16. Binary Search Tree (BST) Properties: Validate BST & Lowest Common Ancestor (LCA) • Data Structures & Algorithms: Blind 75 & Big Tech Interview Prep • Rishabh Ki Kaksha

Data Structures & Algorithms: Blind 75 & Big Tech Interview Prep › 16. Binary Search Tree (BST) Properties: Validate BST & Lowest Common Ancestor (LCA)

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Course Syllabus

Module 1: Big-O Asymptotics, Arrays & Sliding Window

01. Time & Space Complexity Masterclass: Big-O, Big-Theta, Big-Omega & Amortized Analysis 02. Arrays & Hashing: Two Sum, Contains Duplicate & Valid Anagram (Hash Table Lookups) 03. Prefix Sum & Kadane's Algorithm (Maximum Subarray Problem in O(N)) 04. Sliding Window Pattern: Fixed vs Dynamic Windows (Best Time to Buy/Sell Stock)

Module 2: Two Pointers & Binary Search Systems

05. Two Pointers Pattern: Valid Palindrome, 3Sum & Container With Most Water 06. Binary Search Foundations: Search in Rotated Sorted Array & Find Minimum 07. Binary Search on Answer Space: Koko Eating Bananas & Capacity to Ship Packages

Module 3: Linked Lists & Fast-Slow Pointer Patterns

08. Singly vs Doubly Linked Lists & In-Place Pointer Manipulation (Reverse Linked List) 09. Fast & Slow Pointer (Floyd's Cycle Detection): Linked List Cycle & Middle Node 10. Merging & Reordering: Merge Two Sorted Lists, Reorder List & Remove Nth Node

Module 4: Stacks, Queues & Monotonic Stack Architecture

11. Stack Fundamentals: Valid Parentheses & Min Stack in O(1) Time 12. Monotonic Stack Pattern: Daily Temperatures & Next Greater Element 13. Hard Stack Coding: Largest Rectangle in Histogram & Trapping Rain Water

Module 5: Trees, Binary Search Trees & DFS/BFS Traversals

14. Binary Tree Architecture: Max Depth, Same Tree & Invert Binary Tree 15. BFS Level-Order Traversal & Binary Tree Right Side View 16. Binary Search Tree (BST) Properties: Validate BST & Lowest Common Ancestor (LCA) 17. Tree Path Sums & Serialize / Deserialize Binary Tree (Hard)

Module 6: Heaps, Priority Queues & Top-K Problems

18. Min Heap & Max Heap Internals: Array Representation & Heapify in O(N) 19. Top-K Elements Pattern: Kth Largest Element in an Array & Top K Frequent Elements 20. Two-Heap Pattern: Find Median from Data Stream (Hard)

Module 7: Graphs, Topological Sort & Shortest Paths (Dijkstra)

21. Graph Representations (Adjacency Matrix vs List) & DFS/BFS Traversal 22. Matrix Graph Traversal: Number of Islands, Max Area of Island & Clone Graph 23. Topological Sort (Kahn's Algorithm): Course Schedule I & II (Cycle Detection) 24. Disjoint Set Union (DSU / Union-Find): Redundant Connection & Number of Connected Components

Module 8: Dynamic Programming, Backtracking & Bit Manipulation

25. Backtracking Pattern: Subsets, Permutations, Combination Sum & Word Search 26. 1D Dynamic Programming: Climbing Stairs, House Robber & Coin Change 27. Longest Increasing Subsequence (LIS): O(N^2) DP vs O(N log N) Patience Sort 28. 2D Dynamic Programming: Unique Paths, Longest Common Subsequence (LCS) & Edit Distance 29. 0/1 Knapsack Pattern & Partition Equal Subset Sum 30. Bit Manipulation Tricks: Number of 1 Bits (Hamming Weight), Counting Bits & Missing Number

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# 16. Binary Search Tree (BST) Properties: Validate BST & Lowest Common Ancestor (LCA)

> DSA Blind 75 Notes by Rishabh - Topic 16

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### 1. BST Invariant Property 📐

Binary Search Tree (BST) me har node $N$ ke liye:
$$\text{All nodes in Left Subtree} < N.\text{val} < \text{All nodes in Right Subtree}$$
> **The Golden In-Order Rule:** BST ka In-Order Traversal (`Left -> Root -> Right`) hamesha **Strictly Sorted Ascending Order** me hota hai!

---

### 2. LeetCode #98: Validate Binary Search Tree

*Trap:* Sirf immediate children check karna galat hai (`node.left < node`); poore subtree range $[low, high]$ ko propagate karna padta hai!

```python
def isValidBST(root: TreeNode | None) -> bool:
    def validate(node, low, high):
        if not node:
            return True
        if not (low < node.val < high):
            return False
            
        return (validate(node.left, low, node.val) and 
                validate(node.right, node.val, high))
                
    return validate(root, float('-inf'), float('inf'))
```

---

### 3. LeetCode #235: Lowest Common Ancestor (LCA) of BST ($O(H)$)

```python
def lowestCommonAncestor(root: TreeNode, p: TreeNode, q: TreeNode) -> TreeNode:
    curr = root
    while curr:
        if p.val > curr.val and q.val > curr.val:
            curr = curr.right # Both lie in right subtree
        elif p.val < curr.val and q.val < curr.val:
            curr = curr.left  # Both lie in left subtree
        else:
            return curr       # ⚡ Split point found -> LCA!
```

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### 4. Master Comparison Matrix

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### 5. Interview Ke 3 Sawal Is Topic Se

1. **BST me K-th Smallest Element (LeetCode #230) kaise find karte hain?** -> In-order iterative stack traversal karke jaise hi $K$-th element pop ho wahi return kar dete hain.
2. **BST me deletion ke 3 cases kya hote hain?** -> (1) Leaf node (direct delete), (2) Single child (replace with child), (3) 2 children (replace with In-order Successor i.e. min of right subtree).
3. **Self-Balancing BSTs (AVL / Red-Black Tree) ki zaroorat kyu padti hai?** -> Sorted input aane par standard BST degenerate hokar $O(N)$ Linked List ban jata hai; AVL/RB-Trees rotations se height $O(\log N)$ guarantee karte hain.

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**Next Topic:** 17. Tree Path Sums & Serialize / Deserialize Binary Tree (Hard)

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