Folienset 13: Implementierung von Graphen

Algorithmen und Datenstrukturen II
Peter Steffen
AG Praktische Informatik
Technische Fakultät
Universität Bielefeld
Vorlesung Sommer 2009
Peter Steffen
A&D II, Vorlesung 2009
Universität Bielefeld
Teil I
Implementierung von Graphen
Peter Steffen
A&D II, Vorlesung 2009
Universität Bielefeld
Die Klasse Edge
public class Edge {
int v;
int w;
Edge(int v, int w) {
this.v = v;
this.w = w;
}
}
Peter Steffen
A&D II, Vorlesung 2009
Universität Bielefeld
Die Klasse Graph
import java.util.LinkedList;
public class Graph {
private
private
private
private
int vertices;
int edges;
boolean directed;
LinkedList<Integer>[] adjlists;
public Graph(int v, boolean d){
vertices = v;
directed = d;
edges
= 0;
adjlists = new LinkedList[v];
for (int i=0; i<v; i++)
adjlists[i] = new LinkedList<Integer>();
}
int numOfV(){
return vertices;
}
int numOfE(){
return edges;
}
boolean directed(){
return directed;
}
Peter Steffen
A&D II, Vorlesung 2009
Universität Bielefeld
Die Klasse Graph
void insert(Edge e){
adjlists[e.v].add(new Integer(e.w));
edges++;
if (!directed) {
adjlists[e.w].add(new Integer(e.v));
edges++;
}
}
void remove(Edge e){
adjlists[e.v].remove(new Integer(e.w));
edges--;
if (!directed) {
adjlists[e.w].remove(new Integer(e.v));
edges--;
}
}
boolean edge(int v, int w){
return adjlists[v].contains(w);
}
LinkedList<Integer> getAdjList(int v){
return adjlists[v];
}
}
Peter Steffen
A&D II, Vorlesung 2009
Universität Bielefeld
Ein kleiner Test
import java.util.LinkedList;
public class GraphTest{
public static void main(String[] args){
Graph g = new Graph(8, false);
g.insert(new Edge(0,4));
g.insert(new Edge(0,1));
g.insert(new Edge(1,5));
g.insert(new Edge(5,2));
g.insert(new Edge(5,6));
g.insert(new Edge(2,3));
g.insert(new Edge(6,2));
g.insert(new Edge(6,3));
g.insert(new Edge(3,7));
g.insert(new Edge(6,7));
for (int i=0; i<g.numOfV(); i++){
System.out.println("Vertice " + i + ":");
LinkedList<Integer> l = g.getAdjList(i);
for (int j=0; j<l.size(); j++)
System.out.println("Edge to: " + l.get(j).intValue());
}
}
}
Peter Steffen
A&D II, Vorlesung 2009
Universität Bielefeld
Breitensuche
import java.util.LinkedList;
class BFS{
public static void bfs(Graph g, int s){
final char WHITE = 0;
final char GRAY = 1;
final char BLACK = 2;
char[] color = new char[g.numOfV()];
int[] d
= new int[g.numOfV()];
int[] pi
= new int[g.numOfV()];
for (int u=0; u<g.numOfV(); u++){
color[u] = WHITE;
d[u]
= -1;
pi[u]
= -1;
}
color[s] = GRAY;
d[s] = 0;
pi[s] = -1;
Peter Steffen
A&D II, Vorlesung 2009
Universität Bielefeld
Breitensuche
LinkedList<Integer> q = new LinkedList<Integer>();
q.add(new Integer(s));
while (!q.isEmpty()){
int u = q.remove().intValue();
LinkedList<Integer> l = g.getAdjList(u);
for (int i = 0; i<l.size(); i++){
int v = l.get(i).intValue();
if (color[v] == WHITE){
color[v] = GRAY;
d[v] = d[u] + 1;
pi[v] = u;
q.add(new Integer(v));
}
}
color[u] = BLACK;
System.out.println("finished with node " + u);
}
System.out.println("Distances from node " + s + ":");
for(int i = 0; i<g.numOfV(); i++)
System.out.println("Node " + i + ": " + d[i]);
}
}
Peter Steffen
A&D II, Vorlesung 2009
Universität Bielefeld
Tiefensuche
import java.util.LinkedList;
class DFS{
static
static
static
static
static
static
static
final char WHITE = 0;
final char GRAY = 1;
final char BLACK = 2;
char[] color;
int[] pi;
int[] d, f;
int time;
public static void dfs(Graph g){
color = new char[g.numOfV()];
pi
= new int[g.numOfV()];
d
= new int[g.numOfV()];
f
= new int[g.numOfV()];
for(int u=0; u<g.numOfV(); u++){
color[u] = WHITE;
pi[u] = -1;
}
time = 0;
for(int u=0; u<g.numOfV(); u++){
if (color[u] == WHITE)
dfs_visit(g, u);
}
}
Peter Steffen
A&D II, Vorlesung 2009
Universität Bielefeld
Tiefensuche
private static void dfs_visit(Graph g, int u){
color[u] = GRAY;
time++;
d[u] = time;
LinkedList<Integer> l = g.getAdjList(u);
for (int i = 0; i<l.size(); i++){
int v = l.get(i).intValue();
if (color[v] == WHITE){
pi[v] = u;
dfs_visit(g, v);
}
}
color[u] = BLACK;
f[u] = ++time;
System.out.println("finished with node " + u);
System.out.println("d = " + d[u] + ", f = " + f[u]);
}
}
Peter Steffen
A&D II, Vorlesung 2009
Universität Bielefeld
K. Arnold, J. Gosling: JavaTM - Die Programmiersprache.
Addison-Wesley, 1996.
T.H. Cormen, C.E. Leierson, R.L. Rivest: Introduction to
Algorithms. MIT Press, 1990.
D. Flanagan: Java in a Nutshell. O’Reilly & Associates Inc.,
1996.
F. Jobst: Programmieren in Java. Hanser Verlag, 1996.
H. Klaeren: Vom Problem zum Programm. 2.Auflage,
B.G. Teubner Verlag, 1991.
K. Echtle, M. Goedicke: Lehrbuch der Programmierung mit
Java. dpunkt-Verlag, 2000.
Peter Steffen
A&D II, Vorlesung 2009
Universität Bielefeld