Intervals - Data Stream as Disjoint Intervals
What is the space complexity of the optimal balanced tree approach storing n intervals, considering auxiliary data and recursion stack?
What is the space complexity of the optimal balanced tree approach storing n intervals, considering auxiliary data and recursion stack?
medium🪤 Complexity Trap Q6 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze storage of intervals
Intervals stored explicitly require O(n) space.Step 2: Consider recursion or auxiliary space
Balanced tree insertion uses recursion stack O(log n), negligible compared to O(n).Step 3: Consider worst case nested intervals
Nested intervals do not increase space beyond O(n), so O(n) total.Final Answer:
Option C -> Option CQuick Check:
O(n) intervals plus O(log n) stack -> O(n) dominant [OK]
Quick Trick: Intervals stored explicitly dominate space [OK]
Common Mistakes:
MISTAKES- Forgetting recursion stack or assuming quadratic space
Trap Explanation:
PITFALL- Candidates overestimate space due to recursion or nested intervals.
Interviewer Note:
CONTEXT- Tests understanding of space complexity including auxiliary structures.
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