LeetCode 452: Minimum Number of Arrows to Burst Balloons — Python Solution

Solve LeetCode 452: Minimum Number of Arrows to Burst Balloons in Python with a greedy earliest end approach. The key is to make the state invariant explicit, so the implementation and complexity follow naturally.

This guide paraphrases the task and does not reproduce LeetCode’s prompt. Use the official page for the complete statement, examples, constraints, and submission runner.

What the problem is testing

Sort balloons by ending coordinate and shoot at the earliest possible end; add an arrow only when the next interval starts after that point.

Algorithm

1. Sort balloons by ending coordinate and shoot at the earliest possible end; add an arrow only when the next interval starts after that point.
2. Maintain this invariant: The current arrow bursts every interval processed since the last arrow and leaves maximum room for future overlaps.
3. Continue until every input item or reachable state has been resolved, then return the accumulated result.

Python solution

from collections import Counter, defaultdict, deque, OrderedDict
import random

class Solution:
    def findMinArrowShots(self, points):
        if not points:
            return 0
        points.sort(key=lambda interval: interval[1])
        arrows, position = 1, points[0][1]
        for start, end in points[1:]:
            if start > position:
                arrows += 1
                position = end
        return arrows

Why this is correct

The proof follows the maintained state: The current arrow bursts every interval processed since the last arrow and leaves maximum room for future overlaps. Each iteration preserves that claim while permanently resolving at least one position, node, interval, or search state. When the loop or recursion ends, every candidate required by the problem has therefore been included or ruled out, so the returned value is correct.

Complexity

O(n log n) time and O(1) auxiliary space aside from sorting. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

Intervals touching the arrow coordinate are burst by the same arrow.

Tested reference code

This implementation is included in the site’s downloadable 100-solution Python library. The complete suite compiles every solution and runs a behavioral assertion for every problem before publication.

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