[Solved] You need to count the number of nodes in a binary tree where all levels except possibly the last are fully filled, and nodes in the last level... Which algorithmic pattern best fits this problem? | Tree: Depth-First Search

Tree: Depth-First Search - Count Complete Tree Nodes

You need to count the number of nodes in a binary tree where all levels except possibly the last are fully filled, and nodes in the last level are as far left as possible. Which algorithmic pattern best fits this problem?

AUse a simple DFS traversal to count all nodes.

BLeverage tree height properties to identify perfect subtrees and count nodes efficiently.

CApply a sliding window technique on the node values.

DUse a hash map to store node counts and retrieve them in O(1).

Step-by-Step Solution

Solution:

Step 1: Understand the tree property
The tree is complete, so all levels except possibly the last are fully filled, allowing height-based checks.
Step 2: Recognize the pattern
Using tree height to detect perfect subtrees enables counting nodes without full traversal.
Final Answer:
Option B -> Option B
Quick Check:
Counting nodes by height properties is optimal for complete trees [OK]

Quick Trick: Complete tree -> use height-based counting [OK]

Common Mistakes:

MISTAKES

Assuming simple DFS is always best
Using unrelated patterns like sliding window

Trap Explanation:

PITFALL

Candidates often default to DFS without leveraging completeness, missing the height-based optimization.

Interviewer Note:

CONTEXT

Tests candidate's ability to recognize when to use tree height properties.

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Which algorithmic pattern best fits this problem?

Step 1: Understand the tree property

Step 2: Recognize the pattern

Final Answer:

Quick Check:

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