Intervals - Data Stream as Disjoint Intervals
What is the worst-case time complexity of inserting a new number into the data structure maintaining disjoint intervals using a balanced binary search tree with n intervals?
What is the worst-case time complexity of inserting a new number into the data structure maintaining disjoint intervals using a balanced binary search tree with n intervals?
medium📊 Complexity Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand operations
Insertion requires searching and possibly merging intervals.Step 2: Balanced BST complexity
Search and insert operations take O(log n).Step 3: Merging intervals
Merging adjacent intervals is O(1) or constant time per merge.Final Answer:
Option B -> Option BQuick Check:
Balanced BST insertion/search is logarithmic [OK]
Quick Trick: Balanced BST insertion/search is O(log n) [OK]
Common Mistakes:
MISTAKES- Assuming linear time due to merges (merges are constant time)
- Confusing with rebuilding intervals from scratch
Trap Explanation:
PITFALL- Merging intervals is often constant time, not linear.
Interviewer Note:
CONTEXT- Tests knowledge of time complexity for balanced tree operations.
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