What is the most efficient approach to find the minimum number of arrows needed to burst all balloons?
easy🔍 Pattern Recognition Q11 of Q15
Intervals - Minimum Number of Arrows to Burst Balloons
You are given a set of intervals representing horizontal balloons on a number line. Each balloon can be burst by shooting an arrow vertically through any point covered by the balloon's interval. What is the most efficient approach to find the minimum number of arrows needed to burst all balloons?
ASort intervals by their end coordinate and greedily shoot arrows at the earliest possible end to cover maximum balloons.
BSort intervals by their start coordinate and greedily shoot arrows at the start of each balloon.
CUse dynamic programming to find the maximum number of overlapping intervals and subtract from total balloons.
DUse a brute force nested loop to check all pairs of intervals for overlaps and count arrows accordingly.
Step-by-Step Solution
Step 1: Understand the problem constraints
The problem requires minimizing arrows to burst all balloons, which translates to covering intervals with minimum points.
Step 2: Identify the optimal greedy strategy
Sorting by end coordinate allows shooting an arrow at the earliest finishing balloon's end, covering all overlapping balloons starting before that point.
Final Answer:
Option A -> Option A
Quick Check:
Sorting by end coordinate ensures minimal arrows by maximizing coverage [OK]
Quick Trick:Sort intervals by end to greedily cover overlaps [OK]
Common Mistakes:
MISTAKES
Sorting by start coordinate and shooting at start misses optimal overlaps
Using DP unnecessarily complicates the problem
Brute force is too slow for large inputs
Trap Explanation:
PITFALL
Sorting by start coordinate looks plausible but can lead to suboptimal arrow counts because it doesn't guarantee maximum overlap coverage.
Interviewer Note:
CONTEXT
Tests if candidate can recognize the greedy interval scheduling pattern for minimum coverage.
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