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What is the space complexity of the optimized recursive solution with a hash map for index lookup when constructing a binary tree from inorder and postorder traversals of size n?

medium🪤 Complexity Trap Q6 of Q15
Tree: Depth-First Search - Construct Tree from Inorder and Postorder
What is the space complexity of the optimized recursive solution with a hash map for index lookup when constructing a binary tree from inorder and postorder traversals of size n?
AO(1) constant auxiliary space
BO(n) for recursion stack and hash map storage
CO(n^2) due to recursive slicing
DO(log n) due to balanced recursion depth
Step-by-Step Solution
Solution:

  1. Step 1: Account for hash map storage

    Hash map stores n elements -> O(n) space.

  2. Step 2: Consider recursion call stack depth

    Worst case skewed tree -> recursion depth O(n).

  3. Final Answer:

    Option B -> Option B

  4. Quick Check:

    Hash map + recursion stack -> O(n) space [OK]
Quick Trick: Hash map + recursion stack cause O(n) space usage [OK]
Common Mistakes:
MISTAKES
  • Forgetting recursion stack space
  • Assuming constant space
Trap Explanation:
PITFALL
  • Candidates often forget recursion stack space or assume balanced tree depth.
Interviewer Note:
CONTEXT
  • Tests understanding of auxiliary space including recursion stack.
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