What is the time complexity of the optimized recursive approach using a hash map to build a binary tree from preorder and inorder traversals of size n?

medium🪤 Complexity Trap Q5 of Q15

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

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

BO(n^3) because of nested recursion and map operations

CO(n log n) due to recursive splitting and hash map lookups

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

Step-by-Step Solution

Solution:

Step 1: Understand recursion with hash map
Hash map allows O(1) lookup of inorder indices, avoiding array slicing.
Step 2: Count total operations
Each node is visited once, so total time is O(n).
Final Answer:
Option A -> Option A
Quick Check:
Hash map reduces complexity to linear [OK]

Quick Trick: Hash map lookup avoids O(n^2) slicing [OK]

Common Mistakes:

MISTAKES

Assuming slicing causes O(n^2) time

Trap Explanation:

PITFALL

Candidates confuse brute force slicing with optimized index mapping.

Interviewer Note:

CONTEXT

Tests understanding of time complexity optimization

Master "Construct Tree from Preorder and Inorder" in Tree: Depth-First Search

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More Tree: Depth-First Search Quizzes

What is the time complexity of the optimized recursive approach using a hash map to build a binary tree from preorder and inorder traversals of size n?

Step 1: Understand recursion with hash map

Step 2: Count total operations

Final Answer:

Quick Check:

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