c# - Converting Directed Acyclic Graph (DAG) to tree

Question

I'm trying to implement algoritm to convert Directed Acyclic Graph to Tree (for fun, learining, kata, name it). So I come up with the data structure Node:

/// <summary>
/// Represeting a node in DAG or Tree
/// </summary>
/// <typeparam name="T">Value of the node</typeparam>
public class Node<T> 
{
    /// <summary>
    /// creats a node with no child nodes
    /// </summary>
    /// <param name="value">Value of the node</param>
    public Node(T value)
    {
        Value = value;
        ChildNodes = new List<Node<T>>();
    }

    /// <summary>
    /// Creates a node with given value and copy the collection of child nodes
    /// </summary>
    /// <param name="value">value of the node</param>
    /// <param name="childNodes">collection of child nodes</param>
    public Node(T value, IEnumerable<Node<T>> childNodes)
    {
        if (childNodes == null)
        {
            throw new ArgumentNullException("childNodes");
        }
        ChildNodes = new List<Node<T>>(childNodes);
        Value = value;
    }

    /// <summary>
    /// Determines if the node has any child node
    /// </summary>
    /// <returns>true if has any</returns>
    public bool HasChildNodes
    {
        get { return this.ChildNodes.Count != 0; }
    }


    /// <summary>
    /// Travearse the Graph recursively
    /// </summary>
    /// <param name="root">root node</param>
    /// <param name="visitor">visitor for each node</param>
    public void Traverse(Node<T> root, Action<Node<T>> visitor)
    {
        if (root == null)
        {
            throw new ArgumentNullException("root");
        }
        if (visitor == null)
        {
            throw new ArgumentNullException("visitor");
        }

        visitor(root); 
        foreach (var node in root.ChildNodes)
        {
            Traverse(node, visitor);
        }
    }

    /// <summary>
    /// Value of the node
    /// </summary>
    public T Value { get; private set; }

    /// <summary>
    /// List of all child nodes
    /// </summary>
    public List<Node<T>> ChildNodes { get; private set; }
}

It's pretty straightforward. Methods:

/// <summary>
/// Helper class for Node 
/// </summary>
/// <typeparam name="T">Value of a node</typeparam>
public static class NodeHelper
{
    /// <summary>
    /// Converts Directed Acyclic Graph to Tree data structure using recursion.
    /// </summary>
    /// <param name="root">root of DAG</param>
    /// <param name="seenNodes">keep track of child elements to find multiple connections (f.e. A connects with B and C and B also connects with C)</param>
    /// <returns>root node of the tree</returns>
    public static Node<T> DAG2TreeRec<T>(this Node<T> root, HashSet<Node<T>> seenNodes)
    {
        if (root == null)
        {
            throw new ArgumentNullException("root");
        }
        if (seenNodes == null)
        {
            throw new ArgumentNullException("seenNodes");
        }

        var length = root.ChildNodes.Count;
        for (int i = 0; i < length; ++i)
        {
            var node = root.ChildNodes[i];
            if (seenNodes.Contains(node))
            {
                var nodeClone = new Node<T>(node.Value, node.ChildNodes);
                node = nodeClone;
            }
            else
            {
                seenNodes.Add(node);
            }
            DAG2TreeRec(node, seenNodes);
        }
        return root;
    }
    /// <summary>
    /// Converts Directed Acyclic Graph to Tree data structure using explicite stack.
    /// </summary>
    /// <param name="root">root of DAG</param>
    /// <param name="seenNodes">keep track of child elements to find multiple connections (f.e. A connects with B and C and B also connects with C)</param>
    /// <returns>root node of the tree</returns>
    public static Node<T> DAG2Tree<T>(this Node<T> root, HashSet<Node<T>> seenNodes)
    {
        if (root == null)
        {
            throw new ArgumentNullException("root");
        }
        if (seenNodes == null)
        {
            throw new ArgumentNullException("seenNodes");
        }

        var stack = new Stack<Node<T>>();
        stack.Push(root);

        while (stack.Count > 0) 
        {
            var tempNode = stack.Pop();
            var length = tempNode.ChildNodes.Count;
            for (int i = 0; i < length; ++i)
            {
                var node = tempNode.ChildNodes[i];
                if (seenNodes.Contains(node))
                {
                    var nodeClone = new Node<T>(node.Value, node.ChildNodes);
                    node = nodeClone;
                }
                else
                {
                    seenNodes.Add(node);
                }
               stack.Push(node);
            }
        } 
        return root;
    }
}

and test:

    static void Main(string[] args)
    {
        // Jitter preheat
        Dag2TreeTest();
        Dag2TreeRecTest();

        Console.WriteLine("Running time ");
        Dag2TreeTest();
        Dag2TreeRecTest();

        Console.ReadKey();
    }

    public static void Dag2TreeTest()
    {
        HashSet<Node<int>> hashSet = new HashSet<Node<int>>();

        Node<int> root = BulidDummyDAG();

