Tree: Depth-First Search - Balanced Binary Tree
What is the worst-case time complexity of the naive approach that checks if a binary tree is balanced by computing the height of each subtree independently for every node?
What is the worst-case time complexity of the naive approach that checks if a binary tree is balanced by computing the height of each subtree independently for every node?
medium📊 Complexity Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand naive approach
For each node, height is computed by traversing its subtree.Step 2: Calculate complexity
Height computation is O(n) in worst case, done for each of n nodes -> O(n^2).Final Answer:
Option C -> Option CQuick Check:
Repeated height computations cause quadratic time [OK]
Quick Trick: Repeated height calls cause O(n²) time [OK]
Common Mistakes:
MISTAKES- Assuming height computations are cached
- Confusing with optimized O(n) approach
- Underestimating repeated subtree traversals
Trap Explanation:
PITFALL- Thinking height is computed once per node instead of repeatedly
Interviewer Note:
CONTEXT- Tests understanding of naive vs optimized time complexity
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