Java Program to Find the Minimum Cut of a Graph using Karger’s Algorithm

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.

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package com.sanfoundry.graph;
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import java.io.BufferedReader;
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import java.io.FileReader;
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import java.util.ArrayList;
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import java.util.Comparator;
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import java.util.HashSet;
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import java.util.Iterator;
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import java.util.LinkedHashMap;
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import java.util.List;
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import java.util.Map;
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import java.util.Random;
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import java.util.Set;
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import java.util.TreeMap;
```
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public class GlobalMinCut
```
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{
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    private static class Graph
```
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    {
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        private final Map<Integer, Vertex> vertices = new TreeMap<Integer, Vertex>(

                new Comparator<Integer>()

```
                {
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                    @Override
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                    public int compare(Integer arg0, Integer arg1)

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                    {
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                        return arg0.compareTo(arg1);

```
                    }
```
```
                });
```

        private final List<Edge> edges = new ArrayList<Edge>();

```
 
```
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        public void addVertex(Vertex v)
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        {
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            vertices.put(v.lbl, v);
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        }
```
```
 
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        public Vertex getVertex(int lbl)

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        {
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            Vertex v;
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            if ((v = vertices.get(lbl)) == null)

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            {
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                v = new Vertex(lbl);
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                addVertex(v);
```
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            }
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            return v;
```
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        }
```
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    }
```
```
 
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    private static class Vertex
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    {
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        private final int lbl;
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        private final Set<Edge> edges = new HashSet<Edge>();

```
 
```
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        public Vertex(int lbl)
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        {
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            this.lbl = lbl;
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        }
```
```
 
```
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        public void addEdge(Edge edge)
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        {
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            edges.add(edge);
```
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        }
```
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        public Edge getEdgeTo(Vertex v2)

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        {
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            for (Edge edge : edges)
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            {
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                if (edge.contains(this, v2))

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                    return edge;
```
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            }
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            return null;
```
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        }
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    }
```
```
 
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    private static class Edge
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    {
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        private final List<Vertex> ends = new ArrayList<Vertex>();

```
 
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        public Edge(Vertex fst, Vertex snd)

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        {
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            if (fst == null || snd == null)

```
            {
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                throw new IllegalArgumentException("Both vertices are required");

```
            }
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            ends.add(fst);
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            ends.add(snd);
```
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        }
```
```
 
```

        public boolean contains(Vertex v1, Vertex v2)

```
        {
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            return ends.contains(v1) && ends.contains(v2);

```
        }
```
```
 
```

        public Vertex getOppositeVertex(Vertex v)

```
        {
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            if (!ends.contains(v))
```
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            {
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                throw new IllegalArgumentException("Vertex " + v.lbl);

```
            }
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            return ends.get(1 - ends.indexOf(v));

```
        }
```
```
 
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        public void replaceVertex(Vertex oldV, Vertex newV)

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        {
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            if (!ends.contains(oldV))
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            {
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                throw new IllegalArgumentException("Vertex " + oldV.lbl);

```
            }
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            ends.remove(oldV);
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            ends.add(newV);
```
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        }
```
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    }
```
```
 
```
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    public static int minCut(Graph gr)
```
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    {
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        Random rnd = new Random();
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        while (gr.vertices.size() > 2)
```
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        {
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            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);
```
```
        }
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        return gr.edges.size();
```
```
    }
```
```
 
```

    private static Vertex cleanVertex(Graph gr, Vertex v, Edge e)

```
    {
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        gr.vertices.remove(v.lbl);
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        v.edges.remove(e);
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        return v;
```
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    }
```
```
 
```

    private static void redirectEdges(Graph gr, Vertex fromV, Vertex toV)

```
    {
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        for (Iterator<Edge> it = fromV.edges.iterator(); it.hasNext();)

```
        {
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            Edge edge = it.next();
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            it.remove();
```

            if (edge.getOppositeVertex(fromV) == toV)

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            {
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                // remove self-loop
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                toV.edges.remove(edge);
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                gr.edges.remove(edge);
```
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            }
```
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            else
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```
            {
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                edge.replaceVertex(fromV, toV);

```
                toV.addEdge(edge);
```
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            }
```
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        }
```
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    }
```
```
 
```

    public static int[][] getArray(String relPath)

```
    {
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        Map<Integer, List<Integer>> vertices = new LinkedHashMap<Integer, List<Integer>>();

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        FileReader fr;
```
```
        try
```
```
        {
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            fr = new FileReader(relPath);

            BufferedReader br = new BufferedReader(fr);

```
            String line;
```

            while ((line = br.readLine()) != null)

```
            {
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                String[] split = line.trim().split("(\\s)+");

                List<Integer> adjList = new ArrayList<Integer>();

                for (int i = 1; i < split.length; i++)

```
                {
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                    adjList.add(Integer.parseInt(split[i]) - 1);

```
                }
```

                vertices.put(Integer.parseInt(split[0]) - 1, adjList);

```
            }
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            fr.close();
```
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        }
```
```
        catch (Exception e)
```
```
        {
```
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            e.printStackTrace();
```
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        }
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        int[][] array = new int[vertices.size()][];

        for (Map.Entry<Integer, List<Integer>> entry : vertices.entrySet())

```
        {
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            List<Integer> adjList = entry.getValue();

            int[] adj = new int[adjList.size()];

            for (int i = 0; i < adj.length; i++)

```
            {
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                adj[i] = adjList.get(i);

```
            }
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            array[entry.getKey()] = adj;

```
        }
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        return array;
```
```
    }
```
```
 
```

    private static Graph createGraph(int[][] array)

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    {
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        Graph gr = new Graph();
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        for (int i = 0; i < array.length; i++)

```
        {
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            Vertex v = gr.getVertex(i);
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            for (int edgeTo : array[i])
```
```
            {
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                Vertex v2 = gr.getVertex(edgeTo);

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                Edge e;
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                if ((e = v2.getEdgeTo(v)) == null)

```
                {
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                    e = new Edge(v, v2);

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                    gr.edges.add(e);
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                    v.addEdge(e);
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                    v2.addEdge(e);
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                }
```
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            }
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        }
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        return gr;
```
```
    }
```
```
 
```
```
    /**
```
```
     * @param args
```
```
     */
```

    public static void main(String[] args)

```
    {
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        int[][] arr = getArray("GlobalMinCut.txt");

        Map<Integer, Integer> statistics = new LinkedHashMap<Integer, Integer>();

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        int min = arr.length;
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        int iter = arr.length * arr.length;

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        Graph g = createGraph(arr);
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        printGraph(g);
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        for (int i = 0; i < iter; i++)
```
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        {
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            Graph gr = createGraph(arr);

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            int currMin = minCut(gr);
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            min = Math.min(min, currMin);

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            Integer counter;
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            if ((counter = statistics.get(currMin)) == null)

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            {
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                counter = 0;
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            }
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            statistics.put(currMin, counter + 1);

```
        }
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        System.out.println("Min: " + min + " stat: "

                + (statistics.get(min) * 100 / iter) + "%");

```
    }
```
```
 
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    private static void printGraph(Graph gr)

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    {
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        System.out.println("Printing graph");

        for (Vertex v : gr.vertices.values())

```
        {
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            System.out.print(v.lbl + ":");

```
            for (Edge edge : v.edges)
```
```
            {
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                System.out.print(" " + edge.getOppositeVertex(v).lbl);

```
            }
```
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            System.out.println();
```
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        }
```
```
    }
```
```
}
```

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%

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