Ford-Fulkerson Algorithm

Reference: Ford, L. R.; Fulkerson, D. R. (1956). Maximal flow through a network. Canadian Journal of Mathematics. 8: 399–404.

The Ford-Fulkerson algorithm for the maximum flow problem

Variables	Meaning
network	The residual graph, network[i][j] is the residual flow from node i to node j (list)
source	The source node
destination	The destination node
nn	The number of nodes
max_flow	The maximum flow
pred_node	pred_node[i] = j means node j is the predecessor node of node i in the augmenting path (list)

Example

if __name__ == '__main__':
    test_network = [
            [0, 5, 4, 3, 0, 0, 0, 0],
            [0, 0, 0, 0, 5, 3, 0, 0],
            [0, 0, 0, 0, 0, 3, 2, 0],
            [0, 0, 0, 0, 0, 0, 2, 0],
            [0, 5, 0, 0, 0, 0, 0, 4],
            [0, 0, 0, 0, 0, 0, 0, 3],
            [0, 0, 0, 0, 0, 0, 0, 5],
            [0, 0, 0, 0, 0, 0, 0, 0],
        ]
        s = 0
        d = 7
        print(main(test_network, s, d))

Output

11  # The maximum flow is 11