maximum-area-of-a-piece-of-cake-after-horizontal-and-vertical-cuts

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Algorithms

You are given a rectangular cake of size <code>h x w</code> and two arrays of integers <code>horizontalCuts</code> and <code>verticalCuts</code> where:

<ul>
	<li><code>horizontalCuts[i]</code> is the distance from the top of the rectangular cake to the <code>ith</code> horizontal cut and similarly, and</li>
	<li><code>verticalCuts[j]</code> is the distance from the left of the rectangular cake to the <code>jth</code> vertical cut.</li>
</ul>

Return the maximum area of a piece of cake after you cut at each horizontal and vertical position provided in the arrays <code>horizontalCuts</code> and <code>verticalCuts</code>. Since the answer can be a large number, return this modulo <code>109 + 7</code>.

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2020/05/14/leetcode_max_area_2.png" style="width: 225px; height: 240px;" />
<pre>
Input: h = 5, w = 4, horizontalCuts = [1,2,4], verticalCuts = [1,3]
Output: 4 
Explanation: The figure above represents the given rectangular cake. Red lines are the horizontal and vertical cuts. After you cut the cake, the green piece of cake has the maximum area.
</pre>

Example 2:
<img alt="" src="https://assets.leetcode.com/uploads/2020/05/14/leetcode_max_area_3.png" style="width: 225px; height: 240px;" />
<pre>
Input: h = 5, w = 4, horizontalCuts = [3,1], verticalCuts = [1]
Output: 6
Explanation: The figure above represents the given rectangular cake. Red lines are the horizontal and vertical cuts. After you cut the cake, the green and yellow pieces of cake have the maximum area.
</pre>

Example 3:

<pre>
Input: h = 5, w = 4, horizontalCuts = [3], verticalCuts = [3]
Output: 9
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>2 &lt;= h, w &lt;= 109</code></li>
	<li><code>1 &lt;= horizontalCuts.length &lt;= min(h - 1, 105)</code></li>
	<li><code>1 &lt;= verticalCuts.length &lt;= min(w - 1, 105)</code></li>
	<li><code>1 &lt;= horizontalCuts[i] &lt; h</code></li>
	<li><code>1 &lt;= verticalCuts[i] &lt; w</code></li>
	<li>All the elements in <code>horizontalCuts</code> are distinct.</li>
	<li>All the elements in <code>verticalCuts</code> are distinct.</li>
</ul>

maxArea

Maximum Area of a Piece of Cake After Horizontal and Vertical Cuts

Greedy

Array

Sorting

矩形蛋糕的高度为 <code>h</code> 且宽度为 <code>w</code>，给你两个整数数组 <code>horizontalCuts</code> 和 <code>verticalCuts</code>，其中：

<ul>
	<li>&nbsp;<code>horizontalCuts[i]</code> 是从矩形蛋糕顶部到第&nbsp; <code>i</code> 个水平切口的距离</li>
	<li><code>verticalCuts[j]</code> 是从矩形蛋糕的左侧到第 <code>j</code> 个竖直切口的距离</li>
</ul>

请你按数组 <code>horizontalCuts</code> 和 <code>verticalCuts</code> 中提供的水平和竖直位置切割后，请你找出 面积最大 的那份蛋糕，并返回其 面积 。由于答案可能是一个很大的数字，因此需要将结果&nbsp;对&nbsp;<code>109&nbsp;+ 7</code>&nbsp;取余 后返回。

&nbsp;

示例 1：

<img alt="" src="https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/05/30/leetcode_max_area_2.png" />

<pre>
输入：h = 5, w = 4, horizontalCuts = [1,2,4], verticalCuts = [1,3]
输出：4 
解释：上图所示的矩阵蛋糕中，红色线表示水平和竖直方向上的切口。切割蛋糕后，绿色的那份蛋糕面积最大。
</pre>

示例 2：

<img alt="" src="https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/05/30/leetcode_max_area_3.png" />

<pre>
输入：h = 5, w = 4, horizontalCuts = [3,1], verticalCuts = [1]
输出：6
解释：上图所示的矩阵蛋糕中，红色线表示水平和竖直方向上的切口。切割蛋糕后，绿色和黄色的两份蛋糕面积最大。</pre>

示例 3：

<pre>
输入：h = 5, w = 4, horizontalCuts = [3], verticalCuts = [3]
输出：9
</pre>

&nbsp;

提示：

<ul>
	<li><code>2 &lt;= h, w &lt;= 109</code></li>
	<li><code>1 &lt;= horizontalCuts.length &lt;= min(h - 1, 105)</code></li>
	<li><code>1 &lt;= verticalCuts.length &lt;= min(w - 1, 105)</code></li>
	<li><code>1 &lt;= horizontalCuts[i] &lt; h</code></li>
	<li><code>1 &lt;= verticalCuts[i] &lt; w</code></li>
	<li>题目数据保证 <code>horizontalCuts</code> 中的所有元素各不相同</li>
	<li>题目数据保证 <code>verticalCuts</code>&nbsp;中的所有元素各不相同</li>
</ul>