Data structure Tutorials--definition and terminology of the 26th lesson diagram

Teaching Purpose: To master the definition of graphs and the common terms

Teaching Emphasis: The common terminology of graphs

Teaching Difficulties: common terminology of graphs

Teaching Content:

I. Definition of graphs

A graph is a data structure that is a many-to-many relationship between data elements, plus an abstract data type consisting of a set of basic operations.

ADT graph{

A data Object V:V is a collection of data elements that have the same characteristics, called vertex sets.

Data relation R:

R={VR}

Vr={<v,w>|v,w (-V and P (v,w),<v,w> represent arcs from V to W, and predicate P (v,w) defines the meaning or information of the arc <v,w>}

Basic Operations P:

Creategraph (&G,V,VR);

Initial condition: V is the vertex set of the graph, and VR is the set of arcs in the graph.

Operation Result: construct graph G by definition of V and VR

Destroygraph (&G);

Initial condition: Figure G exists

Operation Result: Destroy Figure g

Locatevex (G,u);

Initial condition: Fig g exists, the vertex in U one G has the same characteristic

Operation Result: If there is a vertex u in G, then return the vertex to the position in the diagram; otherwise, other information will be returned.

Getvex (G,V);

Initial condition: The figure G exists, V is a vertex in G

Action Result: Returns the value of V.

Putvex (&g,v,value);

Initial condition: The figure G exists, V is a vertex in G

Operation Result: value of V Assignment

Firstadjvex (G,V);

Initial condition: The figure G exists, V is a vertex in G

Action Result: Returns the first contiguous vertex of V. If the vertex does not have an adjacent vertex in G, it returns "NULL"

Nextadjvex (G,V,W);

Initial conditions: The existence of Fig G, V is a vertex in G, W is the adjacent vertex of v.

Action Result: Returns the next contiguous vertex of V (relative to W). If W is the last contiguous point of V, return "null"

Insertvex (&G,V);

Initial condition: The existence of Fig G, V and vertex in the diagram have the same characteristics

Operation Result: Add a new vertex v in Fig g

Deletevex (&G,V);

Initial condition: The figure G exists, V is a vertex in G

Action Result: delete vertex v in G and its associated arc

INSERTACR (&G,V,W);

Initial conditions: Existence of fig G, V and W are two vertices in g

Operation Result: Add Arc <v,w> in G, if G is non direction, add symmetrical arc <w,v>

Deletearc (&G,V,W);

Initial conditions: Existence of fig G, V and W are two vertices in g

Operation Result: The arc <v,w> is removed in G, and if G is not, the symmetrical arc is also removed <w,v>

Dfstraverser (G,v,visit ());

Initial condition: The existence of Fig G, V is a vertex in G, visit is the application function of vertex

Operation Result: from Vertex v to depth first traverse graph G, and call function visit for each vertex. Once visit () fails, the operation fails.

Bfstraverse (G,v,visit ());

Initial condition: The existence of Fig G, V is a vertex in G, visit is the application function of vertex

Operation Result: from Vertex v breadth first traversal graph G, and call function visit for each vertex. Once visit () fails, the operation fails.

}adt Graph

Ii. Common terms for graphs

On the above figure are: G1= (V1,{A1})

Where: V1={v1,v2,v3,v4} A1={<v1,v2>,<v1,v3>,<v3,v4>,<v4,v1>}

If n is used to represent the number of vertices in the graph, the number of edges or arcs is represented by E:

For a n-1 graph, the range of values for E is 0 to n ()/2, and the non-direction graph with N (n-1)/2 edges is called a complete graph.

For a direction graph, E has a value range of 0 to N (n-1). A direction graph with N (n-1) arcs is called a forward-complete graph.

A graph with few edges or arcs is called a sparse graph, whereas a dense one.

V1 and v2 are mutually adjacent contacts E1 attached to vertex v1 and v2 V1 and v2 Associated V1 is 3 degrees.

For a direction graph, if there is a path between each pair of vertices, the graph is called a strongly connected graph.

Third, summary

Characteristics of graphs

The main difference between a direction graph and a non-direction graph