Which approach guarantees an optimal solution in terms of time and space complexity?
easy🔍 Pattern Recognition Q11 of Q15
Tree: Depth-First Search - Lowest Common Ancestor of Binary Tree
You are given a binary tree and two nodes within it. You need to find the node that is the deepest common ancestor of both nodes. Which approach guarantees an optimal solution in terms of time and space complexity?
AUse a brute force approach by finding paths from root to each node and then comparing the paths.
BBuild a parent pointer map for all nodes, then use ancestor sets to find the lowest common ancestor.
CApply a greedy algorithm that picks the first common node found during a preorder traversal.
DUse dynamic programming to store results of subtrees and combine them to find the ancestor.
Step-by-Step Solution
Solution:
Step 1: Understand problem constraints
The problem requires finding the lowest common ancestor efficiently, ideally in O(n) time and O(n) space.
Step 2: Evaluate approaches
Brute force (A) is correct but less optimal. Greedy (C) fails because it may pick incorrect ancestors. DP (D) is not applicable here. Building parent pointers and using ancestor sets (B) provides an optimal and clean solution.
Final Answer:
Option B -> Option B
Quick Check:
Parent pointer + ancestor set approach is standard optimal solution [OK]
