What is the optimal time complexity of solving LCA?

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 LCA?

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 LCA?

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 LCA?

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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DSA SectionEasy

LCA

Learn how to solve the 'LCA' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function find_lca(tree_arr, p, q) that takes an array representation of a binary tree tree_arr and two node values p and q, and returns the value of their Lowest Common Ancestor (LCA).

Constraints

•2 <= len(tree_arr) <= 1000
•p and q are present in the tree

Examples

Example 1

Input

tree_arr = [3, 5, 1, 6, 2, 0, 8, None, None, 7, 4], p = 5, q = 1

Output

Explanation

The LCA of nodes 5 and 1 is 3.

Example 2

Input

tree_arr = [3, 5, 1, 6, 2, 0, 8, None, None, 7, 4], p = 5, q = 4

Output

Explanation

The LCA of nodes 5 and 4 is 5, since a node can be an ancestor of itself.

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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