304 lines
8.8 KiB
Java
304 lines
8.8 KiB
Java
|
/*This is a java program to find global min cut of the graph. In computer science and graph theory, Karger’s algorithm is a randomized algorithm to compute a minimum cut of a connected graph.*/
|
|||
|
|
|
|||
|
|
|
|||
|
|
import java.io.BufferedReader;
|
|||
|
|
import java.io.FileReader;
|
|||
|
|
import java.util.ArrayList;
|
|||
|
|
import java.util.Comparator;
|
|||
|
|
import java.util.HashSet;
|
|||
|
|
import java.util.Iterator;
|
|||
|
|
import java.util.LinkedHashMap;
|
|||
|
|
import java.util.List;
|
|||
|
|
import java.util.Map;
|
|||
|
|
import java.util.Random;
|
|||
|
|
import java.util.Set;
|
|||
|
|
import java.util.TreeMap;
|
|||
|
|
|
|||
|
|
public class GlobalMinCut
|
|||
|
|
{
|
|||
|
|
private static class Graph
|
|||
|
|
{
|
|||
|
|
private final Map<Integer, Vertex> vertices = new TreeMap<Integer, Vertex>(
|
|||
|
|
new Comparator<Integer>()
|
|||
|
|
{
|
|||
|
|
@Override
|
|||
|
|
public int compare(Integer arg0, Integer arg1)
|
|||
|
|
{
|
|||
|
|
return arg0.compareTo(arg1);
|
|||
|
|
}
|
|||
|
|
});
|
|||
|
|
private final List<Edge> edges = new ArrayList<Edge>();
|
|||
|
|
|
|||
|
|
public void addVertex(Vertex v)
|
|||
|
|
{
|
|||
|
|
vertices.put(v.lbl, v);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public Vertex getVertex(int lbl)
|
|||
|
|
{
|
|||
|
|
Vertex v;
|
|||
|
|
if ((v = vertices.get(lbl)) == null)
|
|||
|
|
{
|
|||
|
|
v = new Vertex(lbl);
|
|||
|
|
addVertex(v);
|
|||
|
|
}
|
|||
|
|
return v;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
private static class Vertex
|
|||
|
|
{
|
|||
|
|
private final int lbl;
|
|||
|
|
private final Set<Edge> edges = new HashSet<Edge>();
|
|||
|
|
|
|||
|
|
public Vertex(int lbl)
|
|||
|
|
{
|
|||
|
|
this.lbl = lbl;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public void addEdge(Edge edge)
|
|||
|
|
{
|
|||
|
|
edges.add(edge);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public Edge getEdgeTo(Vertex v2)
|
|||
|
|
{
|
|||
|
|
for (Edge edge : edges)
|
|||
|
|
{
|
|||
|
|
if (edge.contains(this, v2))
|
|||
|
|
return edge;
|
|||
|
|
}
|
|||
|
|
return null;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
private static class Edge
|
|||
|
|
{
|
|||
|
|
private final List<Vertex> ends = new ArrayList<Vertex>();
|
|||
|
|
|
|||
|
|
public Edge(Vertex fst, Vertex snd)
|
|||
|
|
{
|
|||
|
|
if (fst == null || snd == null)
|
|||
|
|
{
|
|||
|
|
throw new IllegalArgumentException("Both vertices are required");
|
|||
|
|
}
|
|||
|
|
ends.add(fst);
|
|||
|
|
ends.add(snd);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public boolean contains(Vertex v1, Vertex v2)
|
|||
|
|
{
|
|||
|
|
return ends.contains(v1) && ends.contains(v2);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public Vertex getOppositeVertex(Vertex v)
|
|||
|
|
{
|
|||
|
|
if (!ends.contains(v))
|
|||
|
|
{
|
|||
|
|
throw new IllegalArgumentException("Vertex " + v.lbl);
|
|||
|
|
}
|
|||
|
|
return ends.get(1 - ends.indexOf(v));
