MELJUN CORTES DATA STRUCTURES Graph

7/26/2019 MELJUN CORTES DATA STRUCTURES Graph

1/17

Data Structures

Graphs

one of the most versatile structures used in

computer programming

have shape dictated by a physical problem

nodesare called vertices(the singular is vertex)

Graphs * Property of STIPage 1 of 17


2/17

Data Structures

Graphs


circles represent freeway interchanges andstraight lines connecting the circles representfreeways segments

the circles are the verticesand the lines are theedges


3/17

Data Structures

Adjacency

if they are connected by a single edge

Neighbors

Path

a sequence of edges Connected Graphs

Graphs



4/17

Data Structures

Directed and Weighted Graphs

Non-directed graphs- edges dont have adirection

Directed graphs - model situations in which

can go in only one direction along an edge Weight - a number that can represent the

physical distance between two vertices

Graphs



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Data Structures

Vertices

Graphs

class Vertex

{

public char label;

public boolean wasVisited;

public Vertex(char lab)

{


wasVisited = false;

}

}


6/17

Data Structures

Adjacency Matrix

two-dimensional array in which theelements indicate whether an edge is

present between two vertices

Graphs



7/17

Data Structures

Adjacency List

refers to a linked list of a kind examined inthe discussion of recursion

Graphs



8/17

Data Structures

Adding Vertices and Edges to a Graph

Creation of vertex

Inserting the edge

Graphs

vertexList[nVerts++] = new Vertex(F);

addjMat[1][3] = 1;

addjMat[3][1] = 1;



9/17

Data Structures

Graphs

class Graph

{

private final int MAX_VERTS = 20;

private Vertex vertexList[];

private int adjMat[][];

private int nVerts;

public Graph()

{vertexList = new Vertex[MAX_VERTS];

adjMat = new int[MAX_VERTS][MAX_VERTS];

nVerts = 0;

for(int j=0; j


10/17

Data Structures

Depth-First Search

Searches


Rule 1: If possible, visit an adjacent

unvisited vertex, mark it, and push it on the

stack. Rule 2: If you cant follow Rule 1, then, if

possible, pop vertex off the stack.

Rule 3: If you cant follow Rule 1 and Rule

2, its finished.


11/17

Data Structures

Searches

Depth-First Search


public int getAdjUnvisitedVertex(int v)

{

for(int j=0; j


12/17

Data Structures

Depth-First Search

Searches

public void dfs()

{

vertexList[0].wasVisited = true;displayVertex(0);

theStack.push(0);

while( !theStack.isEmpty() )

{


int v = getAdjUnvisitedVertex

( theStack.peek() );

if(v == -1)

theStack.pop();

else

{

vertexList[v].wasVisited = true;

displayVertex(v);

theStack.push(v);

}

}

for(int j=0; j


13/17

Data Structures

Depth-First Search creating a graph object

Searches

Graph theGraph = new Graph();

theGraph.addVertex('A');

theGraph.addVertex('B');

theGraph.addVertex('C');

theGraph.addVertex('D');

theGraph.addVertex('E');

theGraph.addEdge(0, 1);





System.out.print("Visits: ");

theGraph.dfs();

System.out.println();


14/17

Data Structures

Breadth-First Search - stay as close aspossible to the starting point

Searches


Rule 1: Visit the next unvisited vertex (if

there is one) thats adjacent to the current

vertex, mark it, and insert it into the queue.

Rule 2: If you cant carry out Rule 1

because there are no more unvisited

vertices, remove a vertex from the queue (if

possible) and make it the current vertex.

Rule 3: If you cant carry out Rule 2

because the queue is empty, its finished.


15/17

Data Structures

Breadth-First Search

Searches



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Data Structures

Searches

Breadth-First Search

public void bfs()

{

vertexList[0].wasVisited = true;

displayVertex(0);

theQueue.insert(0);

int v2;

while( !theQueue.isEmpty() )


int v1 = theQueue.remove();

while((v2=getAdjUnvisitedVertex(v1)) != -1)

{

vertexList[v2].wasVisited = true;

displayVertex(v2);

theQueue.insert(v2);

}

}

for(int j=0; j


17/17

Data Structures

Minimum Spanning Trees

while( !theStack.isEmpty() )

{


n curren er ex = e ac .pee ;

int v =getAdjUnvisitedVertex(currentVertex);

if(v == -1)

theStack.pop();else

{

vertexList[v].wasVisited = true;

theStack.push(v);

displayVertex(currentVertex);

displayVertex(v);

System.out.print(" ");}

}

for(int j=0; j

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MELJUN CORTES DATA STRUCTURES Graph