Which modification to the binary search + preprocessing approach is necessary to handle this variant correctly and efficiently?
hard🎤 Interviewer Follow-up Q15 of Q15
Intervals - Minimum Interval to Include Each Query
Suppose the problem is modified so that intervals can be reused multiple times for different queries, and queries can be negative integers. Which modification to the binary search + preprocessing approach is necessary to handle this variant correctly and efficiently?
APreprocess intervals by length and use a segment tree to query coverage efficiently for negative and repeated queries.
BNo change needed; the original approach works for reuse and negative queries.
CSort queries and intervals, use a min-heap to maintain active intervals covering queries in order.
DUse brute force checking each interval for each query since reuse breaks binary search assumptions.
Step-by-Step Solution
Solution:
Step 1: Identify challenges with reuse and negative queries
Negative queries require data structures supporting arbitrary ranges; reuse means intervals must be efficiently queried multiple times.
Step 2: Choose appropriate data structure
Segment tree or interval tree allows efficient coverage queries over any integer range and supports multiple queries efficiently.
Step 3: Why other options fail
Min-heap approach requires sorting queries and intervals but doesn't handle negative queries well; brute force is inefficient; original approach assumes positive queries and no reuse.
Final Answer:
Option A -> Option A
Quick Check:
Segment tree supports arbitrary queries and reuse efficiently [OK]
Quick Trick:Segment tree handles arbitrary queries and reuse [OK]
Common Mistakes:
MISTAKES
Assuming original approach works unchanged
Using min-heap without sorting queries
Resorting to brute force unnecessarily
Trap Explanation:
PITFALL
Min-heap approach looks plausible but fails with negative queries and reuse; segment tree is needed.
Interviewer Note:
CONTEXT
Tests candidate's ability to adapt solutions to harder variants and choose advanced data structures.
Master "Minimum Interval to Include Each Query" in Intervals
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