<p>You are given a 2D array of axis-aligned <code>rectangles</code>. Each <code>rectangle[i] = [x<sub>i1</sub>, y<sub>i1</sub>, x<sub>i2</sub>, y<sub>i2</sub>]</code> denotes the <code>i<sup>th</sup></code> rectangle where <code>(x<sub>i1</sub>, y<sub>i1</sub>)</code> are the coordinates of the <strong>bottom-left corner</strong>, and <code>(x<sub>i2</sub>, y<sub>i2</sub>)</code> are the coordinates of the <strong>top-right corner</strong>.</p>

<p>Calculate the <strong>total area</strong> covered by all <code>rectangles</code> in the plane. Any area covered by two or more rectangles should only be counted <strong>once</strong>.</p>

<p>Return <em>the <strong>total area</strong></em>. Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/06/06/rectangle_area_ii_pic.png" style="width: 600px; height: 450px;" />
<pre>
<strong>Input:</strong> rectangles = [[0,0,2,2],[1,0,2,3],[1,0,3,1]]
<strong>Output:</strong> 6
<strong>Explanation:</strong> A total area of 6 is covered by all three rectangles, as illustrated in the picture.
From (1,1) to (2,2), the green and red rectangles overlap.
From (1,0) to (2,3), all three rectangles overlap.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> rectangles = [[0,0,1000000000,1000000000]]
<strong>Output:</strong> 49
<strong>Explanation:</strong> The answer is 10<sup>18</sup> modulo (10<sup>9</sup> + 7), which is 49.
</pre>

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

<ul>
	<li><code>1 &lt;= rectangles.length &lt;= 200</code></li>
	<li><code>rectanges[i].length == 4</code></li>
	<li><code>0 &lt;= x<sub>i1</sub>, y<sub>i1</sub>, x<sub>i2</sub>, y<sub>i2</sub> &lt;= 10<sup>9</sup></code></li>
	<li><code>x<sub>i1 &lt;= </sub>x<sub>i2</sub></code></li>
	<li><code>y<sub>i1 &lt;=</sub> y<sub>i2</sub></code></li>
</ul>

class Solution {
public:
    struct rectangle_t { int x1; int y1; int x2; int y2; };

    constexpr rectangle_t overlap(const rectangle_t& lhs, const rectangle_t& rhs) const {
        return {
            max(lhs.x1, rhs.x1), max(lhs.y1, rhs.y1),
            min(lhs.x2, rhs.x2), min(lhs.y2, rhs.y2),
        };
    }

    constexpr long area(const rectangle_t& rectangle) const {
        return (long)(rectangle.x2 - rectangle.x1) * (long)(rectangle.y2 - rectangle.y1);
    }

    constexpr bool empty(const rectangle_t& rectangle) const {
        return rectangle.x2 < rectangle.x1 || rectangle.y2 < rectangle.y1 || area(rectangle) == 0;
    }

    int rectangleArea(const vector<vector<int>>& rectangles) {
        queue<rectangle_t> q;
        for (const auto& rectangle : rectangles) {
            q.push({rectangle[0], rectangle[1], rectangle[2], rectangle[3]});
        }

        vector<rectangle_t> patches;
        while (!q.empty()) {
            auto top = q.front(); q.pop();

            bool overlaps = false;
            for (const auto& patch : patches) {
                if (const auto o = overlap(top, patch); !empty(o)) {
                    for (auto&& item : array{
                        /* right */rectangle_t{o.x2, top.y1, top.x2, top.y2},
                        /* up    */rectangle_t{top.x1, o.y2, top.x2, top.y2},
                        /* left  */rectangle_t{top.x1, top.y1, o.x1, top.y2},
                        /* bot   */rectangle_t{top.x1, top.y1, top.x2, o.y1},
                    }) {
                        if (!empty(item)) {
                            q.push(move(item));
                        }
                    }
                    overlaps = true;
                    break;
                }
            }
            if (!overlaps) {
                patches.push_back(move(top));
            }
        }

        long total = 0;
        for (const auto& patch : patches) {
            total += area(patch);
            total %= 1000000000 + 7;
        }
        return total;
    }
};
20000