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‎solution/2000-2099/2015.Average Height of Buildings in Each Segment/README.md

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# [2015. Average Height of Buildings in Each Segment](https://leetcode-cn.com/problems/average-height-of-buildings-in-each-segment)
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[English Version](/solution/2000-2099/2015.Average%20Height%20of%20Buildings%20in%20Each%20Segment/README_EN.md)
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## 题目描述
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<!-- 这里写题目描述 -->
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<p>A perfectly straight street is represented by a number line. The street has building(s) on it and is represented by a 2D integer array <code>buildings</code>, where <code>buildings[i] = [start<sub>i</sub>, end<sub>i</sub>, height<sub>i</sub>]</code>. This means that there is a building with <code>height<sub>i</sub></code> in the <strong>half-closed segment</strong> <code>[start<sub>i</sub>, end<sub>i</sub>)</code>.</p>
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<p>You want to <strong>describe</strong> the heights of the buildings on the street with the <strong>minimum</strong> number of non-overlapping <strong>segments</strong>. The street can be represented by the 2D integer array <code>street</code> where <code>street[j] = [left<sub>j</sub>, right<sub>j</sub>, average<sub>j</sub>]</code> describes a <strong>half-closed segment</strong> <code>[left<sub>j</sub>, right<sub>j</sub>)</code> of the road where the <strong>average</strong> heights of the buildings in the<strong> segment</strong> is <code>average<sub>j</sub></code>.</p>
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<ul>
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<li>For example, if <code>buildings = [[1,5,2],[3,10,4]],</code> the street could be represented by <code>street = [[1,3,2],[3,5,3],[5,10,4]]</code> because:
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<ul>
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<li>From 1 to 3, there is only the first building with an average height of <code>2 / 1 = 2</code>.</li>
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<li>From 3 to 5, both the first and the second building are there with an average height of <code>(2+4) / 2 = 3</code>.</li>
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<li>From 5 to 10, there is only the second building with an average height of <code>4 / 1 = 4</code>.</li>
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</ul>
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</li>
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</ul>
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<p>Given <code>buildings</code>, return <em>the 2D integer array </em><code>street</code><em> as described above (<strong>excluding</strong> any areas of the street where there are no buldings). You may return the array in <strong>any order</strong></em>.</p>
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<p>The <strong>average</strong> of <code>n</code> elements is the <strong>sum</strong> of the <code>n</code> elements divided (<strong>integer division</strong>) by <code>n</code>.</p>
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<p>A <strong>half-closed segment</strong> <code>[a, b)</code> is the section of the number line between points <code>a</code> and <code>b</code> <strong>including</strong> point <code>a</code> and <strong>not including</strong> point <code>b</code>.</p>
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<p>&nbsp;</p>
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<p><strong>Example 1:</strong></p>
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<img src="https://cdn.jsdelivr.net/gh/doocs/leetcode@main/solution/2000-2099/2015.Average%20Height%20of%20Buildings%20in%20Each%20Segment/images/image-20210921224001-2.png" style="width: 500px; height: 349px;" />
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<pre>
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<strong>Input:</strong> buildings = [[1,5,2],[3,10,4]]
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<strong>Output:</strong> [[1,3,2],[3,5,3],[5,10,4]]
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<strong>Explanation:</strong>
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From 1 to 3, there is only the first building with an average height of 2 / 1 = 2.
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From 3 to 5, both the first and the second building are there with an average height of (2+4) / 2 = 3.
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From 5 to 10, there is only the second building with an average height of 4 / 1 = 4.
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> buildings = [[1,3,2],[2,5,3],[2,8,3]]
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<strong>Output:</strong> [[1,3,2],[3,8,3]]
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<strong>Explanation:</strong>
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From 1 to 2, there is only the first building with an average height of 2 / 1 = 2.
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From 2 to 3, all three buildings are there with an average height of (2+3+3) / 3 = 2.
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From 3 to 5, both the second and the third building are there with an average height of (3+3) / 2 = 3.
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From 5 to 8, there is only the last building with an average height of 3 / 1 = 3.
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The average height from 1 to 3 is the same so we can group them into one segment.
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The average height from 3 to 8 is the same so we can group them into one segment.
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</pre>
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<p><strong>Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> buildings = [[1,2,1],[5,6,1]]
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<strong>Output:</strong> [[1,2,1],[5,6,1]]
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<strong>Explanation:</strong>
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From 1 to 2, there is only the first building with an average height of 1 / 1 = 1.
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From 2 to 5, there are no buildings, so it is not included in the output.
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From 5 to 6, there is only the second building with an average height of 1 / 1 = 1.
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We cannot group the segments together because an empty space with no buildings seperates the segments.
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</pre>
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<p>&nbsp;</p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 &lt;= buildings.length &lt;= 10<sup>5</sup></code></li>
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<li><code>buildings[i].length == 3</code></li>
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<li><code>0 &lt;= start<sub>i</sub> &lt; end<sub>i</sub> &lt;= 10<sup>8</sup></code></li>
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<li><code>1 &lt;= height<sub>i</sub> &lt;= 10<sup>5</sup></code></li>
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</ul>
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## 解法
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<!-- 这里可写通用的实现逻辑 -->
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<!-- tabs:start -->
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### **Python3**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```python
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```
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### **Java**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```java
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```
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### **...**
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```
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```
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<!-- tabs:end -->

