Summary of various network streams in one sentence)

Maximum stream: dinic or sap

Minimum fee maximum flow: spfa + augmented (the cost value is relatively discrete) or zkw (the cost value is concentrated)

The maximum upstream and downstream streams with a source sink: New s', T'. (I, j, L, R) indicates that I has an edge with a lower bound of L and R between J, split each such edge into (s ', J, 0, L), (I, T', 0, L), (I, j, 0, r-l), add the edge (t, s, 0, max), find the maximum stream from s' to t', and then remove (t, s, 0, max) this edge calculates the maximum stream from S to T

The smallest feasible stream in the upstream and downstream of a source sink: basically the same as above. Change the last step to reverse evaluate the maximum stream from t to S to return the stream; or two points (t, s, 0, max) capacity of this edge

Minimum Cost for upstream and downstream processes with source sink: The Edge splitting method is the same as above, and the maximum minimum fee flow is obtained from s' to t '.

The maximum minimum fee for upstream and downstream of a source exchange is the same as that for upstream and downstream exchange. You need to calculate the maximum minimum fee from T at S (* this is your own YY, maybe not, please advise)

Maximum stream without source sink (global minimum cut of undirected graphs): stoer-Wagner Algorithm

Maximum stream between all vertices without source sink: Divide and conquer. Select two vertices in the current point set to obtain the minimum cut, use this cut to update all the points that span on both sides (not necessarily the points in the current point set), cut your point set into two parts, and perform recursion.

Feasible upstream and downstream streams without source sink: Split edges and run the maximum stream directly from s' to t'

Minimum Cost for upstream and downstream of a non-source sink feasible stream: Split edge, directly from s' to t' run the maximum minimum cost flow

Minimum Cut to minimum short circuit of a plan: the plane area is treated as a point, and the edge weight between two points is the capacity of the sides between the original two plane areas, after completing the first positive infinity edge to the source, find the shortest path from one side of the positive infinity edge to the other side.

What else?