<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:
    //面积之和等于大面积，四个顶点是一次，其他都是两次或者4次;
    bool isRectangleCover(vector<vector<int>>& rectangles) {
        unordered_map<string,int> cnt;
        long area = 0;
        int minx = INT_MAX, maxx=INT_MIN,miny=INT_MAX,maxy=INT_MIN;

        auto getKey = [](int x, int y){
            return to_string(x)+"_"+to_string(y);
        };

        auto inc = [&](int x, int y){
            cnt[getKey(x,y)]++;
        };

        auto getCnt = [&](int x, int y){
            return cnt[getKey(x,y)];
        };

        for(auto& p : rectangles){
            minx = min(minx, p[0]);
            maxx = max(maxx, p[2]);
            miny = min(miny, p[1]);
            maxy = max(maxy, p[3]);

            inc(p[0],p[1]);
            inc(p[2],p[3]);
            inc(p[0],p[3]);
            inc(p[2],p[1]);

            area += 1LL*(p[2]-p[0])*(p[3]-p[1]);
        }

        long bigArea = 1LL*(maxy-miny)*(maxx-minx);

        if (bigArea != area){
            return false;
        }

        if (getCnt(minx,miny)!=1||getCnt(minx,maxy)!=1||getCnt(maxx,miny)!=1||getCnt(maxx, maxy)!=1){
            return false;
        }

        cnt.erase(getKey(minx,miny));
        cnt.erase(getKey(minx,maxy));
        cnt.erase(getKey(maxx,miny));
        cnt.erase(getKey(maxx,maxy));

        for(auto& [_,v] : cnt){
            if(v!=2&&v!=4){
                return false;
            }
        }

        return true;
    }
};
43000