Intervals - Data Stream as Disjoint Intervals
Given the intervals [[1, 2], [4, 5], [7, 10]] after several addNum calls, which of the following sequences of inserted numbers could produce this state?
Given the intervals [[1, 2], [4, 5], [7, 10]] after several addNum calls, which of the following sequences of inserted numbers could produce this state?
hard🔄 Reverse Engineer Q9 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze intervals
Intervals are disjoint: [1,2], [4,5], [7,10].Step 2: Check which sequences produce these intervals
Sequence A inserts 7,8,9,10 forming [7,10] interval; no 3 or 6 to merge intervals.Step 3: Verify other options
Sequence B misses 8,9 so [7,10] wouldn't form; Sequence C inserts 3 merging [1,2] and [4,5]; Sequence D inserts 6 merging [4,5] and [7,10].Final Answer:
Option B -> Option BQuick Check:
Only sequence A matches given intervals exactly [OK]
Quick Trick: Inserted numbers must match interval merges exactly [OK]
Common Mistakes:
MISTAKES- Assuming missing numbers still merge intervals
Trap Explanation:
PITFALL- Candidates fail to reason backward about merges from intervals.
Interviewer Note:
CONTEXT- Tests reverse reasoning from intervals to input sequence.
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