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< a href = "SimpleMaxFlowProgram_8cs.html" > Go to the documentation of this file.< / a > < div class = "fragment" > < div class = "line" > < a name = "l00001" > < / a > < span class = "lineno" > 1< / span >   < span class = "comment" > // Copyright 2010-2018 Google LLC< / span > < / div >
< div class = "line" > < a name = "l00002" > < / a > < span class = "lineno" > 2< / span >   < span class = "comment" > // Licensed under the Apache License, Version 2.0 (the " License" );< / span > < / div >
< div class = "line" > < a name = "l00003" > < / a > < span class = "lineno" > 3< / span >   < span class = "comment" > // you may not use this file except in compliance with the License.< / span > < / div >
< div class = "line" > < a name = "l00004" > < / a > < span class = "lineno" > 4< / span >   < span class = "comment" > // You may obtain a copy of the License at< / span > < / div >
< div class = "line" > < a name = "l00005" > < / a > < span class = "lineno" > 5< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00006" > < / a > < span class = "lineno" > 6< / span >   < span class = "comment" > // http://www.apache.org/licenses/LICENSE-2.0< / span > < / div >
< div class = "line" > < a name = "l00007" > < / a > < span class = "lineno" > 7< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00008" > < / a > < span class = "lineno" > 8< / span >   < span class = "comment" > // Unless required by applicable law or agreed to in writing, software< / span > < / div >
< div class = "line" > < a name = "l00009" > < / a > < span class = "lineno" > 9< / span >   < span class = "comment" > // distributed under the License is distributed on an " AS IS" BASIS,< / span > < / div >
< div class = "line" > < a name = "l00010" > < / a > < span class = "lineno" > 10< / span >   < span class = "comment" > // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.< / span > < / div >
< div class = "line" > < a name = "l00011" > < / a > < span class = "lineno" > 11< / span >   < span class = "comment" > // See the License for the specific language governing permissions and< / span > < / div >
< div class = "line" > < a name = "l00012" > < / a > < span class = "lineno" > 12< / span >   < span class = "comment" > // limitations under the License.< / span > < / div >
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< div class = "line" > < a name = "l00014" > < / a > < span class = "lineno" > 14< / span >   < span class = "comment" > // [START program]< / span > < / div >
< div class = "line" > < a name = "l00015" > < / a > < span class = "lineno" > 15< / span >   < span class = "keyword" > using< / span > System;< / div >
< div class = "line" > < a name = "l00016" > < / a > < span class = "lineno" > 16< / span >   < span class = "keyword" > using< / span > < a class = "code" href = "namespaceGoogle.html" > Google< / a > .< a class = "code" href = "namespaceGoogle_1_1OrTools.html" > OrTools< / a > .< a class = "code" href = "namespaceGoogle_1_1OrTools_1_1Graph.html" > Graph< / a > ;< / div >
< div class = "line" > < a name = "l00017" > < / a > < span class = "lineno" > 17< / span >   < / div >
< div class = "line" > < a name = "l00018" > < / a > < span class = "lineno" > < a class = "line" href = "classSimpleMaxFlowProgram.html" > 18< / a > < / span >   < span class = "keyword" > public< / span > < span class = "keyword" > class < / span > < a class = "code" href = "classSimpleMaxFlowProgram.html" > SimpleMaxFlowProgram< / a > < / 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 = "keyword" > static< / span > < span class = "keywordtype" > void< / span > Main()< / div >
< div class = "line" > < a name = "l00021" > < / a > < span class = "lineno" > 21< / span >   {< / div >
< div class = "line" > < a name = "l00022" > < / a > < span class = "lineno" > 22< / span >   < span class = "comment" > // [START data]< / span > < / div >
< div class = "line" > < a name = "l00023" > < / a > < span class = "lineno" > 23< / span >   < span class = "comment" > // Define three parallel arrays: start_nodes, end_nodes, and the capacities< / span > < / div >
< div class = "line" > < a name = "l00024" > < / a > < span class = "lineno" > 24< / span >   < span class = "comment" > // between each pair. For instance, the arc from node 0 to node 1 has a< / span > < / div >
< div class = "line" > < a name = "l00025" > < / a > < span class = "lineno" > 25< / span >   < span class = "comment" > // capacity of 20.< / span > < / div >
< div class = "line" > < a name = "l00026" > < / a > < span class = "lineno" > 26< / span >   < span class = "comment" > // From Taha' s ' Introduction to Operations Research' ,< / span > < / div >
< div class = "line" > < a name = "l00027" > < / a > < span class = "lineno" > 27< / span >   < span class = "comment" > // example 6.4-2.< / span > < / div >
