Data Structure (2130702)

Threaded Binary Tree

• The wasted NULL links in the binary tree storage representation can be replaced by threads.
• A binary tree is threaded according to particular traversal order. e.g.: Threads for the inorder traversals of tree are pointers to its higher nodes, for this traversal order.
  • If left link of node P is null, then this link is replaced by the address of its predecessor.
  • If right link of node P is null, then it is replaced by the address of its successor.
• Because the left or right link of a node can denote either structural link or a thread, we must somehow be able to distinguish them.
• Method 1:- Represent thread a –ve address.
• Method 2:- To have a separate Boolean flag for each of left and right pointers, node structure for this is given below,

• LTHREAD = true = Denotes leaf thread link.
• LTHREAD = false = Denotes leaf structural link.
• RTHREAD = true = Denotes right threaded link.
• RTHREAD = false = Denotes right structural link.

Head Node

Head node is simply another node which serves as the predecessor and successor of first and last tree nodes. Tree is attached to the left branch of the head node

Advantages

• Inorder traversal is faster than unthreaded version as stack is not required.
• Effectively determines the predecessor and successor for inorder traversal, for unthreaded tree this task is more difficult.
• A stack is required to provide upward pointing information in tree which threading provides.
• It is possible to generate successor or predecessor of any node without having over head of stack with the help of threading.

Disadvantages

• Threaded trees are unable to share common subtrees.
• If –ve addressing is not permitted in programming language, two additional fields are required.
• Insertion into and deletion from threaded binary tree are more time consuming because both thread and structural link must be maintained.

Given a Binary Tree

Fully In-threaded binary tree of given binary tree