Which modification to the optimal balanced tree approach is necessary to handle this correctly?
hard🎤 Interviewer Follow-up Q15 of Q15
Intervals - Data Stream as Disjoint Intervals
Suppose the problem is extended so that numbers can be added multiple times (duplicates allowed), and the intervals must reflect the count of each number (e.g., intervals store counts of coverage). Which modification to the optimal balanced tree approach is necessary to handle this correctly?
AAugment intervals with counts and update counts on insertion; merge intervals only if counts allow.
BKeep the current approach but ignore duplicates since intervals are disjoint sets.
CUse a brute force approach storing all numbers and recomputing intervals with counts on each query.
DReplace balanced tree with a hash map keyed by number to track counts and intervals separately.
Step-by-Step Solution
Solution:
Step 1: Understand the impact of duplicates
Intervals must now track counts, so simple presence is insufficient.
Step 2: Modify data structure
Intervals should store counts per interval or per number; merging must consider counts to avoid losing duplicates.
Step 3: Evaluate options
Ignoring duplicates (B) breaks correctness. Brute force (C) is inefficient. Hash map (D) loses interval ordering benefits. Augmenting intervals with counts (A) preserves efficiency and correctness.
