|
| 1 | +--- |
| 2 | +comments: true |
| 3 | +difficulty: Medium |
| 4 | +edit_url: Antim |
| 5 | +tags: |
| 6 | + - Greedy |
| 7 | + - Array |
| 8 | + - Sorting |
| 9 | +--- |
| 10 | + |
| 11 | +<!-- problem:start --> |
| 12 | + |
| 13 | +# [452. Minimum Number of Arrows to Burst Balloons](https://leetcode.com/problems/minimum-number-of-arrows-to-burst-balloons) |
| 14 | + |
| 15 | +## Description |
| 16 | + |
| 17 | +<!-- description:start --> |
| 18 | + |
| 19 | +<p>There are some spherical balloons taped onto a flat wall that represents the XY-plane. The balloons are represented as a 2D integer array <code>points</code> where <code>points[i] = [x<sub>start</sub>, x<sub>end</sub>]</code> denotes a balloon whose <strong>horizontal diameter</strong> stretches between <code>x<sub>start</sub></code> and <code>x<sub>end</sub></code>. You do not know the exact y-coordinates of the balloons.</p> |
| 20 | + |
| 21 | +<p>Arrows can be shot up <strong>directly vertically</strong> (in the positive y-direction) from different points along the x-axis. A balloon with <code>x<sub>start</sub></code> and <code>x<sub>end</sub></code> is <strong>burst</strong> by an arrow shot at <code>x</code> if <code>x<sub>start</sub> <= x <= x<sub>end</sub></code>. There is <strong>no limit</strong> to the number of arrows that can be shot. A shot arrow keeps traveling up infinitely, bursting any balloons in its path.</p> |
| 22 | + |
| 23 | +<p>Given the array <code>points</code>, return <em>the <strong>minimum</strong> number of arrows that must be shot to burst all balloons</em>.</p> |
| 24 | + |
| 25 | +<p> </p> |
| 26 | +<p><strong class="example">Example 1:</strong></p> |
| 27 | + |
| 28 | +<pre> |
| 29 | +<strong>Input:</strong> points = [[10,16],[2,8],[1,6],[7,12]] |
| 30 | +<strong>Output:</strong> 2 |
| 31 | +<strong>Explanation:</strong> The balloons can be burst by 2 arrows: |
| 32 | +- Shoot an arrow at x = 6, bursting the balloons [2,8] and [1,6]. |
| 33 | +- Shoot an arrow at x = 11, bursting the balloons [10,16] and [7,12]. |
| 34 | +</pre> |
| 35 | + |
| 36 | +<p><strong class="example">Example 2:</strong></p> |
| 37 | + |
| 38 | +<pre> |
| 39 | +<strong>Input:</strong> points = [[1,2],[3,4],[5,6],[7,8]] |
| 40 | +<strong>Output:</strong> 4 |
| 41 | +<strong>Explanation:</strong> One arrow needs to be shot for each balloon for a total of 4 arrows. |
| 42 | +</pre> |
| 43 | + |
| 44 | +<p><strong class="example">Example 3:</strong></p> |
| 45 | + |
| 46 | +<pre> |
| 47 | +<strong>Input:</strong> points = [[1,2],[2,3],[3,4],[4,5]] |
| 48 | +<strong>Output:</strong> 2 |
| 49 | +<strong>Explanation:</strong> The balloons can be burst by 2 arrows: |
| 50 | +- Shoot an arrow at x = 2, bursting the balloons [1,2] and [2,3]. |
| 51 | +- Shoot an arrow at x = 4, bursting the balloons [3,4] and [4,5]. |
| 52 | +</pre> |
| 53 | + |
| 54 | +<p> </p> |
| 55 | +<p><strong>Constraints:</strong></p> |
| 56 | + |
| 57 | +<ul> |
| 58 | + <li><code>1 <= points.length <= 10<sup>5</sup></code></li> |
| 59 | + <li><code>points[i].length == 2</code></li> |
| 60 | + <li><code>-2<sup>31</sup> <= x<sub>start</sub> < x<sub>end</sub> <= 2<sup>31</sup> - 1</code></li> |
| 61 | +</ul> |
| 62 | + |
| 63 | +<!-- description:end --> |
| 64 | + |
| 65 | +## Solutions |
| 66 | + |
| 67 | +<!-- solution:start --> |
| 68 | + |
| 69 | +### Solution 1 |
| 70 | + |
| 71 | +<!-- tabs:start --> |
| 72 | + |
| 73 | +#### Python3 |
| 74 | + |
| 75 | +```python |
| 76 | +class Solution: |
| 77 | + def findMinArrowShots(self, points: List[List[int]]) -> int: |
| 78 | + ans, last = 0, -inf |
| 79 | + for a, b in sorted(points, key=lambda x: x[1]): |
| 80 | + if a > last: |
| 81 | + ans += 1 |
| 82 | + last = b |
| 83 | + return ans |
| 84 | +``` |
| 85 | + |
| 86 | +#### Java |
| 87 | + |
| 88 | +```java |
| 89 | +class Solution { |
| 90 | + public int findMinArrowShots(int[][] points) { |
| 91 | + // 直接 a[1] - b[1] 可能会溢出 |
| 92 | + Arrays.sort(points, Comparator.comparingInt(a -> a[1])); |
| 93 | + int ans = 0; |
| 94 | + long last = -(1L << 60); |
| 95 | + for (var p : points) { |
| 96 | + int a = p[0], b = p[1]; |
| 97 | + if (a > last) { |
| 98 | + ++ans; |
| 99 | + last = b; |
| 100 | + } |
| 101 | + } |
| 102 | + return ans; |
| 103 | + } |
| 104 | +} |
| 105 | +``` |
| 106 | + |
| 107 | +#### C++ |
| 108 | + |
| 109 | +```cpp |
| 110 | +class Solution { |
| 111 | +public: |
| 112 | + int findMinArrowShots(vector<vector<int>>& points) { |
| 113 | + sort(points.begin(), points.end(), [](vector<int>& a, vector<int>& b) { |
| 114 | + return a[1] < b[1]; |
| 115 | + }); |
| 116 | + int ans = 0; |
| 117 | + long long last = -(1LL << 60); |
| 118 | + for (auto& p : points) { |
| 119 | + int a = p[0], b = p[1]; |
| 120 | + if (a > last) { |
| 121 | + ++ans; |
| 122 | + last = b; |
| 123 | + } |
| 124 | + } |
| 125 | + return ans; |
| 126 | + } |
| 127 | +}; |
| 128 | +``` |
| 129 | +
|
| 130 | +
|
| 131 | +<!-- tabs:end --> |
| 132 | +
|
| 133 | +<!-- solution:end --> |
| 134 | +
|
| 135 | +<!-- problem:end --> |
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