‎solution/2000-2099/2015.Average Height of Buildings in Each Segment/README_EN.md

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# [2015. Average Height of Buildings in Each Segment](https://leetcode.com/problems/average-height-of-buildings-in-each-segment)
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[中文文档](/solution/2000-2099/2015.Average%20Height%20of%20Buildings%20in%20Each%20Segment/README.md)
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## Description
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<p>A perfectly straight street is represented by a number line. The street has building(s) on it and is represented by a 2D integer array <code>buildings</code>, where <code>buildings[i] = [start<sub>i</sub>, end<sub>i</sub>, height<sub>i</sub>]</code>. This means that there is a building with <code>height<sub>i</sub></code> in the <strong>half-closed segment</strong> <code>[start<sub>i</sub>, end<sub>i</sub>)</code>.</p>
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<p>You want to <strong>describe</strong> the heights of the buildings on the street with the <strong>minimum</strong> number of non-overlapping <strong>segments</strong>. The street can be represented by the 2D integer array <code>street</code> where <code>street[j] = [left<sub>j</sub>, right<sub>j</sub>, average<sub>j</sub>]</code> describes a <strong>half-closed segment</strong> <code>[left<sub>j</sub>, right<sub>j</sub>)</code> of the road where the <strong>average</strong> heights of the buildings in the<strong> segment</strong> is <code>average<sub>j</sub></code>.</p>
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<ul>
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<li>For example, if <code>buildings = [[1,5,2],[3,10,4]],</code> the street could be represented by <code>street = [[1,3,2],[3,5,3],[5,10,4]]</code> because:
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<ul>
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<li>From 1 to 3, there is only the first building with an average height of <code>2 / 1 = 2</code>.</li>
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<li>From 3 to 5, both the first and the second building are there with an average height of <code>(2+4) / 2 = 3</code>.</li>
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<li>From 5 to 10, there is only the second building with an average height of <code>4 / 1 = 4</code>.</li>
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</ul>
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</li>
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</ul>
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<p>Given <code>buildings</code>, return <em>the 2D integer array </em><code>street</code><em> as described above (<strong>excluding</strong> any areas of the street where there are no buldings). You may return the array in <strong>any order</strong></em>.</p>
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<p>The <strong>average</strong> of <code>n</code> elements is the <strong>sum</strong> of the <code>n</code> elements divided (<strong>integer division</strong>) by <code>n</code>.</p>
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<p>A <strong>half-closed segment</strong> <code>[a, b)</code> is the section of the number line between points <code>a</code> and <code>b</code> <strong>including</strong> point <code>a</code> and <strong>not including</strong> point <code>b</code>.</p>
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<p>&nbsp;</p>
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<p><strong>Example 1:</strong></p>
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<img src="https://cdn.jsdelivr.net/gh/doocs/leetcode@main/solution/2000-2099/2015.Average%20Height%20of%20Buildings%20in%20Each%20Segment/images/image-20210921224001-2.png" style="width: 500px; height: 349px;" />
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<pre>
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<strong>Input:</strong> buildings = [[1,5,2],[3,10,4]]
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<strong>Output:</strong> [[1,3,2],[3,5,3],[5,10,4]]
