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Which approach guarantees an optimal solution that correctly merges overlapping intervals after insertion?

easy🔍 Pattern Recognition Q11 of Q15
Intervals - Insert Interval
You are given a list of non-overlapping intervals sorted by their start times, and a new interval to insert. Which approach guarantees an optimal solution that correctly merges overlapping intervals after insertion?
AUse a greedy approach that inserts the new interval at the end and merges overlapping intervals in one pass without sorting.
BIterate through intervals and insert the new interval in the correct position without sorting, then merge overlapping intervals.
CUse dynamic programming to find the minimal set of merged intervals after insertion.
DAppend the new interval, sort all intervals by start time, then merge overlapping intervals in one pass.
Step-by-Step Solution
Solution:

  1. Step 1: Understand the problem constraints

    The intervals are sorted and non-overlapping initially, but inserting a new interval may cause overlaps.

  2. Step 2: Identify the approach that guarantees correct merging

    Appending and then sorting ensures the new interval is placed correctly relative to others, allowing a single pass merge to handle all overlaps reliably.

  3. Final Answer:

    Option D -> Option D

  4. Quick Check:

    Sorting after insertion ensures correct order for merging [OK]
Quick Trick: Sort after insertion to guarantee correct merge order [OK]
Common Mistakes:
MISTAKES
  • Assuming intervals remain sorted after insertion without sorting
  • Trying to merge without sorting leads to missed overlaps
  • Using DP unnecessarily complicates the problem
Trap Explanation:
PITFALL
  • Option D looks plausible but skipping sorting can cause incorrect merges if newInterval is inserted out of order.
Interviewer Note:
CONTEXT
  • Tests if candidate recognizes the need to reorder intervals before merging after insertion.
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