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Consider the following complete binary tree: 10 / \ 5 15 / \ / 3 7 12 Using an optimal countNodes function that leverages subtree heights, what is the total number of nodes in this tree?

easy🧾 Trace Q3 of Q15

Tree: Depth-First Search - Count Complete Tree Nodes

Consider the following complete binary tree: 10 / \ 5 15 / \ / 3 7 12 Using an optimal countNodes function that leverages subtree heights, what is the total number of nodes in this tree?

A6

B7

C5

D8

Step-by-Step Solution

Solution:

Step 1: Identify the tree structure
The tree has nodes: 10, 5, 15, 3, 7, 12.
Step 2: Count nodes
Counting all nodes: 10, 5, 15, 3, 7, 12 = 6 nodes.
Final Answer:
Option A -> Option A
Quick Check:
Count nodes manually and verify [OK]

Quick Trick: Count nodes directly in small trees [OK]

Common Mistakes:

MISTAKES

Miscounting nodes by including null children
Assuming full last level when it is not
Confusing node values with count

Trap Explanation:

PITFALL

Option B includes an extra node that doesn't exist in the tree.

Interviewer Note:

CONTEXT

Tests ability to manually count nodes and understand tree structure.

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