Explain traversal binary tree and threaded binary tree.

Traversal of Binary Trees:

A binary tree is a data structure where each node has a maximum of two child nodes. Binary tree traversal is a process of visiting all the nodes in a tree in a specific order. There are three common traversal methods:

1. Inorder Traversal:

• Start from the leftmost node.
• Visit the data in the current node.
• Recursively traverse the left subtree.
• Recursively traverse the right subtree.

Inorder traversal prints the data in the sorted order (ascending order for a binary search tree).

Example:

5 / \ 3 8 / \ \ 1 4 11

Inorder traversal: 1 3 4 5 8 11

1. Preorder Traversal:

• Visit the data in the current node.
• Recursively traverse the left subtree.
• Recursively traverse the right subtree.

Preorder traversal prints the data in the order they are stored in the tree.

Example:

5 / \ 3 8 / \ \ 1 4 11

Preorder traversal: 5 3 1 4 8 11

1. Postorder Traversal:

• Recursively traverse the left subtree.
• Recursively traverse the right subtree.
• Visit the data in the current node.

Postorder traversal prints the data in the reverse order of inorder traversal.

Example:

5 / \ 3 8 / \ \ 1 4 11

Postorder traversal: 1 4 3 11 8 5

Threaded Binary Tree:

A threaded binary tree is a binary tree in which each node contains a pointer to its inorder successor. In a threaded binary tree, the left child pointer of a node points to its left child, and the right child pointer points to its inorder successor (or to the first node in the inorder traversal).

Threaded binary trees are used to perform inorder traversal efficiently without using a stack or recursion. To traverse a threaded binary tree, start from the leftmost node and follow the right child pointers until a node with a null right child pointer is reached. This node is the rightmost node in the tree. Now, follow the left child pointers to visit the nodes in inorder.

Advantages of Threaded Binary Trees:

• Efficient inorder traversal: Inorder traversal can be performed in O(n) time without using a stack or recursion.
• Space-efficient: Threaded binary trees do not require additional space for storing links to the inorder successor, as these links are stored in the existing child pointers.

Disadvantages of Threaded Binary Trees:

• Complex to implement: Threaded binary trees are more complex to implement and maintain than regular binary trees.
• Not widely used: Threaded binary trees are not as widely used as regular binary trees due to their complexity.