What is the auxiliary space complexity of the optimized recursive diameter algorithm, considering recursion stack and data structures used?

medium🪤 Complexity Trap Q6 of Q15

Tree: Depth-First Search - Diameter of Binary Tree

AO(n^2)

BO(log n)

CO(n)

DO(1)

Step-by-Step Solution

Solution:

Step 1: Identify recursion stack depth
In worst case (skewed tree), recursion stack depth is O(n), but average case for balanced tree is O(log n).
Step 2: Check auxiliary data structures
Only constant extra variables used; no additional data structures proportional to n.
Final Answer:
Option B -> Option B
Quick Check:
Auxiliary space dominated by recursion stack -> O(log n) average case [OK]

Quick Trick: Recursion stack depth -> O(log n) average case

Common Mistakes:

MISTAKES

Trap Explanation:

PITFALL

Candidates often assume worst-case skewed tree, ignoring average balanced tree scenario.

Interviewer Note:

CONTEXT

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