Description

GraphsGraph ADT-What is a chart?- Graph methodsData structure for diagrams Edge rundown structure, nearness liststructure, contiguousness matrixGraph Traversal-Depth-first hunt Breadth-initially searchDirected diagrams. The Graph Abstract Data Type. . . u. v. (Toronto). (Winnipeg). (u, v). .

Transcripts

Diagrams Ed. 2. furthermore, 3.: Chapter 12 Ed. 4.: Chapter 13

Graphs Graph ADT - What is a diagram? - Graph strategies Data structure for diagrams - Edge list structure, nearness list structure, contiguousness framework Graph Traversal - Depth-first hunt - Breadth-first inquiry Directed charts

The Graph Abstract Data Type

( u , v ) u v (Toronto) (Winnipeg) ( v , u )

u v (New York) (Winnipeg) ( v , u )

self-circle

Graph Methods

Data Structure Exercises 20.1

Data Structure for Graphs

component c1 c2 rank c3

Edge Objects The edge object for an edge e putting away component o has information fields for A reference to o · A Boolean marker of whether e is guided or not · References to the vertex objects in V connected with the endpoint vertices of e (if the edge e is undir ected) or to the root and goal vertices of e (if the edge e is coordinated) · A reference to the position of the edge - object in holder E Note: The last information field is the rank of the edge object in the compartment E if E is a vector.

component With an edge show, a few strategies (edge - based) are quick while others require a few endeavors. For instance, strategies endVertices(), source(), and goal() are quick since we can get to edges straightforwardly. end vertex 1 or 0 end vertex

The Adjacency List Structure contiguousness list The structure for a diagram develops the edge list G structure. Like the edge list structure, the contiguousness list structure has a holder for the vertices and for the edges. V E More information structures and fields are added to vertex questions and edge objects. The vertex object holds a reference to a holder ( ), v I v · called the frequency compartment, that stores references to the edges occurrence on . On the off chance that coordinated edges are permitted, v then we segment ( ) into ( ) , ( ) , and ( ) that I v I v I v I v in ou t un store the in - coming, out - going, and undirected edges occurrence to . v

AC201 AC112 Ottawa JG120 AC200 Vancouver Winnipeg Calgary JG131 WJ75 WJ35 Toronto JG130 The edge object for an edge ( u , v ) holds references to the · positions of the edge in the occurrence compartments I ( u ) and I ( v ). Case:

Here is the manner by which the data is put away: Assume there are n vertices in the chart A vertex v additionally stores an unmistakable whole number key in the extent 0, · 1, … , n - 1, called the list of v (or essentially "record v "). In the n x n cluster A , the cell A [ i , j ] holds a referenc e to · the edge object e that runs from the vertex with list i to the vertex with record j , if such edge exists. On the off chance that the edge e is undirected, we store references to e in both A [ i , j ] and A [ j , i ]. In the event that there is no edge from vertex i to vertex j , we store an invalid item in both A [ i , j ] and A [ j , i ].

Data Structure Exercises 20.2