Network Flow introduction, flow Introduction

Network Flow introduction, flow Introduction

This series of articles only discuss the application of network stream in the informatics Competition

Preface

Network stream is a very huge system in the informatics Olympics. Because the model of this knowledge point is changeable, the modeling method is complicated, and the capability of contestants is demanding, therefore, it is often seen in various difficult and difficult competitions. (At least SDOI is almost once a year)

Network stream is a graph theory problem, while the graph theory problem is a mathematical problem in nature. Therefore, every conclusion in the network flow can be proved in detail by Du Niang.

Concept

Directed Graph: each edge has a directed graph ..

Source point: the entry level is $0 $.

Sink: the point with an outbound degree of $0 $

(It seems that it is not rigorous. You can intuitively feel it: joy :)

Definition: InDirected Graph$ G (V, E) $, if oneSource point$ S $,Settlement point$ T $, and each side $ (u, v) $ has a certainNon-negativeCapacity limit, it is called a network flow chart

Boil a chestnut

 

This is a network flow chart of the standard (nan) quasi (kan ).

S indicates the Source Vertex, T indicates the sink vertex, and the weight of each edge indicates the traffic.

But there is a figure with a wool card. After all, people's exams are not better-looking than others. joy:

Application

With this figure, we can do things on it.

The most basic concepts are:

 

Maximum Flow passive sink with upstream and downstream Feasible Flow source sink with upstream and downstream maximum flow source sink with upstream and downstream minimum flow minimum cost maximum flow no source sink minimum cost Feasible Flow

 

Each part has many classic models, so I plan to elaborate on the knowledge so that you can understand it easily.