Add Ford fulkerson algorithm about cosmos

[the-ethan-hunt]

I am working on the C++ code

[saurabhchalke]

I'll do it in Python

[saurabhchalke]

Added the Python implementation for ford fulkerson in #294

[saurabhchalke]

I would like to contribute to this.

[bamsarts]

#272 added ford fulkerson c++ language

[FredrikAugust]

Shouldn't the ones currently in here using BFS for finding augmenting paths be moved to Edmonds-Karp instead? As Ford-Fulkerson doesn't actually specify what algorithm should be used for finding them.

It is sometimes called a "method" instead of an "algorithm" as the approach to finding augmenting paths in a residual graph is not fully specified [...]

Ford-Fulkersons algorithm

The algorithm is identical to the Ford–Fulkerson algorithm, except that the search order when finding the augmenting path is defined. The path found must be a shortest path that has available capacity. This can be found by a breadth-first search, where we apply a weight of 1 to each edge.

Edmonds-Karp algorithm

Also noticed that at least the python algorithm for Ford-Fulkerson using BFS doesn't take edge weights into account, so it will find shortest paths, and thus be Edmonds-Karp.

[FredrikAugust]

Could perhaps leave Ford-Fulkerson in, but make it take an argument that is the function for finding augmenting paths. Then you could make Edmonds-Karp simply be a call to Ford-Fulkerson with BFS as the augmenting path-finding algorithm.