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Debashis08Debashis08
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feature-test: 0019 max flow relabel to front
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7 files changed

+219
-2
lines changed

7 files changed

+219
-2
lines changed

‎Headers/0003_Graph/0018_MaximumFlowGoldbergGenericPushRelabel.h‎

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#pragma once
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#include<map>
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#include<vector>
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#include<queue>
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using namespace std;

‎Headers/0003_Graph/0019_MaximumFlowRelabelToFront.h‎

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#pragma once
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#include<vector>
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#include<list>
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using namespace std;
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namespace MaximumFlowRelabelToFront
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{
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class Graph
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{
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private:
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int _noOfVertices;
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int _source;
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int _sink;
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int _maximumFlow;
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vector<vector<int>> _adjMatrix;
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vector<vector<int>> _residualGraph;
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vector<int> _excessFlow;
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vector<int> _height;
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vector<bool> _visited;
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list<int> _nodeList;
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void InitializePreflow();
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void Discharge(int nodeU);
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void Push(int nodeU, int nodeV);
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void Relabel(int nodeU);
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public:
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void CreateGraph(int noOfVertices);
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void PushDirectedEdge(int valueU, int valueV, int capacity);
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int FindMaximumFlowRelabelToFront();
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};
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}

‎SourceCodes/0003_Graph/0018_MaximumFlowGoldbergGenericPushRelabel.cc‎

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#include "../Headers/0003_Graph/0018_MaximumFlowGoldbergGenericPushRelabel.h"
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#include<queue>
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#include<climits>
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using namespace std;
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‎SourceCodes/0003_Graph/0019_MaximumFlowRelabelToFront.cc‎

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#include "../Headers/0003_Graph/0019_MaximumFlowRelabelToFront.h"
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#include<climits>
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#include<iterator>
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using namespace std;
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namespace MaximumFlowRelabelToFront
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{
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// Graph Private Member Methods
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// Initializes Pre-Flow in the given Flow Network
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void Graph::InitializePreflow()
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{
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// The height of source is set to highest possible height value
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this->_height[this->_source] = this->_noOfVertices;
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// Iterating over all the vertices
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for (int i = 0; i < this->_noOfVertices; i++)
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{
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// For the all the edges (source, v)
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if (this->_residualGraph[this->_source][i] > 0)
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{
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// v.excessFlow = capacity(source, v)
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this->_excessFlow[i] = this->_residualGraph[this->_source][i];
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// source.excessFlow = source.excessFlow - capacity(source, v)
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this->_excessFlow[this->_source] = this->_excessFlow[this->_source] - this->_residualGraph[this->_source][i];
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// Adjusting the flow and reverse flow along source->v and v->source respectively
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this->_residualGraph[i][this->_source] = this->_residualGraph[this->_source][i];
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this->_residualGraph[this->_source][i] = 0;
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}
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}
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}
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void Graph::Discharge(int nodeU)
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{
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while (this->_excessFlow[nodeU] > 0)
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{
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bool hasPushed = false;
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for (int nodeV = 0; nodeV < this->_noOfVertices; nodeV++)
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{
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if (this->_residualGraph[nodeU][nodeV] > 0 && this->_height[nodeU] == 1 + this->_height[nodeV])
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{
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this->Push(nodeU, nodeV);
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hasPushed = true;
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if (this->_excessFlow[nodeU] == 0)
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{
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break;
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}
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}
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}
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if (!hasPushed)
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{
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this->Relabel(nodeU);
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}
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}
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}
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// Pushes the flow from nodeU to its neighbour vertices
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void Graph::Push(int nodeU, int nodeV)
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{
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// Calculate the flow amount to be added along the edge and excess flow subtracted from nodeU
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int minimumFlow = min(this->_residualGraph[nodeU][nodeV], this->_excessFlow[nodeU]);
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// Adjust the flow and the reverse flow along (nodeU, nodeV)
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this->_residualGraph[nodeU][nodeV] = this->_residualGraph[nodeU][nodeV] - minimumFlow;
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this->_residualGraph[nodeV][nodeU] = this->_residualGraph[nodeV][nodeU] + minimumFlow;
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// Adjust the excess flows in nodeU and nodeV
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this->_excessFlow[nodeU] = this->_excessFlow[nodeU] - minimumFlow;
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this->_excessFlow[nodeV] = this->_excessFlow[nodeV] + minimumFlow;
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}
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// Relabels height of vertex nodeU when there are outgoing non-saturated edges available
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void Graph::Relabel(int nodeU)
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{
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int minimumHeight = INT_MAX;
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// Iterating over all the vertices
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for (int nodeV = 0; nodeV < this->_noOfVertices; nodeV++)
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{
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// For G'.Adj[nodeU] select for which nodeV, height[nodeU] <= height[nodeV]
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if (this->_residualGraph[nodeU][nodeV] > 0 && this->_height[nodeU] <= this->_height[nodeV])
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{
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// Get the minimum height among all these G'.Adj[nodeU]
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minimumHeight = min(minimumHeight, this->_height[nodeV]);
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}
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}
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// Set height[nodeU]
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this->_height[nodeU] = minimumHeight + 1;
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}
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// Graph Public Member Methods
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void Graph::CreateGraph(int noOfVertices)
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{
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this->_noOfVertices = noOfVertices;
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this->_source = 0;
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this->_sink = this->_noOfVertices - 1;
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this->_maximumFlow = 0;
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this->_adjMatrix = vector<vector<int>>(this->_noOfVertices, vector<int>(this->_noOfVertices, 0));
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this->_excessFlow = vector<int>(this->_noOfVertices, 0);
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this->_height = vector<int>(this->_noOfVertices, 0);
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this->_visited = vector<bool>(this->_noOfVertices, false);
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}
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void Graph::PushDirectedEdge(int valueU, int valueV, int capacity)
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{
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this->_adjMatrix[valueU][valueV] = capacity;
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}
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int Graph::FindMaximumFlowRelabelToFront()
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{
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this->_residualGraph = this->_adjMatrix;
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// Initialize Pre-flow
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this->InitializePreflow();
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for (int i = 0; i < this->_noOfVertices; i++)
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{
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if (i != this->_source && i != this->_sink)
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{
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this->_nodeList.push_back(i);
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}
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}
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list<int>::iterator nodeUiterator = this->_nodeList.begin();
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while (nodeUiterator != this->_nodeList.end())
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{
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int oldHeight = this->_height[*nodeUiterator];
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this->Discharge(*nodeUiterator);
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if (this->_height[*nodeUiterator] > oldHeight)
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{
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this->_nodeList.splice(this->_nodeList.begin(), this->_nodeList, nodeUiterator);
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nodeUiterator++;
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}
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else
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{
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nodeUiterator++;
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}
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}
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// Return the excess flow in the sink vertex which is actually the maximum flow along the given flow network
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return this->_excessFlow[this->_sink];
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}
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}

