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What is the overall time complexity of reconstructing a binary tree from inorder and postorder traversals using a recursive approach combined with a hash map for quick index lookups?

medium🌳 Construct Tree Q5 of Q15

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

What is the overall time complexity of reconstructing a binary tree from inorder and postorder traversals using a recursive approach combined with a hash map for quick index lookups?

AO(n log n)

BO(n)

CO(n²)

DO(log n)

Step-by-Step Solution

Solution:

Step 1: Use a hash map for index lookup
Building a hash map for inorder values to indices takes O(n) time.
Step 2: Recursive tree construction
Each node is processed once, and index lookups are O(1) due to the hash map.
Final Answer:
Option B -> Option B
Quick Check:
Each node visited once, no repeated searches [OK]

Quick Trick: Hash map reduces index search to O(1), total O(n) [OK]

Common Mistakes:

MISTAKES

Assuming repeated linear searches cause O(n²) complexity
Confusing traversal time with construction time
Ignoring the hash map optimization

Trap Explanation:

PITFALL

Thinking recursive calls multiply complexity without considering O(1) index lookup

Interviewer Note:

CONTEXT

Tests understanding of algorithmic complexity and optimization using hash maps

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