< div class = "line" > < a name = "l00028" > < / a > < span class = "lineno" > 28< / span >   < span class = "keywordtype" > int< / span > [] startNodes = {0, 0, 0, 1, 1, 2, 2, 3, 3};< / div >
< div class = "line" > < a name = "l00029" > < / a > < span class = "lineno" > 29< / span >   < span class = "keywordtype" > int< / span > [] endNodes = {1, 2, 3, 2, 4, 3, 4, 2, 4};< / div >
< div class = "line" > < a name = "l00030" > < / a > < span class = "lineno" > 30< / span >   < span class = "keywordtype" > int< / span > [] capacities = {20, 30, 10, 40, 30, 10, 20, 5, 20};< / div >
< div class = "line" > < a name = "l00031" > < / a > < span class = "lineno" > 31< / span >   < span class = "comment" > // [END data]< / span > < / div >
< div class = "line" > < a name = "l00032" > < / a > < span class = "lineno" > 32< / span >   < / div >
< div class = "line" > < a name = "l00033" > < / a > < span class = "lineno" > 33< / span >   < span class = "comment" > // [START constraints]< / span > < / div >
< div class = "line" > < a name = "l00034" > < / a > < span class = "lineno" > 34< / span >   < span class = "comment" > // Instantiate a SimpleMaxFlow solver.< / span > < / div >
< div class = "line" > < a name = "l00035" > < / a > < span class = "lineno" > 35< / span >   < a class = "code" href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html" > MaxFlow< / a > maxFlow = < span class = "keyword" > new< / span > < a class = "code" href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html" > MaxFlow< / a > ();< / div >
< div class = "line" > < a name = "l00036" > < / a > < span class = "lineno" > 36< / span >   < / div >
< div class = "line" > < a name = "l00037" > < / a > < span class = "lineno" > 37< / span >   < span class = "comment" > // Add each arc.< / span > < / div >
< div class = "line" > < a name = "l00038" > < / a > < span class = "lineno" > 38< / span >   < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > i = 0; i < startNodes.Length; ++i)< / div >
< div class = "line" > < a name = "l00039" > < / a > < span class = "lineno" > 39< / span >   {< / div >
< div class = "line" > < a name = "l00040" > < / a > < span class = "lineno" > 40< / span >   < span class = "keywordtype" > int< / span > arc = maxFlow.< a class = "code" href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a66eac4815c71eebe1806433677f0254f" > AddArcWithCapacity< / a > (startNodes[i], endNodes[i],< / div >
< div class = "line" > < a name = "l00041" > < / a > < span class = "lineno" > 41< / span >   capacities[i]);< / div >
< div class = "line" > < a name = "l00042" > < / a > < span class = "lineno" > 42< / span >   < span class = "keywordflow" > if< / span > (arc != i) < span class = "keywordflow" > throw< / span > < span class = "keyword" > new< / span > Exception(< span class = "stringliteral" > " Internal error" < / span > );< / div >
< div class = "line" > < a name = "l00043" > < / a > < span class = "lineno" > 43< / span >   }< / div >
< div class = "line" > < a name = "l00044" > < / a > < span class = "lineno" > 44< / span >   < span class = "comment" > // [END constraints]< / span > < / div >
< div class = "line" > < a name = "l00045" > < / a > < span class = "lineno" > 45< / span >   < / div >
< div class = "line" > < a name = "l00046" > < / a > < span class = "lineno" > 46< / span >   < span class = "comment" > // [START solve]< / span > < / div >
< div class = "line" > < a name = "l00047" > < / a > < span class = "lineno" > 47< / span >   < span class = "comment" > // Find the maximum flow between node 0 and node 4.< / span > < / div >
< div class = "line" > < a name = "l00048" > < / a > < span class = "lineno" > 48< / span >   < a class = "code" href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html" > MaxFlow< / a > .< a class = "code" href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a67a0db04d321a74b7e7fcfd3f1a3f70b" > Status< / a > solveStatus = maxFlow.< a class = "code" href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a5e78274982ba66a0e1d32059b14f4f9b" > Solve< / a > (0, 4);< / div >
< div class = "line" > < a name = "l00049" > < / a > < span class = "lineno" > 49< / span >   < span class = "comment" > // [END solve]< / span > < / div >
< div class = "line" > < a name = "l00050" > < / a > < span class = "lineno" > 50< / span >   < / div >
< div class = "line" > < a name = "l00051" > < / a > < span class = "lineno" > 51< / span >   < span class = "comment" > // [START print_solution]< / span > < / div >
< div class = "line" > < a name = "l00052" > < / a > < span class = "lineno" > 52< / span >   < span class = "keywordflow" > if< / span > (solveStatus == < a class = "code" href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html" > MaxFlow< / a > .< a class = "code" href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a67a0db04d321a74b7e7fcfd3f1a3f70b" > Status< / a > .OPTIMAL)< / div >
< div class = "line" > < a name = "l00053" > < / a > < span class = "lineno" > 53< / span >   {< / div >