‎SourceCodes/0003_Graph/CMakeLists.txt‎

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0016_MaximumFlowEdmondsKarp.cc
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0017_MaximumBipartiteMatching.cc
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0018_MaximumFlowGoldbergGenericPushRelabel.cc
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0019_MaximumFlowRelabelToFront.cc
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)
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‎Tests/0003_Graph/0019_MaximumFlowRelabelToFrontTest.cc‎

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#include<gtest/gtest.h>
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#include "../Headers/0003_Graph/0019_MaximumFlowRelabelToFront.h"
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#include "../0000_CommonUtilities/UnitTestHelper.h"
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using namespace std;
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namespace MaximumFlowRelabelToFront
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{
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UnitTestHelper unitTestHelper;
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TEST(MaximumFlowRelabelToFront, SimpleGraph)
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{
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// Arrange
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Graph graph;
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int noOfVertices = 6;
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int expectedMaximumFlow = 23;
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// Act
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graph.CreateGraph(noOfVertices);
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graph.PushDirectedEdge(0, 1, 16);
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graph.PushDirectedEdge(0, 2, 13);
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graph.PushDirectedEdge(1, 3, 12);
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graph.PushDirectedEdge(2, 1, 4);
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graph.PushDirectedEdge(2, 4, 14);
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graph.PushDirectedEdge(3, 2, 9);
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graph.PushDirectedEdge(3, 5, 20);
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graph.PushDirectedEdge(4, 3, 7);
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graph.PushDirectedEdge(4, 5, 4);
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int actualMaximumFlow = graph.FindMaximumFlowRelabelToFront();
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// Assert
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ASSERT_EQ(expectedMaximumFlow, actualMaximumFlow);
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}
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}

‎Tests/0003_Graph/CMakeLists.txt‎

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0016_MaximumFlowEdmondsKarpTest.cc
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0017_MaximumBipartiteMatchingTest.cc
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0018_MaximumFlowGoldbergGenericPushRelabelTest.cc
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0019_MaximumFlowRelabelToFrontTest.cc
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)
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target_link_libraries(

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