C++ Program to Implement Network_Flow Problem

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This C++ Program demonstrates implementation of Network_Flow Problem.

Here is source code of the C++ Program to demonstrate Network_Flow Problem.
The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

  1. /*
  2.  * C++ Program to Implement Network Flow Problem
  3.  */
  4. #include <iostream>
  5. #include <climits>
  6. #include <cstring>
  7. #include <queue>
  8. #define V 6
  9. using namespace std;
  10.  
  11. /*
  12.  *  Returns true if there is a path from source 's' to sink 't' in
  13.  * residual graph. Also fills parent[] to store the path *
  14.  */
  15. bool bfs(int rGraph[V][V], int s, int t, int parent[])
  16. {
  17.     bool visited[V];
  18.     memset(visited, 0, sizeof(visited));
  19.     queue <int> q;
  20.     q.push(s);
  21.     visited[s] = true;
  22.     parent[s] = -1;
  23.     while (!q.empty())
  24.     {
  25.         int u = q.front();
  26.         q.pop();
  27.  
  28.         for (int v=0; v<V; v++)
  29.         {
  30.             if (visited[v]==false && rGraph[u][v] > 0)
  31.             {
  32.                 q.push(v);
  33.                 parent[v] = u;
  34.                 visited[v] = true;
  35.             }
  36.         }
  37.     }
  38.     return (visited[t] == true);
  39. }
  40.  
  41. /*
  42.  *  Returns tne maximum flow from s to t in the given graph
  43.  */
  44. int fordFulkerson(int graph[V][V], int s, int t)
  45. {
  46.     int u, v;
  47.     int rGraph[V][V];
  48.     for (u = 0; u < V; u++)
  49.     {
  50.         for (v = 0; v < V; v++)
  51.              rGraph[u][v] = graph[u][v];
  52.     }
  53.     int parent[V];
  54.     int max_flow = 0;
  55.  
  56.     while (bfs(rGraph, s, t, parent))
  57.     {
  58.         int path_flow = INT_MAX;
  59.         for (v=t; v!=s; v=parent[v])
  60.         {
  61.             u = parent[v];
  62.             path_flow = min(path_flow, rGraph[u][v]);
  63.         }
  64.         for (v = t; v != s; v = parent[v])
  65.         {
  66.             u = parent[v];
  67.             rGraph[u][v] -= path_flow;
  68.             rGraph[v][u] += path_flow;
  69.         }
  70.         max_flow += path_flow;
  71.     }
  72.     return max_flow;
  73. }
  74. /*
  75.  * Main Contains Menu
  76.  */ 
  77. int main()
  78. {
  79.     int graph[V][V] = { {0, 16, 13, 0, 0, 0},
  80.                         {0, 0, 10, 12, 0, 0},
  81.                         {0, 4, 0, 0, 14, 0},
  82.                         {0, 0, 9, 0, 0, 20},
  83.                         {0, 0, 0, 7, 0, 4},
  84.                         {0, 0, 0, 0, 0, 0}
  85.                       };
  86.  
  87.     cout << "The maximum possible flow is " << fordFulkerson(graph, 0, 5);
  88.  
  89.     return 0;
  90. }

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$ g++ nwtwork_flow.cpp
$ a.out
The maximum possible flow is 23
 
------------------
(program exited with code: 0)
Press return to continue

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn