Tree: Depth-First Search - Balanced Binary Tree
What is the time complexity of the brute force approach that separately computes height for each node to check if a binary tree is balanced?
What is the time complexity of the brute force approach that separately computes height for each node to check if a binary tree is balanced?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze height computation calls
Height is computed recursively for each node, and each height call traverses subtree nodes.Step 2: Calculate total calls
For n nodes, height is called at each node, and each call can take O(n) in worst case, leading to O(n^2) total time.Final Answer:
Option A -> Option AQuick Check:
Repeated height calls cause quadratic time [OK]
Quick Trick: Repeated height calls cause O(n²) time [OK]
Common Mistakes:
MISTAKES- Assuming height calls are O(1) leading to O(n) time
- Confusing height with depth or tree height h
- Thinking O(n log n) due to balanced tree assumption
Trap Explanation:
PITFALL- Option D looks correct if candidate thinks height calls cost O(h), but worst case is skewed tree with h = n.
Interviewer Note:
CONTEXT- Checks if candidate understands why naive height computations cause quadratic time.
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