00146" > < / a > < span class = "lineno" > 146< / span >   class_[node2] = node1;< / div >
< div class = "line" > < a name = "l00147" > < / a > < span class = "lineno" > 147< / span >   class_size_[node1] += class_size_[node2];< / div >
< div class = "line" > < a name = "l00148" > < / a > < span class = "lineno" > 148< / span >   }< / div >
< div class = "line" > < a name = "l00149" > < / a > < span class = "lineno" > 149< / span >   < / div >
< div class = "line" > < a name = "l00150" > < / a > < span class = "lineno" > 150< / span >   < span class = "keyword" > private< / span > :< / div >
< div class = "line" > < a name = "l00151" > < / a > < span class = "lineno" > 151< / span >   < span class = "keywordtype" > void< / span > CheckNodeBounds(< a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > node_index) {< / div >
< div class = "line" > < a name = "l00152" > < / a > < span class = "lineno" > 152< / span >   DCHECK_LE(0, node_index);< / div >
< div class = "line" > < a name = "l00153" > < / a > < span class = "lineno" > 153< / span >   DCHECK_LT(node_index, num_nodes_);< / div >
< div class = "line" > < a name = "l00154" > < / a > < span class = "lineno" > 154< / span >   }< / div >
< div class = "line" > < a name = "l00155" > < / a > < span class = "lineno" > 155< / span >   < span class = "comment" > // The exact number of nodes in the graph.< / span > < / div >
< div class = "line" > < a name = "l00156" > < / a > < span class = "lineno" > 156< / span >   < a class = "code" href = "namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582" > NodeIndex< / a > num_nodes_;< / div >
< div class = "line" > < a name = "l00157" > < / a > < span class = "lineno" > 157< / span >   < / div >
< div class = "line" > < a name = "l00158" > < / a > < span class = "lineno" > 158< / span >   < span class = "comment" > // The equivalence class representative for each node.< / span > < / div >
< div class = "line" > < a name = "l00159" > < / a > < span class = "lineno" > 159< / span >   std::vector< NodeIndex> class_;< / 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 = "comment" > // The size of each equivalence class of each node. Used to compress the paths< / span > < / div >
< div class = "line" > < a name = "l00162" > < / a > < span class = "lineno" > 162< / span >   < span class = "comment" > // and therefore achieve better time complexity.< / span > < / div >
< div class = "line" > < a name = "l00163" > < / a > < span class = "lineno" > 163< / span >   std::vector< NodeIndex> class_size_;< / div >
< div class = "line" > < a name = "l00164" > < / a > < span class = "lineno" > 164< / span >   < / div >
< div class = "line" > < a name = "l00165" > < / a > < span class = "lineno" > 165< / span >   DISALLOW_COPY_AND_ASSIGN(< a class = "code" href = "classoperations__research_1_1ConnectedComponents.html#a04bf0bd47cf349309302338120f12465" > ConnectedComponents< / a > );< / div >
< div class = "line" > < a name = "l00166" > < / a > < span class = "lineno" > 166< / span >   };< / div >
< div class = "line" > < a name = "l00167" > < / a > < span class = "lineno" > 167< / span >   < / div >
< div class = "line" > < a name = "l00168" > < / a > < span class = "lineno" > 168< / span >   } < span class = "comment" > // namespace operations_research< / span > < / div >
< div class = "line" > < a name = "l00169" > < / a > < span class = "lineno" > 169< / span >   < / div >
< div class = "line" > < a name = "l00170" > < / a > < span class = "lineno" > 170< / span >   < span class = "preprocessor" > #endif // OR_TOOLS_GRAPH_CONNECTIVITY_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 = "aclassoperations__research_1_1ConnectedComponents_html_a04bf0bd47cf349309302338120f12465" > < div class = "ttname" > < a href = "classoperations__research_1_1ConnectedComponents.html#a04bf0bd47cf349309302338120f12465" > operations_research::ConnectedComponents::ConnectedComponents< / a > < / div > < div class = "ttdeci" > ConnectedComponents()< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "connectivity_8h_source.html#l00069" > connectivity.h:69< / 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 = "aclassoperations__research_1_1ConnectedComponents_html_aeaa04a98ce83a11cc8260f15b7ceb6ce" > < div class = "ttname" > < a href = "classoperations__research_1_1ConnectedComponents.html#aeaa04a98ce83a11cc8260f15b7ceb6ce" > operations_research::ConnectedComponents::CompressPath< / a > < / div > < div class = "ttdeci" > NodeIndex CompressPath(NodeIndex node)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "connectivity_8h_source.html#l00106" > connectivity.h:106< / 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 = "aclassoperations__research_1_1ConnectedComponents_html_ad93186658fbb95624b55f85af74f8ea5" > < div class = "ttname" > < a href = "classoperations__research_1_1ConnectedComponents.html#ad93186658fbb95624b55f85af74f8ea5" > operations_research::ConnectedComponents::GetNumberOfConnectedComponents< / a > < / div > < div class = "ttdeci" > NodeIndex GetNumberOfConnectedComponents()< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "connectivity_8h_source.html#l00129" > connectivity.h:129< / 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 = "aclassoperations__research_1_1ConnectedComponents_html_a0f653082d74e1d7e9d8e97be437ba036" > < div class = "ttname" > < a href = "classoperations__research_1_1ConnectedComponents.html#a0f653082d74e1d7e9d8e97be437ba036" > operations_research::ConnectedComponents::AddGraph< / a > < / div > < div class = "ttdeci" > void AddGraph(const Graph & graph)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "connectivity_8h_source.html#l00095" > connectivity.h:95< / 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_a07ef59a345df6bddab386c943af4238c" > < div class = "ttname" > < a href = "classoperations__research_1_1ConnectedComponents.html#a07ef59a345df6bddab386c943af4238c" > operations_research::ConnectedComponents::AddArc< / a > < / div > < div class = "ttdeci" > void AddArc(NodeIndex tail, NodeIndex head)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "connectivity_8h_source.html#l00083" > connectivity.h:83< / 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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2019-06-13 15:36:14 +02:00
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