Which approach is best to optimize time and space, and why?
hard🎤 Interviewer Follow-up Q15 of Q15
Tree: Depth-First Search - Lowest Common Ancestor of Binary Tree
Suppose the binary tree nodes have parent pointers already, but the tree is very deep (height h). You want to find the Lowest Common Ancestor of two nodes p and q. Which approach is best to optimize time and space, and why?
AUse brute force by checking all ancestors of p and q repeatedly until common ancestor is found.
BUse the parent pointer + ancestor set approach, building a set for p's ancestors and then traversing q's ancestors.
CUse recursive DFS from root to find paths to p and q, then compare paths to find LCA.
DUse the parent pointer + two-pointer technique: move the deeper node up until both nodes are at the same depth, then move both up simultaneously until they meet.
Step-by-Step Solution
Solution:
Step 1: Understand problem constraints
Nodes have parent pointers, tree is deep, so space usage matters.
Step 2: Evaluate approaches
Ancestor set approach (B) uses O(h) space. Recursive DFS (C) and brute force (D) are inefficient for deep trees.
Step 3: Two-pointer technique
Moving deeper node up to equalize depth, then moving both up simultaneously uses O(1) space and O(h) time, optimal for deep trees.
Final Answer:
Option D -> Option D
Quick Check:
Two-pointer approach optimizes space and time for deep trees with parent pointers [OK]
Quick Trick:Two-pointer approach uses O(1) space for LCA with parent pointers [OK]
Common Mistakes:
MISTAKES
Using ancestor sets unnecessarily
Recursing from root wasting time
Brute force repeated ancestor checks
Trap Explanation:
PITFALL
Ancestor set approach looks simpler but uses extra space; two-pointer is more optimal.
Interviewer Note:
CONTEXT
Tests knowledge of advanced LCA techniques and space optimization.
Master "Lowest Common Ancestor of Binary Tree" in Tree: Depth-First Search
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