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

medium🪤 Complexity Trap Q13 of Q15

Tree: Depth-First Search - Construct Tree from Inorder and Postorder

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

AO(n) because each node is processed once and index lookup is O(1)

BO(n^2) due to repeated slicing of arrays

CO(n log n) because of balanced tree recursion depth

DO(n) but with O(n) auxiliary space for recursion stack and hash map

Step-by-Step Solution

Step 1: Analyze time complexity
Using a hash map avoids repeated linear searches, so each node is processed once -> O(n) time.
Step 2: Analyze space complexity
Hash map stores n elements, recursion stack can be up to O(n) in skewed trees, so total auxiliary space is O(n).
Final Answer:
Option A -> Option A
Quick Check:
Time is O(n), space includes recursion stack and hash map [OK]

Quick Trick: Hash map reduces search to O(1), recursion stack adds O(n) space [OK]

Common Mistakes:

MISTAKES

Assuming slicing causes O(n^2) time
Ignoring recursion stack space
Confusing balanced tree depth with complexity

Trap Explanation:

PITFALL

Option D incorrectly mixes time and space complexity; time complexity is O(n).

Interviewer Note:

CONTEXT

Checks if candidate understands both time and space complexity nuances in recursion with hash maps.

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