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Given the final arrow count is 3 for the input intervals [[1,5],[2,6],[7,10],[8,11],[12,15]], which of the following could be the arrow positions chosen by the optimal greedy algorithm?

hard🔄 Reverse Engineer Q9 of Q15
Intervals - Minimum Number of Arrows to Burst Balloons
Given the final arrow count is 3 for the input intervals [[1,5],[2,6],[7,10],[8,11],[12,15]], which of the following could be the arrow positions chosen by the optimal greedy algorithm?
A[5, 10, 15]
B[6, 11, 15]
C[1, 7, 12]
D[2, 8, 14]
Step-by-Step Solution
Solution:

  1. Step 1: Sort intervals by end

    Sorted: [1,5],[2,6],[7,10],[8,11],[12,15]

  2. Step 2: Greedy arrow placement

    First arrow at 6 covers [1,5],[2,6]; second at 11 covers [7,10],[8,11]; third at 15 covers [12,15].

  3. Final Answer:

    Option B -> Option B

  4. Quick Check:

    Arrow positions match interval ends covering all balloons [OK]
Quick Trick: Arrows placed at earliest possible interval ends [OK]
Common Mistakes:
MISTAKES
  • Choosing arrow positions at starts or arbitrary points
Trap Explanation:
PITFALL
  • Candidates may pick start points or midpoints, missing minimal coverage.
Interviewer Note:
CONTEXT
  • Tests ability to reverse engineer arrow positions from output.
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