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If the definition of a balanced binary tree changes to require the difference in the total number of nodes (not height) between left and right subtrees of every node to be at most 1, which approach is most efficient to verify this?

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Tree: Depth-First Search - Balanced Binary Tree
If the definition of a balanced binary tree changes to require the difference in the total number of nodes (not height) between left and right subtrees of every node to be at most 1, which approach is most efficient to verify this?
APostorder traversal returning subtree node counts with early imbalance detection
BLevel order traversal counting nodes at each level
CPreorder traversal computing heights and node counts separately
DRepeated BFS from each node to count subtree nodes
Step-by-Step Solution
Solution:

  1. Step 1: Understand new definition

    Balance depends on node count difference, not height.

  2. Step 2: Use postorder traversal

    Postorder allows bottom-up aggregation of node counts.

  3. Step 3: Early imbalance detection

    If difference > 1, propagate failure immediately to avoid extra work.

  4. Final Answer:

    Option A -> Option A

  5. Quick Check:

    Bottom-up count aggregation with early exit is efficient [OK]
Quick Trick: Use postorder to count nodes and detect imbalance early [OK]
Common Mistakes:
MISTAKES
  • Using BFS repeatedly causing high complexity
  • Mixing height and node count concepts
  • Not propagating imbalance early
Trap Explanation:
PITFALL
  • Assuming height-based methods apply directly to node count balance
Interviewer Note:
CONTEXT
  • Tests ability to adapt balanced tree checks to new balance criteria
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