452. Minimum Number of Arrows to Burst Balloons

题目

There are some spherical balloons taped onto a flat wall that represents the XY-plane. The balloons are represented as a 2D integer array points where points[i] = [xstart, xend] denotes a balloon whose horizontal diameter stretches between xstart and xend. You do not know the exact y-coordinates of the balloons.

Arrows can be shot up directly vertically (in the positive y-direction) from different points along the x-axis. A balloon with xstart and xend is burst by an arrow shot at x if xstart <= x <= xend. There is no limit to the number of arrows that can be shot. A shot arrow keeps traveling up infinitely, bursting any balloons in its path.

Given the array points, return the minimum number of arrows that must be shot to burst all balloons.

 

Example 1:

Input: points = [[10,16],[2,8],[1,6],[7,12]]
Output: 2
Explanation: The balloons can be burst by 2 arrows:
- Shoot an arrow at x = 6, bursting the balloons [2,8] and [1,6].
- Shoot an arrow at x = 11, bursting the balloons [10,16] and [7,12].

Example 2:

Input: points = [[1,2],[3,4],[5,6],[7,8]]
Output: 4
Explanation: One arrow needs to be shot for each balloon for a total of 4 arrows.

Example 3:

Input: points = [[1,2],[2,3],[3,4],[4,5]]
Output: 2
Explanation: The balloons can be burst by 2 arrows:
- Shoot an arrow at x = 2, bursting the balloons [1,2] and [2,3].
- Shoot an arrow at x = 4, bursting the balloons [3,4] and [4,5].

 

Constraints:

• 1 <= points.length <= 105
• points[i].length == 2
• -231 <= xstart < xend <= 231 - 1

Related Topics

贪心

数组

排序

👍 1098

👎 0

思路

和 435有相似之处，贪心算法最重要的是找到约束条件，并根据恰好的约束条件补全代码

解法

# leetcode submit region begin(Prohibit modification and deletion)
class Solution:
    def findMinArrowShots(self, points: List[List[int]]) -> int:
        points.sort(key=lambda x:x[1])
        res = 0
        max_flag = float('-inf')
        for start, end in points:
            if start > max_flag:
                max_flag = end
                res += 1
        return  res
# leetcode submit region end(Prohibit modification and deletion)

复杂度分析

• 时间复杂度 O(nlogn)
  • 主要用于数组排序
• 空间复杂度 O(1)