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Merge pull request #64 from Debashis08/release
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‎Headers/0003_Graph/0018_MaximumFlowGoldbergGenericPushRelabel.h

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#pragma once
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#include<vector>
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#include<queue>
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using namespace std;
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namespace MaximumFlowGoldbergGenericPushRelabel
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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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queue<int> _nodeQueue;
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void InitializePreflow();
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bool CheckOverFlow();
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bool Push(int nodeU);
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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 FindMaximumFlowGoldbergGenericPushRelabel();
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};
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}

‎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<climits>
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using namespace std;
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namespace MaximumFlowGoldbergGenericPushRelabel
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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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// Checks if there is any vertex which has excess flow
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bool Graph::CheckOverFlow()
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{
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// Iterating over all of the vertices
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for (int i = 0; i < this->_noOfVertices; i++)
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{
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// Checks if the current vertex is not any special vertex like source, sink
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// and also if there is excess flow in the current vertex and it is already not present in the queue
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if (i!=this->_source && i!=this->_sink && this->_excessFlow[i] > 0 && this->_visited[i] == false)
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{
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// Insert the current vertex into the queue
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this->_nodeQueue.push(i);
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// Mark it as visited, so until it leaves the queue it is not inserted again even if all the excess flow is neutralized
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this->_visited[i] = true;
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}
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}
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// Checks if there is no vertex having excess flow then returns false
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if (this->_nodeQueue.empty())
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{
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return false;
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}
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return true;
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}
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// Pushes the flow from nodeU to its neighbour vertices
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bool Graph::Push(int nodeU)
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{
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int nodeV = -1;
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int minimumFlow = INT_MAX;
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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 G'.Adj[nodeU] select the vertex if edge (nodeU, i) is non-saturated and height[nodeU] == height[i] + 1
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if (this->_residualGraph[nodeU][i] > 0 && this->_height[nodeU] == this->_height[i] + 1)
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{
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nodeV = i;
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break;
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}
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}
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// Checks if any neighbour vertex found having non-saturated edge
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if (nodeV != -1)
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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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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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// Return that the Push operation is successful
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return true;
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}
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// Return that the Push operation is not successful
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return false;
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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::FindMaximumFlowGoldbergGenericPushRelabel()
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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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// Checks if there is some vertices which have excess flow
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while (this->CheckOverFlow())
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{
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// Get the vertex
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int nodeU = this->_nodeQueue.front();
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// Checks if the Push operation is successful
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if (this->Push(nodeU))
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{
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// Then remove the vertex from queue and set visited[nodeU] = true
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// so that on next CheckOverFlow() method call this vertex can be discovered if it still has some excess flow
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this->_nodeQueue.pop();
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this->_visited[nodeU] = false;
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}
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// If the Push operation is not successful
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else
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{
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// Then Relabel nodeU without removing it from the queue
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this->Relabel(nodeU);
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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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}

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