apeeyush / mincost-flow

Implementation of minimum cost flow algorithm

Minimum Cost Flow

An implementation of minimum cost flow algorithm.

Implementation Idea

Transform network G to a residual network and add source and sink
Detect and remove negative cycles using Bellman Ford if there is some flow in the network
Successive Shortest Path:
  while ( Gx contains a path from s to t and the required flow is not obtained ) do
    Find any shortest path P from s to t using Bellman Ford
    Augment flow along P
    update Gx

Input Format

• First line contains two integers denoting the number of vertices and the number of edges in the network.
• Next line contains an integer denoting the additional flow required from source to sink.
• Next line contains two integers denoting the source and sink in the network.
• This is followed by multiple lines (equal to the number of edges to be specific) with each line describing an edge. - Each edge is described as contains 5 integers denoting s, t, capacity, cost and current flow.

Setup and running instructions

All code is present in mincost.cpp. You can compile it using

g++ mincost.cpp

You can also try some of the sample examples present in the repository as folloes:

./a.out < examples/input1
./a.out < examples/input2
./a.out < examples/input3
./a.out < examples/input4

Licence

The code is released under the MIT License.