Double Threaded Binary Tree

So, in this blog, you will get to know about the “Double Threaded Binary Tree”. However, before embarking on a double-threaded binary tree, you need to first understand what a threaded binary tree is. But, we already have a blog on this data structure but still, we will first dive into this topic so those who are unfamiliar with this topic may gain a good understanding.

Explain the threaded binary tree in data structure with a suitable example:

Threaded Binary has a special pointer called “thread”. This thread is used to point to the higher nodes for their null values. 

Threaded binary trees are of two types:

1. One-way threaded binary tree
2. Two-way threaded binary tree

To understand the concept of the threaded binary tree, we will start with a one-way threaded binary tree example.

So, for example, we have a binary tree, whose Inorder sequence is D, B, E, A, F, C, G( by following the LEFT ROOT RIGHT approach).

So, to make this binary tree into a single-way threaded binary tree, we have to make the thread ( special pointers) for the leaf node only. And the reason for this is to simplify the traversal process by providing direct links (threads) to the in-order predecessor and successor nodes.

So, to make pointers or threads,

1. First, we have to see leaf nodes, and for the null entry, we will thread towards the higher parent node according to the Inorder sequence.
2. For this tree, the Inorder sequence is D, B, E, A, F, C, G.
3. So, the leaf node D, the higher next parent node is B, so we make a thread from D right child null node towards B parent node. 
4. For leaf node E, the higher parent node is A. So we make a thread towards A.
5. Next, for the F node, the higher root node is C. 
6. And finally, for G, there is no successor node. So, it left child will remain null.

Note: In Single way threaded binary tree, we have to follow one approach that is :

• We make threads for the left child of the leaf node or make threads for the right child of the leaf node.
• We can’t swap in between that some leaf node threads are for the right child and some are pointed towards the left child.
• Also, in two-way threading, we can make the threads from both sides.

Advantages of Threaded Binary Tree:

1. In a threaded binary tree, we can traverse the nodes easily without the use of any extra data structure. Also, it will help us to save a lot of memory as well as time.
2. Threaded data structure provides simplicity in the code.
3. Threaded Binary Trees also provide efficient backward traversal without the need for additional logic or data structure. 

What is Double threaded binary tree?

So, coming to our main topic, A Double Threaded Binary Tree is a special form of a binary tree data structure that has a functionality of a regular binary tree but each leaf node contains additional pointers called “threads” on both the left and right side of the mode. And these nodes are linked to their in-order predecessor and successor nodes.

These threads in two way threaded binary tree provide a way to navigate the tree both in the usual left-to-right manner as well as right-to-left, enhancing the tree’s versatility and simplifying certain operations like searching for specific elements, performing in-order traversal, and many more.

What is the main purpose of using Double threaded Binary tree?

The main need for a Double Threaded Binary Tree is that it allows easy in-order traversal without the need for recursive calls or a stack data structure to keep track of all the visited nodes.

Also, with the help of the threads, it becomes very easy to move from one node to another node in very less time and space requirements.

How do Two ways threaded binary tree work?

Two ways threaded binary tree work in the same way as a single-threaded binary tree, but the difference is that single-threaded work only on one side but in two way threaded binary tree has threads on both sides.
For example, in the above image, we can clearly see that, for leaf node D, according to Inorder traversal, the D node has no left side because the D node is the first node in the traversal. And after node D we have the B node which is a parent node, so D’s right child node will be pointed towards the B node.

Talking about the need for threads, these threads provide a way to navigate the tree both in the usual left-to-right manner as well as right-to-left, enhancing the tree’s versatility and simplifying certain operations like searching for specific elements, performing in-order traversal, and more.

Double-threaded binary tree c++ code:

For creating a Double Threaded Binary Tree (Two-Way Threaded Binary Tree), we have to construct a binary tree while adding extra threads to every leaf node.
So, let’s start with the step-by-step algorithm for creating a Two-Way Threaded Binary Tree:

1. We have to first start with an empty tree and for that, we have to set the root to nullptr.
2. Next, for inserting a new node with a given value,
   • First, create a new node with some value.
   • If the tree is empty that is root value is equal to nullptr, set the new node as the root and return it.
   • Else, start traversing with the root node as the current node and repeat the following steps until the insertion point is found.
3. After this,
   • If the new node value is less than the current node’s value, move towards the left child node.
   • If the new node value is greater than or equal to the current node’s value, move towards the right child node.
   • Finally, when the insertion point is found that is node is reached at the end of the tree, then, insert the new node as the child node based on the value comparison.
4. Once the tree is constructed, add the threads pointers to make the binary tree to double threaded binary tree.
5. Now, perform an in-order traversal of the tree, maintaining a previous pointer initialized to nullptr. For each node in the traversal:
   • If the left child of the node is nullptr, set the left child to the previous node, and set the leftThread flag to true.
   • If the right child of the previous node is nullptr, set the right child to the current node, and set the rightThread flag to true.
   • Update the previous pointer to the current node for the next iteration.
6. Now, finally, the Two-Way Threaded Binary Tree is now constructed with threads for efficient traversal in both in-order and reverse in-order directions.