Java Program to Find the Minimum Number of Edges to Remove to Disconnect a Graph

This is a java program to find bridges in a graph.

Here is the source code of the Java Program to Find Minimum Number of Edges to Cut to make the Graph Disconnected. 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.hardgraph;
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import java.util.Iterator;
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import java.util.NoSuchElementException;

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import java.util.Scanner;
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import java.util.Stack;
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```
 
```

class Bag<Item> implements Iterable<Item>

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{
```

    private int        N;    // number of elements in bag

    private Node<Item> first; // beginning of bag

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```
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    // helper linked list class
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    private static class Node<Item>
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    {
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        private Item       item;
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```
        private Node<Item> next;
```
```
    }
```
```
 
```
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    public Bag()
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    {
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        first = null;
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        N = 0;
```
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    }
```
```
 
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    public boolean isEmpty()
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    {
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        return first == null;
```
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    }
```
```
 
```
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    public int size()
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    {
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        return N;
```
```
    }
```
```
 
```
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    public void add(Item item)
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    {
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        Node<Item> oldfirst = first;
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        first = new Node<Item>();
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        first.item = item;
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        first.next = oldfirst;
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        N++;
```
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    }
```
```
 
```
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    public Iterator<Item> iterator()
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    {
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        return new ListIterator<Item>(first);

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    }
```
```
 
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    // an iterator, doesn't implement remove() since it's optional

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    @SuppressWarnings("hiding")
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    private class ListIterator<Item> implements Iterator<Item>

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    {
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        private Node<Item> current;
```
```
 
```

        public ListIterator(Node<Item> first)

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        {
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            current = first;
```
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        }
```
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```
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        public boolean hasNext()
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        {
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            return current != null;
```
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        }
```
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```
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        public void remove()
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        {
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            throw new UnsupportedOperationException();

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        }
```
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```
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        public Item next()
```
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        {
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            if (!hasNext())
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                throw new NoSuchElementException();

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            Item item = current.item;
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            current = current.next;
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            return item;
```
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        }
```
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    }
```
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}
```
```
 
```
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class BridgeGraph
```
```
{
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    private final int      V;
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    private int            E;
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    private Bag<Integer>[] adj;
```
```
 
```
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    @SuppressWarnings("unchecked")
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```
    public BridgeGraph(int V)
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    {
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        if (V < 0)
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            throw new IllegalArgumentException(

                    "Number of vertices must be nonnegative");

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        this.V = V;
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        this.E = 0;
```

        adj = (Bag<Integer>[]) new Bag[V];

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        for (int v = 0; v < V; v++)
```
```
        {
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            adj[v] = new Bag<Integer>();

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        }
```

        System.out.println("Enter the number of edges: ");

        Scanner sc = new Scanner(System.in);

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        int E = sc.nextInt();
```
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        if (E < 0)
```
```
        {
```
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            sc.close();
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            throw new IllegalArgumentException(

                    "Number of edges must be nonnegative");

```
        }
```
```
        for (int i = 0; i < E; i++)
```
```
        {
```
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            int v = sc.nextInt();
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            int w = sc.nextInt();
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            addEdge(v, w);
```
```
        }
```
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        sc.close();
```
```
    }
```
```
 
```
```
    public BridgeGraph(BridgeGraph G)
```
```
    {
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        this(G.V());
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        this.E = G.E();
```
```
        for (int v = 0; v < G.V(); v++)
```
```
        {
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            // reverse so that adjacency list is in same order as original

            Stack<Integer> reverse = new Stack<Integer>();

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            for (int w : G.adj[v])
```
```
            {
```
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                reverse.push(w);
```
```
            }
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            for (int w : reverse)
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```
            {
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                adj[v].add(w);
```
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            }
```
```
        }
```
```
    }
```
```
 
```
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    public int V()
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```
    {
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        return V;
```
```
    }
```
```
 
```
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    public int E()
```
```
    {
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        return E;
```
```
    }
```
```
 
```
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    public void addEdge(int v, int w)
```
```
    {
```
```
        if (v < 0 || v >= V)
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            throw new IndexOutOfBoundsException();

```
        if (w < 0 || w >= V)
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            throw new IndexOutOfBoundsException();

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        E++;
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        adj[v].add(w);
```
```
        adj[w].add(v);
```
```
    }
```
```
 
```
```
    public Iterable<Integer> adj(int v)
```
```
    {
```
```
        if (v < 0 || v >= V)
```

            throw new IndexOutOfBoundsException();

```
        return adj[v];
```
```
    }
```
```
 
```
```
    public String toString()
```
```
    {
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        StringBuilder s = new StringBuilder();

        String NEWLINE = System.getProperty("line.separator");

        s.append(V + " vertices, " + E + " edges " + NEWLINE);

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        for (int v = 0; v < V; v++)
```
```
        {
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            s.append(v + ": ");
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            for (int w : adj[v])
```
```
            {
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                s.append(w + " ");
```
```
            }
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            s.append(NEWLINE);
```
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        }
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        return s.toString();
```
```
    }
```
```
}
```
```
 
```
```
public class BridgesinGraph
```
```
{
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    private int   bridges; // number of bridges

```
    private int   cnt;    // counter
```

    private int[] pre;    // pre[v] = order in which dfs examines v

    private int[] low;    // low[v] = lowest preorder of any vertex connected

```
                           // to v
```
```
 
```

    public BridgesinGraph(BridgeGraph G)

```
    {
```
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        low = new int[G.V()];
```
```
        pre = new int[G.V()];
```
```
        for (int v = 0; v < G.V(); v++)
```
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            low[v] = -1;
```
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        for (int v = 0; v < G.V(); v++)
```
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            pre[v] = -1;
```
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        for (int v = 0; v < G.V(); v++)
```
```
            if (pre[v] == -1)
```
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                dfs(G, v, v);
```
```
    }
```
```
 
```
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    public int components()
```
```
    {
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        return bridges + 1;
```
```
    }
```
```
 
```

    private void dfs(BridgeGraph G, int u, int v)

```
    {
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        pre[v] = cnt++;
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```
        low[v] = pre[v];
```
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        for (int w : G.adj(v))
```
```
        {
```
```
            if (pre[w] == -1)
```
```
            {
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                dfs(G, v, w);
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                low[v] = Math.min(low[v], low[w]);

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                if (low[w] == pre[w])
```
```
                {
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                    System.out.println(v + "-" + w + " is a bridge");

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                    bridges++;
```
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                }
```
```
            }
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            // update low number - ignore reverse of edge leading to v

```
            else if (w != u)
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                low[v] = Math.min(low[v], pre[w]);

```
        }
```
```
    }
```
```
 
```

    public static void main(String[] args)

```
    {
```

        Scanner sc = new Scanner(System.in);

        System.out.println("Enter the number of vertices: ");

        BridgeGraph G = new BridgeGraph(sc.nextInt());

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

        BridgesinGraph bridge = new BridgesinGraph(G);

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        System.out
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                .println("Edge connected components = " + bridge.components());

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        sc.close();
```
```
    }
```
```
}
```

Output:

$ javac BridgesinGraph.ajav
$ java BridgesinGraph
 
Enter the number of vertices: 
6
Enter the number of edges: 
7
0 1
1 2
1 3
3 4
4 5
5 3
5 2
6 vertices, 7 edges 
0: 1 
1: 3 2 0 
2: 5 1 
3: 5 4 1 
4: 5 3 
5: 2 3 4 
 
0-1 is a bridge
Edge connected components = 2

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