Interesting Problem on Trees - 2

Q1. Given a Binary Search Tree and a node, modify the Binary Search Tree to make the given node as the root.

Q2.  Given a Binary Tree, find two nodes which are at the farthest distance.

Hint: Duke's CS 

Q3. Given a Binary Tree, print the nodes in vertical order.

Example:

Hint:

Order the nodes by the number we get for each of them.


Q4.  Given a sorted array, design a method to find out how many Binary Search Trees can be created for the sorted array.


Q5. Given two Binary Search Tree,  discuss and algorithm to generate a unified sorted list.


Q6. Given a Binary Tree, give a method to obtain the sum of all the nodes.


Q7. Given a Binary Search Tree, find the in-order successor of each of the nodes.


Q8. Given a Binary Search Tree, replace the value of each node with the sum of all its in-order successors.




Q9. Given a binary tree, design a method to find its depth.

Hint: Depth(T)= 1+ max( depth(T.left), depth(T.right))




Q10.  Given a binary tree and a sum S, design a method to verify if there is a path from root to any of the nodes whose sum is equal to S.


Hint:  verify(node, sum)
         {
             Sum = sum - node.value;
             if(sum == 0)  {
                        print result
                        Exit
            }
            else{
                if(sum.left != null) verify(sum.left, Sum);
                if(sum.right != null) verify(sum.right, Sum)
            }
         }