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Which modification to the greedy algorithm is correct to find the maximum number of non-overlapping intervals under this new condition?

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Intervals - Non-overlapping Intervals (Max Non-Overlap)
Suppose intervals can be reused multiple times (i.e., you can select the same interval multiple times if it does not overlap with itself). Which modification to the greedy algorithm is correct to find the maximum number of non-overlapping intervals under this new condition?
ASort intervals by end time and greedily select intervals, resetting last_end after each selection to allow reuse.
BUse dynamic programming to consider multiple selections of intervals, since greedy no longer works.
CSort intervals by start time and greedily select intervals without updating last_end to allow reuse.
DSort intervals by end time and greedily select intervals, but allow intervals to be selected multiple times by not updating last_end.
Step-by-Step Solution
  1. Step 1: Understand reuse changes problem

    Allowing reuse means intervals can be selected multiple times, breaking the greedy assumption of one-time selection.
  2. Step 2: Identify correct approach

    Dynamic programming is needed to explore multiple selections and ensure maximum count without overlap.
  3. Final Answer:

    Option B -> Option B
  4. Quick Check:

    Greedy fails with reuse; DP handles multiple selections [OK]
Quick Trick: Reuse breaks greedy; DP needed for multiple selections [OK]
Common Mistakes:
MISTAKES
  • Trying to reuse intervals by resetting last_end incorrectly
  • Ignoring overlap constraints when reusing intervals
  • Assuming greedy still works unchanged
Trap Explanation:
PITFALL
  • Options that try to tweak greedy look plausible but fail on overlapping reuse cases.
Interviewer Note:
CONTEXT
  • Tests candidate's ability to adapt approach when problem constraints change.
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