[Solved] You are given a binary tree that is complete (all levels except possibly the last are fully filled, and nodes in the last... Which approach guarantees the optimal time complexity for this problem? | Tree: Depth-First Search

Tree: Depth-First Search - Count Complete Tree Nodes

You are given a binary tree that is complete (all levels except possibly the last are fully filled, and nodes in the last level are as far left as possible). You need to count the total number of nodes efficiently. Which approach guarantees the optimal time complexity for this problem?

APerform a simple DFS traversal counting all nodes, which takes O(n) time.

BUse the tree height to check if subtrees are perfect and recursively count nodes, achieving O((log n)^2) time.

CApply a greedy approach by counting nodes level by level until the last incomplete level.

DUse a breadth-first search (BFS) traversal to count nodes, which is efficient for complete trees.

Step-by-Step Solution

Solution:

Step 1: Understand the problem constraints
The tree is complete, so the height can be used to identify perfect subtrees quickly.
Step 2: Recognize the optimal approach
Using the height to check if left or right subtree is perfect allows skipping large parts of the tree, reducing complexity to O((log n)^2).
Final Answer:
Option B -> Option B
Quick Check:
Optimal approach leverages tree height and completeness [OK]

Quick Trick: Use tree height to skip perfect subtrees [OK]

Common Mistakes:

MISTAKES

Assuming BFS or simple DFS is optimal
Using greedy level counting without height checks

Trap Explanation:

PITFALL

Many think BFS or simple DFS is best due to simplicity, but they miss the height-based pruning advantage.

Interviewer Note:

CONTEXT

Tests if candidate can identify the specialized approach exploiting tree completeness.

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Which approach guarantees the optimal time complexity for this problem?

Step 1: Understand the problem constraints

Step 2: Recognize the optimal approach

Final Answer:

Quick Check:

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