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BST Traversal Techniques
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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

Python3
Python3
. . . .

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

Python3
Python3
. . . .

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

Python3
Python3
. . . .

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).

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