< div class = "line" > < a name = "l00054" > < / a > < span class = "lineno" > 54< / span >   Console.WriteLine(< span class = "stringliteral" > " Max. flow: " < / span > + maxFlow.< a class = "code" href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#aed1e8fa4267c0a2360847a2f8fd1ee95" > OptimalFlow< / a > ());< / div >
< div class = "line" > < a name = "l00055" > < / a > < span class = "lineno" > 55< / span >   Console.WriteLine(< span class = "stringliteral" > " " < / span > );< / div >
< div class = "line" > < a name = "l00056" > < / a > < span class = "lineno" > 56< / span >   Console.WriteLine(< span class = "stringliteral" > " Arc Flow / Capacity" < / span > );< / div >
< div class = "line" > < a name = "l00057" > < / a > < span class = "lineno" > 57< / span >   < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > i = 0; i < maxFlow.< a class = "code" href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a84633dc5be4b4ebf2bde7f60e664ed52" > NumArcs< / a > (); ++i)< / div >
< div class = "line" > < a name = "l00058" > < / a > < span class = "lineno" > 58< / span >   {< / div >
< div class = "line" > < a name = "l00059" > < / a > < span class = "lineno" > 59< / span >   Console.WriteLine(maxFlow.< a class = "code" href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#af78c832e5a9d686751aff0d21ac8f3e4" > Tail< / a > (i) + < span class = "stringliteral" > " -> " < / span > +< / div >
< div class = "line" > < a name = "l00060" > < / a > < span class = "lineno" > 60< / span >   maxFlow.< a class = "code" href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#ad6ab95970447703dcf73d01dda07a3d2" > Head< / a > (i) + < span class = "stringliteral" > " " < / span > +< / div >
< div class = "line" > < a name = "l00061" > < / a > < span class = "lineno" > 61< / span >   < span class = "keywordtype" > string< / span > .Format(< span class = "stringliteral" > " {0,3}" < / span > , maxFlow.< a class = "code" href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a4db64727a4ade79cd3e10b10966a88a9" > Flow< / a > (i)) + < span class = "stringliteral" > " / " < / span > +< / div >
< div class = "line" > < a name = "l00062" > < / a > < span class = "lineno" > 62< / span >   < span class = "keywordtype" > string< / span > .Format(< span class = "stringliteral" > " {0,3}" < / span > , maxFlow.< a class = "code" href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a6812340dd92c7eaf5c34080fce687db6" > Capacity< / a > (i)));< / div >
< div class = "line" > < a name = "l00063" > < / a > < span class = "lineno" > 63< / span >   }< / div >
< div class = "line" > < a name = "l00064" > < / a > < span class = "lineno" > 64< / span >   }< / div >
< div class = "line" > < a name = "l00065" > < / a > < span class = "lineno" > 65< / span >   < span class = "keywordflow" > else< / span > < / div >
< div class = "line" > < a name = "l00066" > < / a > < span class = "lineno" > 66< / span >   {< / div >
< div class = "line" > < a name = "l00067" > < / a > < span class = "lineno" > 67< / span >   Console.WriteLine(< span class = "stringliteral" > " Solving the max flow problem failed. Solver status: " < / span > +< / div >
< div class = "line" > < a name = "l00068" > < / a > < span class = "lineno" > 68< / span >   solveStatus);< / div >
< div class = "line" > < a name = "l00069" > < / a > < span class = "lineno" > 69< / span >   }< / div >
< div class = "line" > < a name = "l00070" > < / a > < span class = "lineno" > 70< / span >   < span class = "comment" > // [END print_solution]< / span > < / div >
< div class = "line" > < a name = "l00071" > < / a > < span class = "lineno" > 71< / span >   }< / div >
< div class = "line" > < a name = "l00072" > < / a > < span class = "lineno" > 72< / span >   }< / div >
< div class = "line" > < a name = "l00073" > < / a > < span class = "lineno" > 73< / span >   < span class = "comment" > // [END program]< / span > < / div >
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< / div > <!-- fragment --> < / div > <!-- contents -->
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< div class = "ttc" id = "aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html_a5e78274982ba66a0e1d32059b14f4f9b" > < div class = "ttname" > < a href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a5e78274982ba66a0e1d32059b14f4f9b" > Google.OrTools.Graph.MaxFlow.Solve< / a > < / div > < div class = "ttdeci" > MaxFlow.Status Solve(int source, int sink)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "MaxFlow_8cs_source.html#l00080" > MaxFlow.cs:80< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceGoogle_1_1OrTools_1_1Graph_html" > < div class = "ttname" > < a href = "namespaceGoogle_1_1OrTools_1_1Graph.html" > Google.OrTools.Graph< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "LinearSumAssignment_8cs_source.html#l00011" > LinearSumAssignment.cs:11< / a > < / div > < / div >
