Threaded Binary trees, Traversing Threaded Binary trees

Threaded binary trees are a variation of binary trees where every node maintains a reference to either its in-order predecessor or its in-order successor. This additional information allows for efficient traversal of the tree without the need for recursion or a stack.

There are two types of threaded binary trees:

Single-threaded binary tree: Each node has a thread (reference) either to its in-order predecessor or its in-order successor, but not both.
Double-threaded binary tree: Each node has threads to both its in-order predecessor and its in-order successor.

Here’s a brief overview of the process of making a binary tree threaded:

For each node, if its left child is null, it should point to its in-order predecessor, and if its right child is null, it should point to its in-order successor.
These threads are used to traverse the tree without using recursion or a stack.

Now, let’s discuss traversing threaded binary trees:

Traversing Threaded Binary Trees:

Traversing a threaded binary tree can be done using the threads instead of recursive calls or a stack. The two common traversals for threaded binary trees are:

In-order Traversal:
- Start from the leftmost node.
- At each node, follow the thread (if present) to its in-order successor.
- Continue this process until you reach the rightmost node.
Reverse In-order Traversal:
- Start from the rightmost node.
- At each node, follow the thread (if present) to its in-order predecessor.
- Continue this process until you reach the leftmost node.

Here’s an example of in-order traversal of a single-threaded binary tree:

python

def inorder_traversal_threaded(root):


current = leftmost(root)


while current:


print(current.value)


if current.thread:


current = current.thread


else:


current = leftmost(current.right)

def leftmost(node):
while node and node.left:
node = node.left
return node

Similarly, you can implement the reverse in-order traversal.

It’s important to note that threaded binary trees require additional space to store the threads, and maintaining these threads requires careful manipulation during insertion and deletion operations to keep the tree threaded correctly. However, they can offer advantages in terms of space and time efficiency for certain operations like traversal.