rectangle-overlap

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Algorithms

An axis-aligned rectangle is represented as a list <code>[x1, y1, x2, y2]</code>, where <code>(x1, y1)</code> is the coordinate of its bottom-left corner, and <code>(x2, y2)</code> is the coordinate of its top-right corner. Its top and bottom edges are parallel to the X-axis, and its left and right edges are parallel to the Y-axis.

Two rectangles overlap if the area of their intersection is positive. To be clear, two rectangles that only touch at the corner or edges do not overlap.

Given two axis-aligned rectangles <code>rec1</code> and <code>rec2</code>, return <code>true</code> if they overlap, otherwise return <code>false</code>.

&nbsp;
Example 1:

<div class="example-block">
Input: rec1 = [0,0,2,2], rec2 = [1,1,3,3]

Output: true

Explanation:

The rectangles overlap in the region with corners at <code>(1,1)</code>, <code>(2,1)</code>, <code>(1,2)</code>, and <code>(2,2)</code>.

This region has positive area, so the rectangles overlap.
</div>

Example 2:

<div class="example-block">
Input: rec1 = [0,0,1,1], rec2 = [1,0,2,1]

Output: false

Explanation:

The rectangles share the vertical edge where <code>x = 1</code>, but they do not have any common interior region.

Since their intersection has zero area, the rectangles do not overlap.
</div>

Example 3:

<div class="example-block">
Input: rec1 = [0,0,1,1], rec2 = [2,2,3,3]

Output: false

Explanation:

The rectangles are completely separate. Rectangle <code>rec1</code> ends at <code>x = 1</code> and <code>y = 1</code>, while <code>rec2</code> starts at <code>x = 2</code> and <code>y = 2</code>.

Therefore, they have no common points and do not overlap.
</div>

&nbsp;
Constraints:

<ul>
	<li><code>rec1.length == 4</code></li>
	<li><code>rec2.length == 4</code></li>
	<li><code>-109 &lt;= rec1[i], rec2[i] &lt;= 109</code></li>
	<li><code>rec1</code> and <code>rec2</code> represent a valid rectangle with a non-zero area.</li>
</ul>

第 85 场周赛

weekly-contest-85

isRectangleOverlap

中级工程师

Rectangle Overlap

Rectangle Area

rectangle-area

矩形面积

Geometry

Math

矩形以列表 <code>[x1, y1, x2, y2]</code> 的形式表示，其中 <code>(x1, y1)</code> 为左下角的坐标，<code>(x2, y2)</code> 是右上角的坐标。矩形的上下边平行于 x 轴，左右边平行于 y 轴。

如果相交的面积为 正 ，则称两矩形重叠。需要明确的是，只在角或边接触的两个矩形不构成重叠。

给出两个矩形 <code>rec1</code> 和 <code>rec2</code> 。如果它们重叠，返回 <code>true</code>；否则，返回 <code>false</code> 。

&nbsp;

示例 1：

<div class="example-block">
输入： rec1 = [0,0,2,2], rec2 = [1,1,3,3]

输出： true

解释：

两个矩形在由 <code>(1,1)</code>、<code>(2,1)</code>、<code>(1,2)</code> 和 <code>(2,2)</code> 四个顶点围成的区域内重叠。

该区域的面积大于零，因此两个矩形重叠。
</div>

示例 2：

<div class="example-block">
输入： rec1 = [0,0,1,1], rec2 = [1,0,2,1]

输出： false

解释：

两个矩形共用 <code>x = 1</code> 处的竖直边，但它们没有任何公共的内部区域。

由于它们的交集面积为零，因此两个矩形不重叠。
</div>

示例 3：

<div class="example-block">
输入： rec1 = [0,0,1,1], rec2 = [2,2,3,3]

输出： false

解释：

两个矩形完全分离。矩形 <code>rec1</code> 在 <code>x = 1</code> 和 <code>y = 1</code> 处结束，而矩形 <code>rec2</code> 从 <code>x = 2</code> 和 <code>y = 2</code> 处开始。

因此，它们没有任何公共点，也就不存在重叠。
</div>
&nbsp;

提示：

<ul>
	<li><code>rec1.length == 4</code></li>
	<li><code>rec2.length == 4</code></li>
	<li><code>-109 &lt;= rec1[i], rec2[i] &lt;= 109</code></li>
	<li><code>rec1</code> 和 <code>rec2</code> 表示一个面积不为零的有效矩形</li>
</ul>