0% completed
In a Binary Search Tree (BST), traversal refers to visiting each node in a specific order. There are three main types of depth-first traversal techniques:
1. Inorder Traversal
Inorder traversal visits the nodes in the order: Left Subtree → Root → Right Subtree.
In a Binary Search Tree (BST), this traversal returns the nodes in ascending sorted order.
Step-by-Step Algorithm
- Step 1: Traverse the left subtree recursively.
- Step 2: Visit (process) the current node.
- Step 3: Traverse the right subtree recursively.
Code
Complexity Analysis
- Time Complexity: O(n), where n is the number of nodes (each node is visited once).
- Space Complexity: O(h) due to recursion, where h is the height of the tree (O(n) in worst-case, O(log n) for balanced BST).
2. Preorder Traversal
Preorder traversal visits nodes in the order: Root → Left Subtree → Right Subtree.
This method is useful for cloning trees or for generating a prefix expression from an expression tree.
Step-by-Step Algorithm
- Step 1: Visit (process) the current node.
- Step 2: Traverse the left subtree recursively.
- Step 3: Traverse the right subtree recursively.
Code
Complexity Analysis
- Time Complexity: O(n), as each node is processed once.
- Space Complexity: O(h), where h is the height of the tree, due to recursion (worst-case O(n) in skewed trees, O(log n) in balanced trees).
3. Postorder Traversal
Postorder traversal visits nodes in the order: Left Subtree → Right Subtree → Root.
This approach is useful for deleting trees or evaluating postfix expressions.
Step-by-Step Algorithm
- Step 1: Traverse the left subtree recursively.
- Step 2: Traverse the right subtree recursively.
- Step 3: Visit (process) the current node.
Code
Complexity Analysis
- Time Complexity: O(n), since each node is visited once.
- Space Complexity: O(h), where h is the height of the tree due to recursion (worst-case O(n) in skewed trees, O(log n) in balanced trees).
.....
.....
.....
Table of Contents
Contents are not accessible
Contents are not accessible
Contents are not accessible
Contents are not accessible
Contents are not accessible