Perfect Rectangle
<p>Given an array <code>rectangles</code> where <code>rectangles[i] = [x<sub>i</sub>, y<sub>i</sub>, a<sub>i</sub>, b<sub>i</sub>]</code> represents an axis-aligned rectangle. The bottom-left point of the rectangle is <code>(x<sub>i</sub>, y<sub>i</sub>)</code> and the top-right point of it is <code>(a<sub>i</sub>, b<sub>i</sub>)</code>.</p>

<p>Return <code>true</code> <em>if all the rectangles together form an exact cover of a rectangular region</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0300-0399/0391.Perfect%20Rectangle/images/perectrec1-plane.jpg" style="width: 300px; height: 294px;" />
<pre>
<strong>Input:</strong> rectangles = [[1,1,3,3],[3,1,4,2],[3,2,4,4],[1,3,2,4],[2,3,3,4]]
<strong>Output:</strong> true
<strong>Explanation:</strong> All 5 rectangles together form an exact cover of a rectangular region.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0300-0399/0391.Perfect%20Rectangle/images/perfectrec2-plane.jpg" style="width: 300px; height: 294px;" />
<pre>
<strong>Input:</strong> rectangles = [[1,1,2,3],[1,3,2,4],[3,1,4,2],[3,2,4,4]]
<strong>Output:</strong> false
<strong>Explanation:</strong> Because there is a gap between the two rectangular regions.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0300-0399/0391.Perfect%20Rectangle/images/perfecrrec4-plane.jpg" style="width: 300px; height: 294px;" />
<pre>
<strong>Input:</strong> rectangles = [[1,1,3,3],[3,1,4,2],[1,3,2,4],[2,2,4,4]]
<strong>Output:</strong> false
<strong>Explanation:</strong> Because two of the rectangles overlap with each other.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= rectangles.length &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>rectangles[i].length == 4</code></li>
	<li><code>-10<sup>5</sup> &lt;= x<sub>i</sub> &lt; a<sub>i</sub> &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>5</sup> &lt;= y<sub>i</sub> &lt; b<sub>i</sub> &lt;= 10<sup>5</sup></code></li>
</ul>
Geometry; Array; Hash Table; Math; Line Sweep
type pair struct {
	first  int
	second int
}

func isRectangleCover(rectangles [][]int) bool {
	area := 0
	minX, minY := rectangles[0][0], rectangles[0][1]
	maxX, maxY := rectangles[0][2], rectangles[0][3]

	cnt := make(map[pair]int)
	for _, r := range rectangles {
		area += (r[2] - r[0]) * (r[3] - r[1])

		minX = min(minX, r[0])
		minY = min(minY, r[1])
		maxX = max(maxX, r[2])
		maxY = max(maxY, r[3])

		cnt[pair{r[0], r[1]}]++
		cnt[pair{r[0], r[3]}]++
		cnt[pair{r[2], r[3]}]++
		cnt[pair{r[2], r[1]}]++
	}

	if area != (maxX-minX)*(maxY-minY) ||
		cnt[pair{minX, minY}] != 1 ||
		cnt[pair{minX, maxY}] != 1 ||
		cnt[pair{maxX, maxY}] != 1 ||
		cnt[pair{maxX, minY}] != 1 {
		return false
	}

	delete(cnt, pair{minX, minY})
	delete(cnt, pair{minX, maxY})
	delete(cnt, pair{maxX, maxY})
	delete(cnt, pair{maxX, minY})

	for _, c := range cnt {
		if c != 2 && c != 4 {
			return false
		}
	}
	return true
}