[Solved] In the naive recursive approach to find the diameter of a binary tree, the height of each subtree is... What is the overall time complexity of this approach in terms of n, the number of nodes? | Tree: Depth-First Search

Tree: Depth-First Search - Diameter of Binary Tree

In the naive recursive approach to find the diameter of a binary tree, the height of each subtree is recalculated multiple times. What is the overall time complexity of this approach in terms of n, the number of nodes?

AO(n<sup>2</sup>)

BO(n log n)

CO(n)

DO(log n)

Step-by-Step Solution

Solution:

Step 1: Understand the naive approach
For each node, the algorithm computes the height of its left and right subtrees separately.
Step 2: Analyze height computation cost
Computing height for a subtree rooted at a node takes O(n) in the worst case.
Step 3: Total cost
Since height is computed for every node, total time is O(n) * O(n) = O(n²).
Final Answer:
Option A -> Option A
Quick Check:
Repeated height calculations cause quadratic time [OK]

Quick Trick: Repeated height calls cause O(n^2) time complexity [OK]

Common Mistakes:

MISTAKES

Assuming height calculation is O(1)
Confusing with optimized O(n) approach
Ignoring repeated subtree height computations

Trap Explanation:

PITFALL

Thinking height calculation is constant time leads to underestimating complexity.

Interviewer Note:

CONTEXT

Tests understanding of recursive complexity and inefficiencies in naive tree algorithms.

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What is the overall time complexity of this approach in terms of n, the number of nodes?

Step 1: Understand the naive approach

Step 2: Analyze height computation cost

Step 3: Total cost

Final Answer:

Quick Check:

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