<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://assets.leetcode.com/uploads/2021/03/27/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://assets.leetcode.com/uploads/2021/03/27/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://assets.leetcode.com/uploads/2021/03/27/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>

class Solution {
public:
    bool isRectangleCover(vector<vector<int>>& rectangles) {
        if(rectangles.size() == 1)
            return true;
        int mostLEFT = INT_MAX, mostBOTTOM = INT_MAX;
        int mostRIGHT = INT_MIN, mostTOP = INT_MIN;
        unordered_set<string> vertexSet;
        int sum_area = 0;
        
        for (const auto& rect : rectangles) {
            int x1 = rect[0], y1 = rect[1];
            int x2 = rect[2], y2 = rect[3];
            
            mostLEFT = min(mostLEFT, x1);
            mostBOTTOM = min(mostBOTTOM, y1);
            mostRIGHT = max(mostRIGHT, x2);
            mostTOP = max(mostTOP, y2);
            
            sum_area += (x2 - x1) * (y2 - y1);
            
            vector<string> vertices = {
                to_string(x1) + "_" + to_string(y1),
                to_string(x1) + "_" + to_string(y2),
                to_string(x2) + "_" + to_string(y1),
                to_string(x2) + "_" + to_string(y2)
            };
            
            for (const auto& vertex : vertices) {
                if (vertexSet.count(vertex)) {
                    vertexSet.erase(vertex);
                } else {
                    vertexSet.insert(vertex);
                }
            }
        }
        
        if (vertexSet.size() != 4 ||
            !vertexSet.count(to_string(mostLEFT) + "_" + to_string(mostBOTTOM)) ||
            !vertexSet.count(to_string(mostLEFT) + "_" + to_string(mostTOP)) ||
            !vertexSet.count(to_string(mostRIGHT) + "_" + to_string(mostBOTTOM)) ||
            !vertexSet.count(to_string(mostRIGHT) + "_" + to_string(mostTOP))) {
            return false;
        }
        
        return sum_area == (mostRIGHT - mostLEFT) * (mostTOP - mostBOTTOM);
    }
};

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