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Consider the following code snippet implementing the optimal countNodes function for a complete binary tree. Given the tree: 1 / \ 2 3 / 4 What is the final return value of countNodes(root)?

easy🧾 Code Trace Q12 of Q15

Tree: Depth-First Search - Count Complete Tree Nodes

Consider the following code snippet implementing the optimal countNodes function for a complete binary tree. Given the tree: 1 / \ 2 3 / 4 What is the final return value of countNodes(root)?

A4

B3

C5

D6

Step-by-Step Solution

Solution:

Step 1: Calculate tree height
Height h = 3 (nodes 1 -> 2 -> 4).
Step 2: Binary search on last level nodes
Last level has indices 0 to 3. Check existence: - idx=0 exists (node 4) - idx=1 does not exist So left ends at 1.
Final Answer:
Option A -> Option A
Quick Check:
Count = (2^(3-1)-1) + left = 3 + 1 = 4 [OK]

Quick Trick: Count = perfect nodes + last level nodes found [OK]

Common Mistakes:

MISTAKES

Off-by-one in binary search bounds
Miscounting last level nodes

Trap Explanation:

PITFALL

Candidates often miscalculate last level node indices or final sum.

Interviewer Note:

CONTEXT

Tests ability to trace binary search and existence check in optimal code.

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