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What is the space complexity of the recursive DFS approach to find the Lowest Common Ancestor in a binary tree with n nodes and height h?

medium🪤 Complexity Trap Q6 of Q15
Tree: Depth-First Search - Lowest Common Ancestor of Binary Tree
What is the space complexity of the recursive DFS approach to find the Lowest Common Ancestor in a binary tree with n nodes and height h?
AO(h) due to recursion call stack depth
BO(1) constant space since no extra data structures used
CO(n) due to storing all nodes in recursion stack
DO(n) due to storing parent pointers
Step-by-Step Solution
Solution:

  1. Step 1: Analyze recursion stack space

    Recursive DFS uses call stack up to height h -> O(h).

  2. Step 2: Analyze auxiliary space

    No additional data structures are used in recursive DFS approach.

  3. Final Answer:

    Option A -> Option A

  4. Quick Check:

    Recursion stack depth dominates space usage [OK]
Quick Trick: Recursion stack space is O(h) [OK]
Common Mistakes:
MISTAKES
  • Confusing recursion stack with parent map space
Trap Explanation:
PITFALL
  • Candidates confuse recursion stack space with auxiliary data structures.
Interviewer Note:
CONTEXT
  • Tests space complexity understanding of recursive DFS
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