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g0301_0400.s0391_perfect_rectangle.readme.md Maven / Gradle / Ivy

391\. Perfect Rectangle

Hard

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