C++ Program to Implement The Edmonds-Karp Algorithm

This is a C++ Program to Implement the Edmonds-Karp algorithm to calculate maximum flow between source and sink vertex.

Algorithm:

Begin
   function edmondsKarp() :
      initiate flow as 0.
      If there is an augmenting path from source to sink, add the path to flow.
      Return flow.
End

Example Code

#include<cstdio>
#include<queue>
#include<cstring>
#include<vector>
#include<iostream>
using namespace std;
int c[10][10];
int flowPassed[10][10];
vector<int> g[10];
int parList[10];
int currentPathC[10];
int bfs(int sNode, int eNode)//breadth first search
{
   memset(parList, -1, sizeof(parList));
   memset(currentPathC, 0, sizeof(currentPathC));
   queue<int> q;//declare queue vector
   q.push(sNode);
   parList[sNode] = -1;//initialize parlist’s source node
   currentPathC[sNode] = 999;//initialize currentpath’s source node
   while(!q.empty())// if q is not empty
   {
      int currNode = q.front();
      q.pop();
      for(int i=0; i<g[currNode].size(); i++)
      {
         int to = g[currNode][i];
         if(parList[to] == -1)
         {
            if(c[currNode][to] - flowPassed[currNode][to] > 0)
            {
               parList[to] = currNode;
               currentPathC[to] = min(currentPathC[currNode],
               c[currNode][to] - flowPassed[currNode][to]);
               if(to == eNode)
               {
                  return currentPathC[eNode];
               }
               q.push(to);
            }
         }
      }
   }
   return 0;
}
int edmondsKarp(int sNode, int eNode)
{
   int maxFlow = 0;
   while(true)
   {
      int flow = bfs(sNode, eNode);
      if (flow == 0)
      {
         break;
      }
      maxFlow += flow;
      int currNode = eNode;
      while(currNode != sNode)
      {
         int prevNode = parList[currNode];
         flowPassed[prevNode][currNode] += flow;
         flowPassed[currNode][prevNode] -= flow;
         currNode = prevNode;
      }
   }
return maxFlow;
}
int main()
{
   int nodCount, edCount;
   cout<<"enter the number of nodes and edges\n";
   cin>>nodCount>>edCount;
   int source, sink;
   cout<<"enter the source and sink\n";
   cin>>source>>sink;
   for(int ed = 0; ed < edCount; ed++)
   {
      cout<<"enter the start and end vertex along with capacity\n";
      int from, to, cap;
      cin>>from>>to>>cap;
      c[from][to] = cap;
      g[from].push_back(to);
      g[to].push_back(from);
   }
   int maxFlow = edmondsKarp(source, sink);
   cout<<endl<<endl<<"Max Flow is:"<<maxFlow<<endl;
}

Output

enter the number of nodes and edges
6
7
enter the source and sink
0
4
enter the start and end vertex along with capacity
0
1
14
enter the start and end vertex along with capacity
2
4
10
enter the start and end vertex along with capacity
6
7
9
enter the start and end vertex along with capacity
5
2
10
enter the start and end vertex along with capacity
1
4
12
enter the start and end vertex along with capacity
2
0
15
enter the start and end vertex along with capacity
5
3
15
Max Flow is:12