Struktura dat grafu a Algorithms (Příklad)
Sarah Chen
⚡ Chytré shrnutí
Graph Data Structure is a non-linear collection of vertices and edges where each edge links a pair of vertices. Graphs model real-world networks such as maps, social connections, and web pages, and support many powerful algorithms.
Co je to graf v datové struktuře?
A graph is a non-linear data structure that consists of vertices and edges, where vertices contain the information or data, and the edges work as a link between a pair of vertices.
It is used to solve real-world problems like finding the best route to the destination location and the route for telecommunications and social networks. Users are considered a node in the Graph, and the wires are the edges connecting the users.
Pokud jsou hrany reprezentovány jako E a vrcholy jsou reprezentovány jako V, pak lze graf G zapsat jako množinu vrcholů a hran, jako např. G (V, E).
Příklad grafu v datové struktuře
Here is a simple example of a graph data structure:
It is a simple undirected graph (one kind of Graph). Here the set of vertices is: {A, B, C, D, E, F}. Two vertices create an edge. For example, A and B are linked with an edge. However, A and F are not linked with any edges.
Terminologie grafů v datové struktuře
The following are some important terms used in the graph data structure:
| Období | Description |
|---|---|
| Vrchol | Each data element is called a vertex or a node. In the above image, A, B, C, D & E are the vertices. |
| Hrana (oblouk) | Connecting links between two nodes or vertices are called an edge (Arc). It has two ends and is represented as (startingVertex, endingVertex). |
| Neorientovaný okraj | Je to obousměrná hrana. |
| Režie Edge | Je to jednosměrná hrana. |
| Zatížená hrana | An edge with a value on it. |
| Stupeň | In a Graph, the number of edges connected to a vertex is called a degree. |
| Indegree | Celkový počet příchozích hran připojených k vrcholu. |
| Outdegree | Celkový počet odchozích hran připojených k vrcholu. |
| Vlastní smyčka | Hrana se nazývá vlastní smyčka, pokud se její dva koncové body shodují. |
| Sousedství | Vertices are said to be adjacent if an edge is connected between them. |
Typy grafů v datové struktuře
Zde je seznam těch nejběžnějších typy grafů v datové struktuře:
- Režírovaný graf
- Neorientovaný graf
- Vážený graf
- Obousměrný graf
- Nekonečný graf
- Null Graph
- Triviální graf
- Více grafů
- Kompletní graf
- Připojený graf
- Cyklický graf
- Řízený acyklický graf (DAG)
- Graf cyklu
- Bipartitní graf
- Eulerův graf
- Hamiltonův graf
How to Represent a Graph in Data Structure?
A graph is commonly stored in memory using one of two representations. The choice affects how much memory the graph uses and how fast common operations run.
- Adjacency Matrix: A two-dimensional V × V array where cell [i][j] is 1 (or the edge weight) if an edge exists between vertex i and vertex j, and 0 otherwise. It allows O(1) edge lookup but uses O(V²) space, making it best for dense graphs.
- Adjacency List: An array of lists where each vertex stores a list of its neighbouring vertices. It uses O(V + E) space and is efficient for sparse graphs, which is why most real-world graphs use it.
You can read more about these in the adjacency list and matrix representation of a graph výukový program.
Aplikace grafové datové struktury
A graph has many use cases. There are a lot of algorithms that use Graphs. Here are some of the applications of the Graph:
- Google Maps uses graphs to find the intersection of two roads and calculate the distance between two locations. For example, Dijkstra, for finding the shortest distance between the source and destination location.
- Facebook uses Graphs to find the mutual friends of the users. Its algorithm considers each user as a node of a graph.
- For resource allocation, a DAG (Directed Acyclic Graph) is used. It checks the dependency of the resources.
- Jedno Google Vyhledávače používají grafy k vytváření pozic webových stránek.
- Mapaping Zařízení používá datovou strukturu grafu.
- A router and its protocol use the Graph to learn the path to the destination.