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<strong>Explanation:</strong>
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From 1 to 3, there is only the first building with an average height of 2 / 1 = 2.
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From 3 to 5, both the first and the second building are there with an average height of (2+4) / 2 = 3.
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From 5 to 10, there is only the second building with an average height of 4 / 1 = 4.
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> buildings = [[1,3,2],[2,5,3],[2,8,3]]
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<strong>Output:</strong> [[1,3,2],[3,8,3]]
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<strong>Explanation:</strong>
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From 1 to 2, there is only the first building with an average height of 2 / 1 = 2.
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From 2 to 3, all three buildings are there with an average height of (2+3+3) / 3 = 2.
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From 3 to 5, both the second and the third building are there with an average height of (3+3) / 2 = 3.
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From 5 to 8, there is only the last building with an average height of 3 / 1 = 3.
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The average height from 1 to 3 is the same so we can group them into one segment.
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The average height from 3 to 8 is the same so we can group them into one segment.
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</pre>
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<p><strong>Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> buildings = [[1,2,1],[5,6,1]]
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<strong>Output:</strong> [[1,2,1],[5,6,1]]
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<strong>Explanation:</strong>
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From 1 to 2, there is only the first building with an average height of 1 / 1 = 1.
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From 2 to 5, there are no buildings, so it is not included in the output.
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From 5 to 6, there is only the second building with an average height of 1 / 1 = 1.
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We cannot group the segments together because an empty space with no buildings seperates the segments.
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</pre>
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<p>&nbsp;</p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 &lt;= buildings.length &lt;= 10<sup>5</sup></code></li>
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<li><code>buildings[i].length == 3</code></li>
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<li><code>0 &lt;= start<sub>i</sub> &lt; end<sub>i</sub> &lt;= 10<sup>8</sup></code></li>
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<li><code>1 &lt;= height<sub>i</sub> &lt;= 10<sup>5</sup></code></li>
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</ul>
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## Solutions
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<!-- tabs:start -->
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### **Python3**
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```python
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```
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### **Java**
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```java
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```
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### **...**
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```
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```
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<!-- tabs:end -->

‎solution/2000-2099/2015.Average Height of Buildings in Each Segment/images/image-20210921224001-2.png

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‎solution/2000-2099/2016.Maximum Difference Between Increasing Elements/README.md

