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What is the overall time complexity of the parent-pointer + ancestor set approach to find the Lowest Common Ancestor in a binary tree with n nodes and height h?

medium📊 Complexity Q5 of Q15
Tree: Depth-First Search - Lowest Common Ancestor of Binary Tree
What is the overall time complexity of the parent-pointer + ancestor set approach to find the Lowest Common Ancestor in a binary tree with n nodes and height h?
AO(h) time, where h is the height of the tree
BO(log n) time, assuming balanced tree
CO(n) time, where n is the total number of nodes
DO(h^2) time due to repeated ancestor checks
Step-by-Step Solution
Solution:

  1. Step 1: Build parent pointers

    Building the parent map requires traversing all nodes, which takes O(n) time.

  2. Step 2: Traverse ancestors of p and q

    Each traversal takes O(h) time, but building the map dominates.

  3. Step 3: Total time complexity

    Overall time complexity is O(n) due to preprocessing.

  4. Final Answer:

    Option C -> Option C

  5. Quick Check:

    Preprocessing dominates query time [OK]
Quick Trick: Preprocessing parent pointers costs O(n) [OK]
Common Mistakes:
MISTAKES
  • Confusing per-query cost with preprocessing cost
  • Assuming O(h) includes building parent pointers
Trap Explanation:
PITFALL
  • Mistaking preprocessing cost as per-query cost
Interviewer Note:
CONTEXT
  • Tests understanding of time complexity of parent-pointer + ancestor set method
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