Breadth-first traversal

Question

I was trying to solve one interview question, but for that I have to travel the binary tree level by level. I have designed BinaryNode with having below variable

private object data;
private BinaryNode left;
private BinaryNode right;

Could someone please help to write the BreadthFirstSearch method inside my BinarySearchTree class?

Update: Thanks everyone for your inputs. So this was the interview question. "Given a binary search tree, design an algorithm which creates a linked list of all the nodes at each depth (i.e., if you have a tree with depth D, you’ll have D linked lists)".

Here is my Method, let me know your expert comment.

public List<LinkedList<BNode>> FindLevelLinkList(BNode root)
    {
        Queue<BNode> q = new Queue<BNode>();
        // List of all nodes starting from root.
        List<BNode> list = new List<BNode>();
        q.Enqueue(root);
        while (q.Count > 0)
        {
            BNode current = q.Dequeue();
            if (current == null)
                continue;
            q.Enqueue(current.Left);
            q.Enqueue(current.Right);
            list.Add(current);
        }

        // Add tree nodes of same depth into individual LinkedList. Then add all LinkedList into a List
        LinkedList<BNode> LL = new LinkedList<BNode>();
        List<LinkedList<BNode>> result = new List<LinkedList<BNode>>();
        LL.AddLast(root);
        int currentDepth = 0;
        foreach (BNode node in list)
        {
           if (node != root)
            {
                if (node.Depth == currentDepth)
                {
                    LL.AddLast(node);
                }
                else
                {
                    result.Add(LL);
                    LL = new LinkedList<BNode>();
                    LL.AddLast(node);
                    currentDepth++;
                }
            }
        }

        // Add the last linkedlist
        result.Add(LL);
        return result;
    }

Answer 1

A breadth first search is usually implemented with a queue, a depth first search using a stack.

Queue<Node> q = new Queue<Node>();
q.Enqueue(root);
while(q.Count > 0)
{
    Node current = q.Dequeue();
    if(current == null)
        continue;
    q.Enqueue(current.Left);
    q.Enqueue(current.Right);

    DoSomething(current);
}

As an alternative to checking for null after dequeuing you can check before adding to the Queue. I didn't compile the code, so it might contain some small mistakes.

---

A fancier (but slower) version that integrates well with LINQ:

public static IEnumerable<T> BreadthFirstTopDownTraversal<T>(T root, Func<T, IEnumerable<T>> children)
{
    var q = new Queue<T>();
    q.Enqueue(root);
    while (q.Count > 0)
    {
        T current = q.Dequeue();
        yield return current;
        foreach (var child in children(current))
            q.Enqueue(child);
    }
}

Which can be used together with a Children property on Node:

IEnumerable<Node> Children { get { return new []{ Left, Right }.Where(x => x != null); } }

...

foreach(var node in BreadthFirstTopDownTraversal(root, node => node.Children))
{
   ...
}

Answer 2

using DFS approach: The tree traversal is O(n)

public class NodeLevel
{
    public TreeNode Node { get; set;}
    public int Level { get; set;}
}

public class NodeLevelList
{
    private Dictionary<int,List<TreeNode>> finalLists = new Dictionary<int,List<TreeNode>>();

    public void AddToDictionary(NodeLevel ndlvl)
    {
        if(finalLists.ContainsKey(ndlvl.Level))
        {
            finalLists[ndlvl.Level].Add(ndlvl.Node);
        }
        else
        {
            finalLists.Add(ndlvl.Level,new List<TreeNode>(){ndlvl.Node});
        }
    }

    public Dictionary<int,List<TreeNode>> GetFinalList()
    {
        return finalLists;
    }
}

The method that does traversal:

public static void DFSLevel(TreeNode root, int level, NodeLevelList nodeLevelList)
{
    if(root == null)
        return;

    nodeLevelList.AddToDictionary(new NodeLevel{Node = root, Level = level});

    level++;

    DFSLevel(root.Left,level,nodeLevelList);
    DFSLevel(root.Right,level,nodeLevelList);

}

Answer 3

var queue = new Queue<BinaryNode>();
queue.Enqueue(rootNode);

while(queue.Any())
{
  var currentNode = queue.Dequeue();
  if(currentNode.data == searchedData)
  {
    break;
  }

  if(currentNode.Left != null)
    queue.Enqueue(currentNode.Left);

  if(currentNode.Right != null)
    queue.Enqueue(currentNode.Right);
}