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Description
tab: English
<p>A city's <strong>skyline</strong> is the outer contour of the silhouette formed by all the buildings in that city when viewed from a distance. Given the locations and heights of all the buildings, return <em>the <strong>skyline</strong> formed by these buildings collectively</em>.</p>
<p>The geometric information of each building is given in the array <code>buildings</code> where <code>buildings[i] = [left<sub>i</sub>, right<sub>i</sub>, height<sub>i</sub>]</code>:</p>
<ul>
<li><code>left<sub>i</sub></code> is the x coordinate of the left edge of the <code>i<sup>th</sup></code> building.</li>
<li><code>right<sub>i</sub></code> is the x coordinate of the right edge of the <code>i<sup>th</sup></code> building.</li>
<li><code>height<sub>i</sub></code> is the height of the <code>i<sup>th</sup></code> building.</li>
</ul>
<p>You may assume all buildings are perfect rectangles grounded on an absolutely flat surface at height <code>0</code>.</p>
<p>The <strong>skyline</strong> should be represented as a list of "key points" <strong>sorted by their x-coordinate</strong> in the form <code>[[x<sub>1</sub>,y<sub>1</sub>],[x<sub>2</sub>,y<sub>2</sub>],...]</code>. Each key point is the left endpoint of some horizontal segment in the skyline except the last point in the list, which always has a y-coordinate <code>0</code> and is used to mark the skyline's termination where the rightmost building ends. Any ground between the leftmost and rightmost buildings should be part of the skyline's contour.</p>
<p><b>Note:</b> There must be no consecutive horizontal lines of equal height in the output skyline. For instance, <code>[...,[2 3],[4 5],[7 5],[11 5],[12 7],...]</code> is not acceptable; the three lines of height 5 should be merged into one in the final output as such: <code>[...,[2 3],[4 5],[12 7],...]</code></p>
<p> </p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/12/01/merged.jpg" style="width: 800px; height: 331px;" />
<pre>
<strong>Input:</strong> buildings = [[2,9,10],[3,7,15],[5,12,12],[15,20,10],[19,24,8]]
<strong>Output:</strong> [[2,10],[3,15],[7,12],[12,0],[15,10],[20,8],[24,0]]
<strong>Explanation:</strong>
Figure A shows the buildings of the input.
Figure B shows the skyline formed by those buildings. The red points in figure B represent the key points in the output list.
</pre>
<p><strong class="example">Example 2:</strong></p>
<pre>
<strong>Input:</strong> buildings = [[0,2,3],[2,5,3]]
<strong>Output:</strong> [[0,3],[5,0]]
</pre>
<p> </p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>1 <= buildings.length <= 10<sup>4</sup></code></li>
<li><code>0 <= left<sub>i</sub> < right<sub>i</sub> <= 2<sup>31</sup> - 1</code></li>
<li><code>1 <= height<sub>i</sub> <= 2<sup>31</sup> - 1</code></li>
<li><code>buildings</code> is sorted by <code>left<sub>i</sub></code> in non-decreasing order.</li>
</ul>
---
[submissions](https://leetcode.com/problems/the-skyline-problem/submissions/) | [solutions](https://leetcode.com/problems/the-skyline-problem/solutions/)
tab: 中文
<p>城市的 <strong>天际线</strong> 是从远处观看该城市中所有建筑物形成的轮廓的外部轮廓。给你所有建筑物的位置和高度，请返回 <em>由这些建筑物形成的<strong> 天际线</strong></em> 。</p>
<p>每个建筑物的几何信息由数组 <code>buildings</code> 表示，其中三元组 <code>buildings[i] = [lefti, righti, heighti]</code> 表示：</p>
<ul>
<li><code>left<sub>i</sub></code> 是第 <code>i</code> 座建筑物左边缘的 <code>x</code> 坐标。</li>
<li><code>right<sub>i</sub></code> 是第 <code>i</code> 座建筑物右边缘的 <code>x</code> 坐标。</li>
<li><code>height<sub>i</sub></code> 是第 <code>i</code> 座建筑物的高度。</li>
</ul>
<p>你可以假设所有的建筑都是完美的长方形，在高度为 <code>0</code> 的绝对平坦的表面上。</p>
<p><strong>天际线</strong> 应该表示为由 “关键点” 组成的列表，格式 <code>[[x<sub>1</sub>,y<sub>1</sub>],[x<sub>2</sub>,y<sub>2</sub>],...]</code> ，并按 <strong>x 坐标 </strong>进行 <strong>排序</strong> 。<strong>关键点是水平线段的左端点</strong>。列表中最后一个点是最右侧建筑物的终点，<code>y</code> 坐标始终为 <code>0</code> ，仅用于标记天际线的终点。此外，任何两个相邻建筑物之间的地面都应被视为天际线轮廓的一部分。</p>
<p><strong>注意：</strong>输出天际线中不得有连续的相同高度的水平线。例如 <code>[...[2 3], [4 5], [7 5], [11 5], [12 7]...]</code> 是不正确的答案；三条高度为 5 的线应该在最终输出中合并为一个：<code>[...[2 3], [4 5], [12 7], ...]</code></p>
<p> </p>
<p><strong>示例 1：</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/12/01/merged.jpg" style="height: 331px; width: 800px;" />
<pre>
<strong>输入：</strong>buildings = [[2,9,10],[3,7,15],[5,12,12],[15,20,10],[19,24,8]]
<strong>输出：</strong>[[2,10],[3,15],[7,12],[12,0],[15,10],[20,8],[24,0]]
<strong>解释：</strong>
图 A<strong> </strong>显示输入的所有建筑物的位置和高度，
图 B 显示由这些建筑物形成的天际线。图 B 中的红点表示输出列表中的关键点。</pre>
<p><strong>示例 2：</strong></p>
<pre>
<strong>输入：</strong>buildings = [[0,2,3],[2,5,3]]
<strong>输出：</strong>[[0,3],[5,0]]
</pre>
<p> </p>
<p><strong>提示：</strong></p>
<ul>
<li><code>1 <= buildings.length <= 10<sup>4</sup></code></li>
<li><code>0 <= left<sub>i</sub> < right<sub>i</sub> <= 2<sup>31</sup> - 1</code></li>
<li><code>1 <= height<sub>i</sub> <= 2<sup>31</sup> - 1</code></li>
<li><code>buildings</code> 按 <code>left<sub>i</sub></code> 非递减排序</li>
</ul>
---
[提交记录](https://leetcode.cn/problems/the-skyline-problem/submissions/) | [题解](https://leetcode.cn/problems/the-skyline-problem/solution/)
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