What is the optimal time complexity of solving Lowest Common Ancestor of BST?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Lowest Common Ancestor of BST?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Lowest Common Ancestor of BST?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Lowest Common Ancestor of BST?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Lowest Common Ancestor of BST

Learn how to solve the 'Lowest Common Ancestor of BST' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Given a binary search tree (BST), find the lowest common ancestor (LCA) node of two given nodes in the BST.

According to the definition of LCA: "The lowest common ancestor is defined between two nodes p and q as the lowest node in T that has both p and q as descendants (where we allow a node to be a descendant of itself)."

The BST is represented as a level-order list. Implement a function lowestCommonAncestor(root: list, p: int, q: int) -> int that returns the value of the LCA node.

Constraints

•The number of nodes in the tree is in the range [2, 100000]
•-1000000000 <= Node.val <= 1000000000
•All Node.val are unique
•p != q
•p and q will exist in the BST

Examples

Example 1

Input

[6,2,8,0,4,7,9,None,None,3,5], 2, 8

Output

Explanation

The LCA of nodes 2 and 8 is 6, which is the root.

Example 2

Input

[6,2,8,0,4,7,9,None,None,3,5], 2, 4

Output

Explanation

The LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself.

Example 3

Input

[2,1], 2, 1

Output

Explanation

The LCA of nodes 2 and 1 is 2.

Need a Hint?

Perform a recursive tree traversal (DFS) or level-order traversal (BFS) using a queue/stack.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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