# Java Program to Implement an Algorithm to Find the Global min Cut in a Graph

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.

Here is the source code of the Java Program to Implement an Algorithm to Find the Global min Cut in a Graph. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

package com.maixuanviet.graph;

import java.util.ArrayList;
import java.util.Comparator;
import java.util.HashSet;
import java.util.Iterator;
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>();

{
vertices.put(v.lbl, v);
}

public Vertex getVertex(int lbl)
{
Vertex v;
if ((v = vertices.get(lbl)) == null)
{
v = new Vertex(lbl);
}
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 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");
}
}

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);
}
}

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);
}
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);
}
}
}

public static int[][] getArray(String relPath)
{
Map<Integer, List<Integer>> vertices = new LinkedHashMap<Integer, List<Integer>>();
try
{
String line;
while ((line = br.readLine()) != null)
{
String[] split = line.trim().split("(\\s)+");
for (int i = 1; i < split.length; i++)
{
}
}
fr.close();
}
catch (Exception e)
{
e.printStackTrace();
}
int[][] array = new int[vertices.size()][];
for (Map.Entry<Integer, List<Integer>> entry : vertices.entrySet())
{
for (int i = 0; i < adj.length; i++)
{
}
}
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);
}
}
}
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();
}
}
}


Output:

$javac GlobalMinCut.java$ java GlobalMinCut

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%