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public void replaceVertex(Vertex oldV, Vertex newV)
|
|||
|
|
{
|
|||
|
|
if (!ends.contains(oldV))
|
|||
|
|
{
|
|||
|
|
throw new IllegalArgumentException("Vertex " + oldV.lbl);
|
|||
|
|
}
|
|||
|
|
ends.remove(oldV);
|
|||
|
|
ends.add(newV);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public static int minCut(Graph gr)
|
|||
|
|
{
|
|||
|
|
Random rnd = new Random();
|
|||
|
|
while (gr.vertices.size() > 2)
|
|||
|
|
{
|
|||
|
|
Edge edge = gr.edges.remove(rnd.nextInt(gr.edges.size()));
|
|||
|
|
Vertex v1 = cleanVertex(gr, edge.ends.get(0), edge);
|
|||
|
|
Vertex v2 = cleanVertex(gr, edge.ends.get(1), edge);
|
|||
|
|
// contract
|
|||
|
|
Vertex mergedVertex = new Vertex(v1.lbl);
|
|||
|
|
redirectEdges(gr, v1, mergedVertex);
|
|||
|
|
redirectEdges(gr, v2, mergedVertex);
|
|||
|
|
gr.addVertex(mergedVertex);
|
|||
|
|
}
|
|||
|
|
return gr.edges.size();
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
private static Vertex cleanVertex(Graph gr, Vertex v, Edge e)
|
|||
|
|
{
|
|||
|
|
gr.vertices.remove(v.lbl);
|
|||
|
|
v.edges.remove(e);
|
|||
|
|
return v;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
private static void redirectEdges(Graph gr, Vertex fromV, Vertex toV)
|
|||
|
|
{
|
|||
|
|
for (Iterator<Edge> it = fromV.edges.iterator(); it.hasNext();)
|
|||
|
|
{
|
|||
|
|
Edge edge = it.next();
|
|||
|
|
it.remove();
|
|||
|
|
if (edge.getOppositeVertex(fromV) == toV)
|
|||
|
|
{
|
|||
|
|
// remove self-loop
|
|||
|
|
toV.edges.remove(edge);
|
|||
|
|
gr.edges.remove(edge);
|
|||
|
|
}
|
|||
|
|
else
|
|||
|
|
{
|
|||
|
|
edge.replaceVertex(fromV, toV);
|
|||
|
|
toV.addEdge(edge);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public static int[][] getArray(String relPath)
|
|||
|
|
{
|
|||
|
|
Map<Integer, List<Integer>> vertices = new LinkedHashMap<Integer, List<Integer>>();
|
|||
|
|
FileReader fr;
|
|||
|
|
try
|
|||
|
|
{
|
|||
|
|
fr = new FileReader(relPath);
|
|||
|
|
BufferedReader br = new BufferedReader(fr);
|
|||
|
|
String line;
|
|||
|
|
while ((line = br.readLine()) != null)
|
|||
|
|
{
|
|||
|
|
String[] split = line.trim().split("(\\s)+");
|
|||
|
|
List<Integer> adjList = new ArrayList<Integer>();
|
|||
|
|
for (int i = 1; i < split.length; i++)
|
|||
|
|
{
|
|||
|
|
adjList.add(Integer.parseInt(split[i]) - 1);
|
|||
|
|
}
|
|||
|
|
vertices.put(Integer.parseInt(split[0]) - 1, adjList);
|
|||
|
|
}
|
|||
|
|
fr.close();
|
|||
|
|
}
|
|||
|
|
catch (Exception e)
|
|||
|
|
{
|
|||
|
|
e.printStackTrace();
|
|||
|
|
}
|
|||
|
|
int[][] array = new int[vertices.size()][];
|
|||
|
|
for (Map.Entry<Integer, List<Integer>> entry : vertices.entrySet())
|
|||
|
|
{
|
|||
|
|
List<Integer> adjList = entry.getValue();
|
|||
|
|
int[] adj = new int[adjList.size()];
|
|||
|
|
for (int i = 0; i < adj.length; i++)
|
|||
|
|
{
|
|||
|
|
adj[i] = adjList.get(i);
|
|||
|
|
}
|
|||
|
|
array[entry.getKey()] = adj;
|
|||
|
|
}
|
|||
|
|
return array;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