        Stopwatch stopwatch = new Stopwatch();
        stopwatch.Start();
        var treeNode = root.DAG2Tree<int>(hashSet);
        stopwatch.Stop();

        Console.WriteLine(string.Format("Dag 2 Tree = {0}ms",stopwatch.ElapsedMilliseconds));

    }

    private static Node<int> BulidDummyDAG()
    {
        Node<int> node2 = new Node<int>(2);
        Node<int> node4 = new Node<int>(4);
        Node<int> node3 = new Node<int>(3);
        Node<int> node5 = new Node<int>(5);
        Node<int> node6 = new Node<int>(6);
        Node<int> node7 = new Node<int>(7);
        Node<int> node8 = new Node<int>(8);
        Node<int> node9 = new Node<int>(9);
        Node<int> node10 = new Node<int>(10);
        Node<int> root  = new Node<int>(1);

        //making DAG                   
        root.ChildNodes.Add(node2);    
        root.ChildNodes.Add(node3);    
        node3.ChildNodes.Add(node2);   
        node3.ChildNodes.Add(node4);   
        root.ChildNodes.Add(node5);    
        node4.ChildNodes.Add(node6);   
        node4.ChildNodes.Add(node7);
        node5.ChildNodes.Add(node8);
        node2.ChildNodes.Add(node9);
        node9.ChildNodes.Add(node8);
        node9.ChildNodes.Add(node10);

        var length = 10000;
        Node<int> tempRoot = node10; 
        for (int i = 0; i < length; i++)
        {
            var nextChildNode = new Node<int>(11 + i);
            tempRoot.ChildNodes.Add(nextChildNode);
            tempRoot = nextChildNode;
        }

        return root;
    }

    public static void Dag2TreeRecTest()
    {
        HashSet<Node<int>> hashSet = new HashSet<Node<int>>();

        Node<int> root = BulidDummyDAG();

        Stopwatch stopwatch = new Stopwatch();
        stopwatch.Start();
        var treeNode = root.DAG2TreeRec<int>(hashSet);
        stopwatch.Stop();

        Console.WriteLine(string.Format("Dag 2 Tree Rec = {0}ms",stopwatch.ElapsedMilliseconds));
    }

What is more, data structure need some improvment:

• Overriding GetHash, toString, Equals, == operator
• implementing IComparable
• LinkedList is probably a better choice

Also, before the conversion there are certian thigs that need to be checked:

• Multigraphs
• If it's DAG (Cycles)
• Diamnods in DAG
• Multiple roots in DAG

All in all, it narrows down to a few questions: How can I improve the conversion? Since this is a recurion it's possible to blow up the stack. I can add stack to memorize it. If I do continuation-passing style, will I be more efficient?

I feel that immutable data structure in this case would be better. Is it correct?

Is Childs the right name ? :)

Answer 1

Algorithm:

• As you observed, some nodes appear twice in the output. If the node 2 had children, the whole subtree would appear twice. If you want each node to appear just once, replace

  if (hashSet.Contains(node))
  {
      var nodeClone = new Node<T>(node.Value, node.Childs);
      node = nodeClone;
  }
  

  with

  if (hashSet.Contains(node))
  {
      // node already seen -> do nothing
  }
  

• I wouldn't be too worried about the size of the stack or performance of recursion. However, you could replace your Depth-first-search with Breadth-first-search which would result in nodes closer to the root being visited earlier, thus yielding a more "natural" tree (in your picture you already numbered the nodes in BFS order).

   var seenNodes = new HashSet<Node>();
   var q = new Queue<Node>();
   q.Enqueue(root);
   seenNodes.Add(root);   
  
   while (q.Count > 0) {
       var node = q.Dequeue();
       foreach (var child in node.Childs) {
           if (!seenNodes.Contains(child )) {
               seenNodes.Add(child);
               q.Enqueue(child);
       }
   }
  

  The algorithm handles diamonds and cycles.

• Multiple roots

  Just declare a class Graph which will contain all the vertices

  class Graph
  {
      public List<Node> Nodes { get; private set; }
      public Graph()
      {
          Nodes = new List<Node>();
      }    
  }
  

---

Code:

• the hashSet could be named seenNodes.

• Instead of

  var length = root.Childs.Count;
  for (int i = 0; i < length; ++i)
  {
      var node = root.Childs[i];
  

  write

  foreach (var child in root.Childs)
  

• In Traverse, the visitor is quite unnecessary. You could rather have a method which yields all the nodes of the tree (in the same order traverse does) and it is up to user to do whatever with the nodes:

  foreach(var node in root.TraverseRecursive())
  {
      Console.WriteLine(node.Value);
  }
  

• If you override GetHashCode and Equals, the algorithm will no more be able to distinguish between two different Nodes with same value, which is probably not what you want.

• I don't see any reason why LinkedList would be better here than List, except for the reallocations (Capacity 2,4,8,16,...) which List does when adding nodes.