CareerCup

For the second example, how are you supposed to merge subtrees to form a single tree?

It's not clear to me what we need to do when the we are returning the middle of the tree.
If the specified height starts from 0 then:

class Node:
    left , right, data = None, None, 0    
    def __init__(self, data, l, r):
        # initializes the data members
        self.left = l
        self.right = r
        self.data = data

def copyToH(n, h, H):
  if h <= H:
    lc = copyToH(n.left,  h+1, H)
    rc = copyToH(n.right, h+1, H)
    return new Node(n.data, lc, rc)
  else: return None

I don't understand what you ask? More details?

wrong question - or incomplete

Question not clear. I suppose you want to traverse a specific interval of a binary tree. The code is pre-order traversal.

public static void traverseByInterval(BinaryTreeNode root, int l, int h) {
    if (root == null) {
      return;
    }
    if (l > h) {
      return;
    }
    if (l <= 0 && h >= 0) {
      System.out.print(root.data + " ");
    }
    traverseByInterval(root.left, l - 1, h - 1);
    traverseByInterval(root.right, l - 1, h - 1);
  }