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# [2016. 增量元素之间的最大差值](https://leetcode-cn.com/problems/maximum-difference-between-increasing-elements)
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[English Version](/solution/2000-2099/2016.Maximum%20Difference%20Between%20Increasing%20Elements/README_EN.md)
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## 题目描述
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<!-- 这里写题目描述 -->
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<p>给你一个下标从 <strong>0</strong> 开始的整数数组 <code>nums</code> ，该数组的大小为 <code>n</code> ，请你计算 <code>nums[j] - nums[i]</code> 能求得的 <strong>最大差值 </strong>，其中 <code>0 &lt;= i &lt; j &lt; n</code> 且 <code>nums[i] &lt; nums[j]</code> 。</p>
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<p>返回 <strong>最大差值</strong> 。如果不存在满足要求的 <code>i</code> 和 <code>j</code> ，返回 <code>-1</code> 。</p>
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<p>&nbsp;</p>
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<p><strong>示例 1：</strong></p>
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<pre><strong>输入：</strong>nums = [7,<em><strong>1</strong></em>,<em><strong>5</strong></em>,4]
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<strong>输出：</strong>4
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<strong>解释：</strong>
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最大差值出现在 i = 1 且 j = 2 时，nums[j] - nums[i] = 5 - 1 = 4 。
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注意，尽管 i = 1 且 j = 0 时 ，nums[j] - nums[i] = 7 - 1 = 6 &gt; 4 ，但 i &gt; j 不满足题面要求，所以 6 不是有效的答案。
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</pre>
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<p><strong>示例 2：</strong></p>
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<pre><strong>输入：</strong>nums = [9,4,3,2]
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<strong>输出：</strong>-1
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<strong>解释：</strong>
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不存在同时满足 i &lt; j 和 nums[i] &lt; nums[j] 这两个条件的 i, j 组合。
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</pre>
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<p><strong>示例 3：</strong></p>
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<pre><strong>输入：</strong>nums = [<em><strong>1</strong></em>,5,2,<em><strong>10</strong></em>]
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<strong>输出：</strong>9
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<strong>解释：</strong>
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最大差值出现在 i = 0 且 j = 3 时，nums[j] - nums[i] = 10 - 1 = 9 。
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</pre>
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<p>&nbsp;</p>
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<p><strong>提示：</strong></p>
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<ul>
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<li><code>n == nums.length</code></li>
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<li><code>2 &lt;= n &lt;= 1000</code></li>
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<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
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</ul>
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## 解法
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<!-- 这里可写通用的实现逻辑 -->
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<!-- tabs:start -->
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### **Python3**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```python
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```
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### **Java**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```java
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```
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### **...**
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```
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```
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<!-- tabs:end -->

‎solution/2000-2099/2016.Maximum Difference Between Increasing Elements/README_EN.md

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# [2016. Maximum Difference Between Increasing Elements](https://leetcode.com/problems/maximum-difference-between-increasing-elements)
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[中文文档](/solution/2000-2099/2016.Maximum%20Difference%20Between%20Increasing%20Elements/README.md)
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## Description
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<p>Given a <strong>0-indexed</strong> integer array <code>nums</code> of size <code>n</code>, find the <strong>maximum difference</strong> between <code>nums[i]</code> and <code>nums[j]</code> (i.e., <code>nums[j] - nums[i]</code>), such that <code>0 &lt;= i &lt; j &lt; n</code> and <code>nums[i] &lt; nums[j]</code>.</p>
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<p>Return <em>the <strong>maximum difference</strong>. </em>If no such <code>i</code> and <code>j</code> exists, return <code>-1</code>.</p>
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<p>&nbsp;</p>
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<p><strong>Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [7,<strong><u>1</u></strong>,<strong><u>5</u></strong>,4]
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<strong>Output:</strong> 4
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<strong>Explanation:</strong>
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The maximum difference occurs with i = 1 and j = 2, nums[j] - nums[i] = 5 - 1 = 4.
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Note that with i = 1 and j = 0, the difference nums[j] - nums[i] = 7 - 1 = 6, but i &gt; j, so it is not valid.
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [9,4,3,2]
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<strong>Output:</strong> -1
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<strong>Explanation:</strong>
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There is no i and j such that i &lt; j and nums[i] &lt; nums[j].
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</pre>
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<p><strong>Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [<strong><u>1</u></strong>,5,2,<strong><u>10</u></strong>]
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<strong>Output:</strong> 9
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<strong>Explanation:</strong>
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The maximum difference occurs with i = 0 and j = 3, nums[j] - nums[i] = 10 - 1 = 9.
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</pre>
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<p>&nbsp;</p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>n == nums.length</code></li>
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<li><code>2 &lt;= n &lt;= 1000</code></li>
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<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
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</ul>
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## Solutions
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<!-- tabs:start -->
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### **Python3**
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```python
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```
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### **Java**
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```java
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```
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### **...**
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```
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```
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<!-- tabs:end -->

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