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:

**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:

**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:

**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:

**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

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