What is the auxiliary space complexity of the min-heap approach for Minimum Interval to Include Each Query with n intervals and m queries?

medium🪤 Complexity Trap Q6 of Q15

Intervals - Minimum Interval to Include Each Query

AO(1)

BO(m)

CO(n + m)

DO(n)

Step-by-Step Solution

Solution:

Step 1: Identify data structures
Min-heap stores active intervals, which can be up to O(n) in worst case.
Step 2: Consider output array
Result array is O(m), but auxiliary space excludes output.
Step 3: Combine auxiliary space
Auxiliary space is dominated by heap and sorting structures, O(n).
Final Answer:
Option D -> Option D
Quick Check:
Heap size bounded by number of intervals [OK]

Quick Trick: Heap stores intervals, so space is O(n) [OK]

Common Mistakes:

MISTAKES

Trap Explanation:

PITFALL

Candidates often underestimate heap space or confuse output space with auxiliary space.

Interviewer Note:

CONTEXT

Tests understanding of auxiliary space vs output space in interval heap approach

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