Question

I want to add Bi-Directional Iterator (like Iterator exported by std::set) in my Parametrized BinaryTree class but I’m unable to comeup with any algorithm.

Simply structure of Binary tree node is , it contains three pointers , left , right , parent:

Answer 1

With the given structure you want to proceed like this:

1. To start the iteration you would find the left-most node.
2. To go to the next node the operation depends on where you currently are:
   1. If your node has a right child you go to this child and find its left-most successor (if there is no left child the node you are on is the next node).
   2. If you nodes doesn’t have a right child you move up the chain of parents until you find a parent for which you used the link to the left node: the next node becomes this node.
3. To move in the other direction you reverse the roles of left and right.

Effectively, this is implements a stack-less in-order traversal of the tree. If your tree isn’t changed while iterating (an unlikely scenario) or you don’t have a link to the parent node, you can maintain the stack explicitly in the iterator.