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Given the sorted intervals [[1,4],[5,8],[9,12]] and the overlap check returns True, which of the following could be the original input intervals before sorting?

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Intervals - Meeting Rooms I
Given the sorted intervals [[1,4],[5,8],[9,12]] and the overlap check returns True, which of the following could be the original input intervals before sorting?
A[[5,8],[9,12],[1,4]]
B[[1,4],[4,8],[8,12]]
C[[1,5],[4,8],[9,12]]
D[[1,4],[5,8],[9,12]]
Step-by-Step Solution
Solution:
  1. Step 1: Check if intervals overlap

    Sorted intervals have no overlaps: 4 ≤ 5 and 8 ≤ 9.
  2. Step 2: Identify original input matching sorted order

    Only [[1,4],[5,8],[9,12]] matches sorted intervals exactly, others have overlaps or different order.
  3. Final Answer:

    Option D -> Option D
  4. Quick Check:

    Original input matches sorted non-overlapping intervals [OK]
Quick Trick: Original input must sort to given intervals [OK]
Common Mistakes:
MISTAKES
  • Picking inputs that cause overlaps
  • Ignoring sorting effect
Trap Explanation:
PITFALL
  • Candidates may pick inputs that do not sort to given intervals or cause overlaps.
Interviewer Note:
CONTEXT
  • Tests reasoning backwards from output to input.
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