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How does this constraint affect the approach to find the minimum number of arrows needed to burst all balloons?

hard🎤 Interviewer Follow-up Q10 of Q15
Intervals - Minimum Number of Arrows to Burst Balloons
Suppose balloons are represented as intervals on a real number line, but now arrows can only be shot at integer points. How does this constraint affect the approach to find the minimum number of arrows needed to burst all balloons?
AWe need to adjust the greedy algorithm to shoot arrows at the ceiling of interval ends
BWe must use dynamic programming to handle discrete arrow positions
CThe problem reduces to interval coloring instead of coverage
DThe original greedy algorithm works unchanged since intervals contain integers
Step-by-Step Solution
Solution:

  1. Step 1: Understand integer shooting constraint

    Arrows must be at integer points, so shooting exactly at interval end may not be possible if end is fractional.

  2. Step 2: Adjust greedy approach

    Shooting at ceiling of interval end ensures arrow covers the interval while respecting integer positions.

  3. Step 3: Impact on minimal arrows

    This adjustment may increase arrows needed but preserves greedy strategy.

  4. Final Answer:

    Option A -> Option A

  5. Quick Check:

    Ceiling adjustment handles integer shooting constraint [OK]
Quick Trick: Shoot arrows at ceiling of interval ends for integer points [OK]
Common Mistakes:
MISTAKES
  • Assuming original algorithm works without modification
Trap Explanation:
PITFALL
  • Candidates often overlook discrete shooting constraints affecting arrow placement.
Interviewer Note:
CONTEXT
  • Tests ability to adapt greedy algorithms to discrete constraints.
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