Java Program to Create a Minimal Set of All Edges Whose Addition will Convert it to a Strongly Connected DAG

This is a java program to find the edges other than feedback arc set so that all the edges contribute to directed acyclic graph.

Here is the source code of the Java Program to Create a Minimal Set of All Edges Whose Addition will Convert it to a Strongly Connected DAG. 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.HashMap;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Scanner;
 
class Graph
{
    private Map<Integer, List<Integer>> adjacencyList;
 
    public Graph(int v)
    {
        adjacencyList = new HashMap<Integer, List<Integer>>();
        for (int i = 1; i <= v; i++)
            adjacencyList.put(i, new LinkedList<Integer>());
    }
 
    public void setEdge(int from, int to)
    {
        if (to > adjacencyList.size() || from > adjacencyList.size())
            System.out.println("The vertices does not exists");
        /*
         * List<Integer> sls = adjacencyList.get(to);
         * sls.add(from);
         */
        List<Integer> dls = adjacencyList.get(from);
        dls.add(to);
    }
 
    public List<Integer> getEdge(int to)
    {
        /*
         * if (to > adjacencyList.size())
         * {
         * System.out.println("The vertices does not exists");
         * return null;
         * }
         */
        return adjacencyList.get(to);
    }
 
    public Graph checkDAG()
    {
        Integer count = 0;
        Iterator<Integer> iteratorI = this.adjacencyList.keySet().iterator();
        Integer size = this.adjacencyList.size() - 1;
        System.out.println("Minimal set of edges: ");
        while (iteratorI.hasNext())
        {
            Integer i = iteratorI.next();
            List<Integer> adjList = this.adjacencyList.get(i);
            if (count == size)
            {
                return this;
            }
            if (adjList.size() == 0)
            {
                count++;
                Iterator<Integer> iteratorJ = this.adjacencyList.keySet()
                        .iterator();
                while (iteratorJ.hasNext())
                {
                    Integer j = iteratorJ.next();
                    List<Integer> li = this.adjacencyList.get(j);
                    if (li.contains(i))
                    {
                        li.remove(i);
                        System.out.println(i + " -> " + j);
                    }
                }
                this.adjacencyList.remove(i);
                iteratorI = this.adjacencyList.keySet().iterator();
            }
        }
        return this;
    }
 
    public Map<Integer, List<Integer>> getFeedbackArcSet(int v)
    {
        int[] visited = new int[v + 1];
        Iterator<Integer> iterator = this.adjacencyList.keySet().iterator();
        Map<Integer, List<Integer>> l = new HashMap<Integer, List<Integer>>();
        while (iterator.hasNext())
        {
            Integer i = iterator.next();
            List<Integer> list = this.adjacencyList.get(i);
            visited[i] = 1;
            if (list.size() != 0)
            {
                for (int j = 0; j < list.size(); j++)
                {
                    if (visited[list.get(j)] == 1)
                    {
                        l.put(i, new LinkedList<Integer>());
                        l.get(i).add(j);
                    }
                    else
                    {
                        visited[list.get(j)] = 1;
                    }
                }
            }
        }
        return l;
    }
 
    public void printAllEdges(Graph copyG, int v)
    {
        Map<Integer, List<Integer>> edges = this.getFeedbackArcSet(v);
        Iterator<Integer> iterator = copyG.adjacencyList.keySet().iterator();
        while (iterator.hasNext())
        {
            Integer i = iterator.next();
            List<Integer> edgeList = this.getEdge(i);
            if (edgeList.size() != 0)
            {
                for (int j = 0; j < edgeList.size(); j++)
                {
                    if (edges.containsKey(i) && edges.get(i).contains(j))
                        continue;
                    else
                    {
                        System.out.print(i + " -> " + edgeList.get(j));
                    }
                }
                System.out.println();
            }
        }
    }
 
    public void printGraph()
    {
        System.out.println("The Graph is: ");
        Iterator<Integer> iterator = this.adjacencyList.keySet().iterator();
        while (iterator.hasNext())
        {
            Integer i = iterator.next();
            List<Integer> edgeList = this.getEdge(i);
            if (edgeList.size() != 0)
            {
                System.out.print(i);
                for (int j = 0; j < edgeList.size(); j++)
                {
                    System.out.print(" -> " + edgeList.get(j));
                }
                System.out.println();
            }
        }
    }
}
 
public class MinimalSetofEdgesforDAG
{
    public static void main(String args[])
    {
        int v, e, count = 1, to, from;
        Scanner sc = new Scanner(System.in);
        Graph glist;
        try
        {
            System.out.println("Enter the number of vertices: ");
            v = sc.nextInt();
            System.out.println("Enter the number of edges: ");
            e = sc.nextInt();
            glist = new Graph(v);
            System.out.println("Enter the edges in the graph : <from> <to>");
            while (count <= e)
            {
                to = sc.nextInt();
                from = sc.nextInt();
                glist.setEdge(to, from);
                count++;
            }
            Graph copyofGlist = new Graph(v);
            copyofGlist = glist;
            glist.printGraph();
            Graph modified = glist.checkDAG();
            modified.printAllEdges(copyofGlist, v);
        }
        catch (Exception E)
        {
            System.out
                    .println("You are trying to access empty adjacency list of a node.");
        }
        sc.close();
    }
}

Output:

$ javac MinimalSetofEdgesforDAG.java
$ java MinimalSetofEdgesforDAG
 
Enter the number of vertices: 
6
Enter the number of edges: 
7
Enter the edges in the graph : <from> <to>
1 2
2 3
2 4
4 5
5 6
6 3
6 4
The Graph is: 
1 -> 2
2 -> 3 -> 4
4 -> 5
5 -> 6
6 -> 3 -> 4
Minimal set of edges: 
3 -> 2
3 -> 6
1 -> 2
2 -> 4
4 -> 5
5 -> 6