Algorithm: Max Flow Problem

reference 【Introduction to Algorithm Chapter 26】

Problem Setting

We aim to determine the maximum shipment rate achievable for transporting material from the source location to the sink location while adhering to all capacity limitations.

1.1 Flow networkds

A flow network G = (V, E) is a directed graph wherein each edge (u, v), which is part of the set E, possesses a non-negative capacity c(u, v) that is greater than or equal to zero.

We further mandate that an edge(u, v) is contained within E. Consequently, no edge(v, u) exists in the opposite direction.

If (u, v) is not belong to