< div class = "ttc" id = "aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html_a66eac4815c71eebe1806433677f0254f" > < div class = "ttname" > < a href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a66eac4815c71eebe1806433677f0254f" > Google.OrTools.Graph.MaxFlow.AddArcWithCapacity< / a > < / div > < div class = "ttdeci" > int AddArcWithCapacity(int tail, int head, long capacity)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "MaxFlow_8cs_source.html#l00050" > MaxFlow.cs:50< / a > < / div > < / div >
< div class = "ttc" id = "aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html_a4db64727a4ade79cd3e10b10966a88a9" > < div class = "ttname" > < a href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a4db64727a4ade79cd3e10b10966a88a9" > Google.OrTools.Graph.MaxFlow.Flow< / a > < / div > < div class = "ttdeci" > long Flow(int arc)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "MaxFlow_8cs_source.html#l00090" > MaxFlow.cs:90< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceGoogle_html" > < div class = "ttname" > < a href = "namespaceGoogle.html" > Google< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "KInt64Vector_8cs_source.html#l00011" > KInt64Vector.cs:11< / a > < / div > < / div >
< div class = "ttc" id = "aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html" > < div class = "ttname" > < a href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html" > Google.OrTools.Graph.MaxFlow< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "MaxFlow_8cs_source.html#l00013" > MaxFlow.cs:13< / a > < / div > < / div >
< div class = "ttc" id = "aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html_a84633dc5be4b4ebf2bde7f60e664ed52" > < div class = "ttname" > < a href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a84633dc5be4b4ebf2bde7f60e664ed52" > Google.OrTools.Graph.MaxFlow.NumArcs< / a > < / div > < div class = "ttdeci" > int NumArcs()< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "MaxFlow_8cs_source.html#l00060" > MaxFlow.cs:60< / a > < / div > < / div >
< div class = "ttc" id = "aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html_a67a0db04d321a74b7e7fcfd3f1a3f70b" > < div class = "ttname" > < a href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a67a0db04d321a74b7e7fcfd3f1a3f70b" > Google.OrTools.Graph.MaxFlow.Status< / a > < / div > < div class = "ttdeci" > Status< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "MaxFlow_8cs_source.html#l00095" > MaxFlow.cs:95< / a > < / div > < / div >
< div class = "ttc" id = "aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html_ad6ab95970447703dcf73d01dda07a3d2" > < div class = "ttname" > < a href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#ad6ab95970447703dcf73d01dda07a3d2" > Google.OrTools.Graph.MaxFlow.Head< / a > < / div > < div class = "ttdeci" > int Head(int arc)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "MaxFlow_8cs_source.html#l00070" > MaxFlow.cs:70< / a > < / div > < / div >
< div class = "ttc" id = "aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html_aed1e8fa4267c0a2360847a2f8fd1ee95" > < div class = "ttname" > < a href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#aed1e8fa4267c0a2360847a2f8fd1ee95" > Google.OrTools.Graph.MaxFlow.OptimalFlow< / a > < / div > < div class = "ttdeci" > long OptimalFlow()< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "MaxFlow_8cs_source.html#l00085" > MaxFlow.cs:85< / a > < / div > < / div >
< div class = "ttc" id = "aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html_a6812340dd92c7eaf5c34080fce687db6" > < div class = "ttname" > < a href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a6812340dd92c7eaf5c34080fce687db6" > Google.OrTools.Graph.MaxFlow.Capacity< / a > < / div > < div class = "ttdeci" > long Capacity(int arc)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "MaxFlow_8cs_source.html#l00075" > MaxFlow.cs:75< / a > < / div > < / div >
< div class = "ttc" id = "aclassSimpleMaxFlowProgram_html" > < div class = "ttname" > < a href = "classSimpleMaxFlowProgram.html" > SimpleMaxFlowProgram< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "SimpleMaxFlowProgram_8cs_source.html#l00018" > SimpleMaxFlowProgram.cs:18< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceGoogle_1_1OrTools_html" > < div class = "ttname" > < a href = "namespaceGoogle_1_1OrTools.html" > Google.OrTools< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "KInt64Vector_8cs_source.html#l00011" > KInt64Vector.cs:11< / a > < / div > < / div >
< div class = "ttc" id = "aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html_af78c832e5a9d686751aff0d21ac8f3e4" > < div class = "ttname" > < a href = "classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#af78c832e5a9d686751aff0d21ac8f3e4" > Google.OrTools.Graph.MaxFlow.Tail< / a > < / div > < div class = "ttdeci" > int Tail(int arc)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "MaxFlow_8cs_source.html#l00065" > MaxFlow.cs:65< / a > < / div > < / div >
2019-08-07 18:01:08 -07:00
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