Week 27 of 43
Advanced DSA
WEEK 27 LEARNING MODULE
Binary Search Trees (BST) & Invariant Properties
Explores the BST invariant property, $O(h)$ search, insertion, and three-case node deletion (using in-order successors), tree validation, and lowest common ancestors.
4 Practice Problems3 Core ConceptsVerified Curriculum: high Confidence
What You'll Learn
- ✓Master the BST Invariant: left subtree $< node <$ right subtree.
- ✓Implement BST Search, Insertion, and Deletion (0, 1, and 2 children with In-order Successor).
- ✓Leverage the property that In-order Traversal of a BST produces strictly sorted output.
- ✓Validate BST integrity using bounded recursive range checking `(low, high)`.
- ✓Find Lowest Common Ancestor (LCA) in BST in $O(h)$ time.
Core Concepts
BST Invariant Property
For every node, all left subtree values are strictly smaller, and all right subtree values are strictly greater.
BST Node Deletion
O(h)Handling cases: leaf node, single child, and two children (replacing with in-order successor).
BST Range Validation
O(n) time, O(h) spaceChecking node values against permissible (min_allowed, max_allowed) intervals.
Algorithms Covered
BST Search ($O(h)$)BST Insertion ($O(h)$)BST Node Deletion ($O(h)$)BST ValidationBST Lowest Common Ancestor ($O(h)$)
Data Structures Applied
Binary Search Tree (BST)
“A tree with strong roots laughs at storms.”
— Malay Proverb
Lecture Materials (1)
Official Slide Deck0.9 MB
In Transit
Trees_II.pdf
Topic: Trees II
Format: PDF