# 0391. Perfect Rectangle

<https://leetcode.com/problems/perfect-rectangle>

## Description

Given an array `rectangles` where `rectangles[i] = [xi, yi, ai, bi]` represents an axis-aligned rectangle. The bottom-left point of the rectangle is `(xi, yi)` and the top-right point of it is `(ai, bi)`.

Return `true` *if all the rectangles together form an exact cover of a rectangular region*.

**Example 1:**

![](https://assets.leetcode.com/uploads/2021/03/27/perectrec1-plane.jpg)

```
**Input:** rectangles = [[1,1,3,3],[3,1,4,2],[3,2,4,4],[1,3,2,4],[2,3,3,4]]
**Output:** true
**Explanation:** All 5 rectangles together form an exact cover of a rectangular region.
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2021/03/27/perfectrec2-plane.jpg)

```
**Input:** rectangles = [[1,1,2,3],[1,3,2,4],[3,1,4,2],[3,2,4,4]]
**Output:** false
**Explanation:** Because there is a gap between the two rectangular regions.
```

**Example 3:**

![](https://assets.leetcode.com/uploads/2021/03/27/perfectrec3-plane.jpg)

```
**Input:** rectangles = [[1,1,3,3],[3,1,4,2],[1,3,2,4],[3,2,4,4]]
**Output:** false
**Explanation:** Because there is a gap in the top center.
```

**Example 4:**

![](https://assets.leetcode.com/uploads/2021/03/27/perfecrrec4-plane.jpg)

```
**Input:** rectangles = [[1,1,3,3],[3,1,4,2],[1,3,2,4],[2,2,4,4]]
**Output:** false
**Explanation:** Because two of the rectangles overlap with each other.
```

**Constraints:**

* `1 <= rectangles.length <= 2 * 104`
* `rectangles[i].length == 4`
* `-105 <= xi, yi, ai, bi <= 105`

## ac

```java
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://jaywin.gitbook.io/leetcode/solutions/0391-perfect-rectangle.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.