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If the data stream problem is extended to support removing numbers while maintaining disjoint intervals, which data structure or approach is best suited for efficient updates?

hard🔁 Follow-up Q10 of Q15

Intervals - Data Stream as Disjoint Intervals

If the data stream problem is extended to support removing numbers while maintaining disjoint intervals, which data structure or approach is best suited for efficient updates?

ABalanced binary search tree with interval counts and lazy updates

BSimple array storing all numbers and rebuilding intervals on removal

CStack to track insertion order and remove last inserted number

DHash set storing numbers without interval structure

Step-by-Step Solution

Solution:

Step 1: Understand removal complexity
Removing numbers requires updating intervals dynamically.
Step 2: Balanced BST with counts
Allows efficient insertions, removals, and interval merges/splits.
Step 3: Other options
Arrays and stacks are inefficient; hash sets lack interval info.
Final Answer:
Option A -> Option A
Quick Check:
Balanced BST supports dynamic insertions and removals [OK]

Quick Trick: Use balanced BST with counts for dynamic removals [OK]

Common Mistakes:

MISTAKES

Using arrays leads to costly rebuilds on removals
Stacks and hash sets do not maintain intervals

Trap Explanation:

PITFALL

Simple data structures fail to efficiently handle removals and merges.

Interviewer Note:

CONTEXT

Tests knowledge of advanced data structures for dynamic interval updates.

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