<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>>& rectangle) {
        int minr=1e9,minc=1e9,maxr=0,maxc=0;
        set<pair<int,int>>set1;
        for(auto v:rectangle){
            minc=min(minc,v[0]);
            minr=min(minr,v[1]);
            maxc=max(maxc,v[2]);
            maxr=max(maxr,v[3]);
            vector<pair<int,int>>vv;
            vv.push_back({v[0],v[1]});
            vv.push_back({v[0],v[3]});
            vv.push_back({v[2],v[1]});
            vv.push_back({v[2],v[3]});
            for(auto p:vv){
                if(set1.count(p))set1.erase(p);
                else set1.insert(p);
            }
        }
        long long area=(long long)(maxr-minr)*(maxc-minc);
        long long cnt=0;
        for(auto v:rectangle){
            cnt+=(long long)(v[2]-v[0])*(v[3]-v[1]);
        }
        set<pair<int,int>>set2;
        set2.insert({minc,minr});
        set2.insert({maxc,minr});
        set2.insert({minc,maxr});
        set2.insert({maxc,maxr});
        if(cnt==area && set1==set2){
            return true;
        }
        return false;
    }

};
47000