private static Graph createGraph(int[][] array)
|
|||
|
|
{
|
|||
|
|
Graph gr = new Graph();
|
|||
|
|
for (int i = 0; i < array.length; i++)
|
|||
|
|
{
|
|||
|
|
Vertex v = gr.getVertex(i);
|
|||
|
|
for (int edgeTo : array[i])
|
|||
|
|
{
|
|||
|
|
Vertex v2 = gr.getVertex(edgeTo);
|
|||
|
|
Edge e;
|
|||
|
|
if ((e = v2.getEdgeTo(v)) == null)
|
|||
|
|
{
|
|||
|
|
e = new Edge(v, v2);
|
|||
|
|
gr.edges.add(e);
|
|||
|
|
v.addEdge(e);
|
|||
|
|
v2.addEdge(e);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
return gr;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/**
|
|||
|
|
* @param args
|
|||
|
|
*/
|
|||
|
|
public static void main(String[] args)
|
|||
|
|
{
|
|||
|
|
int[][] arr = getArray("GlobalMinCut.txt");
|
|||
|
|
Map<Integer, Integer> statistics = new LinkedHashMap<Integer, Integer>();
|
|||
|
|
int min = arr.length;
|
|||
|
|
int iter = arr.length * arr.length;
|
|||
|
|
Graph g = createGraph(arr);
|
|||
|
|
printGraph(g);
|
|||
|
|
for (int i = 0; i < iter; i++)
|
|||
|
|
{
|
|||
|
|
Graph gr = createGraph(arr);
|
|||
|
|
int currMin = minCut(gr);
|
|||
|
|
min = Math.min(min, currMin);
|
|||
|
|
Integer counter;
|
|||
|
|
if ((counter = statistics.get(currMin)) == null)
|
|||
|
|
{
|
|||
|
|
counter = 0;
|
|||
|
|
}
|
|||
|
|
statistics.put(currMin, counter + 1);
|
|||
|
|
}
|
|||
|
|
System.out.println("Min: " + min + " stat: "
|
|||
|
|
+ (statistics.get(min) * 100 / iter) + "%");
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
private static void printGraph(Graph gr)
|
|||
|
|
{
|
|||
|
|
System.out.println("Printing graph");
|
|||
|
|
for (Vertex v : gr.vertices.values())
|
|||
|
|
{
|
|||
|
|
System.out.print(v.lbl + ":");
|
|||
|
|
for (Edge edge : v.edges)
|
|||
|
|
{
|
|||
|
|
System.out.print(" " + edge.getOppositeVertex(v).lbl);
|
|||
|
|
}
|
|||
|
|
System.out.println();
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/*
|
|||
|
|
|
|||
|
|
Printing graph
|
|||
|
|
0: 35 38 17 18 14 22
|
|||
|
|
1: 35 8 17 3 25 22
|
|||
|
|
2: 34 15 5 10
|
|||
|
|
3: 23 1 17 22
|
|||
|
|
4: 7 20 13 28
|
|||
|
|
5: 2 33 15 34
|
|||
|
|
6: 32 27 37 29
|
|||
|
|
7: 13 11 30 4 28
|
|||
|
|
8: 38 16 12 1 9 19
|
|||
|
|
9: 28 8 11 13 19
|
|||
|
|
10: 15 32 2 25 29
|
|||
|
|
11: 19 13 7 9
|
|||
|
|
12: 8 23 38 19
|
|||
|
|
13: 11 7 9 4
|
|||
|
|
14: 18 35 25 0
|
|||
|
|
15: 34 31 2 10 29 16 5
|
|||
|
|
16: 8 15 39 37 27 31
|
|||
|
|
17: 0 38 23 1 3
|
|||
|
|
18: 14 25 0 26
|
|||
|
|
19: 11 12 8 9
|
|||
|
|
20: 28 4 24 36
|
|||
|
|
21: 31 33 39 34
|
|||
|
|
22: 35 0 1 3
|
|||
|
|
23: 3 17 12 38
|
|||
|
|
24: 30 28 36 20
|
|||
|
|
25: 26 18 14 10 1 30
|
|||
|
|
26: 25 36 28 30 18
|
|||
|
|
27: 31 6 37 16
|
|||
|
|
28: 9 26 20 24 7 4
|
|||
|
|
29: 36 15 32 6 10
|
|||
|
|
30: 7 24 26 25 36
|
|||
|
|
31: 15 21 27 39 16
|
|||
|
|
32: 6 10 29 37
|
|||
|
|
33: 21 5 39 34
|
|||
|
|
34: 15 2 21 5 33
|
|||
|
|
35: 0 1 14 22
|
|||
|
|
36: 29 26 24 30 20
|
|||
|
|
37: 39 16 6 27 32
|
|||
|
|
38: 0 8 17 12 23
|
|||
|
|
39: 37 31 21 16 33
|
|||
|
|
Min: 3 stat: 6%
|