<p>A city&#39;s <strong>skyline</strong> is the outer contour of the silhouette formed by all the buildings in that city when viewed from a distance. Given the locations and heights of all the buildings, return <em>the <strong>skyline</strong> formed by these buildings collectively</em>.</p>

<p>The geometric information of each building is given in the array <code>buildings</code> where <code>buildings[i] = [left<sub>i</sub>, right<sub>i</sub>, height<sub>i</sub>]</code>:</p>

<ul>
	<li><code>left<sub>i</sub></code> is the x coordinate of the left edge of the <code>i<sup>th</sup></code> building.</li>
	<li><code>right<sub>i</sub></code> is the x coordinate of the right edge of the <code>i<sup>th</sup></code> building.</li>
	<li><code>height<sub>i</sub></code> is the height of the <code>i<sup>th</sup></code> building.</li>
</ul>

<p>You may assume all buildings are perfect rectangles grounded on an absolutely flat surface at height <code>0</code>.</p>

<p>The <strong>skyline</strong> should be represented as a list of &quot;key points&quot; <strong>sorted by their x-coordinate</strong> in the form <code>[[x<sub>1</sub>,y<sub>1</sub>],[x<sub>2</sub>,y<sub>2</sub>],...]</code>. Each key point is the left endpoint of some horizontal segment in the skyline except the last point in the list, which always has a y-coordinate <code>0</code> and is used to mark the skyline&#39;s termination where the rightmost building ends. Any ground between the leftmost and rightmost buildings should be part of the skyline&#39;s contour.</p>

<p><b>Note:</b> There must be no consecutive horizontal lines of equal height in the output skyline. For instance, <code>[...,[2 3],[4 5],[7 5],[11 5],[12 7],...]</code> is not acceptable; the three lines of height 5 should be merged into one in the final output as such: <code>[...,[2 3],[4 5],[12 7],...]</code></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/12/01/merged.jpg" style="width: 800px; height: 331px;" />
<pre>
<strong>Input:</strong> buildings = [[2,9,10],[3,7,15],[5,12,12],[15,20,10],[19,24,8]]
<strong>Output:</strong> [[2,10],[3,15],[7,12],[12,0],[15,10],[20,8],[24,0]]
<strong>Explanation:</strong>
Figure A shows the buildings of the input.
Figure B shows the skyline formed by those buildings. The red points in figure B represent the key points in the output list.
</pre>

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

<pre>
<strong>Input:</strong> buildings = [[0,2,3],[2,5,3]]
<strong>Output:</strong> [[0,3],[5,0]]
</pre>

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

<ul>
	<li><code>1 &lt;= buildings.length &lt;= 10<sup>4</sup></code></li>
	<li><code>0 &lt;= left<sub>i</sub> &lt; right<sub>i</sub> &lt;= 2<sup>31</sup> - 1</code></li>
	<li><code>1 &lt;= height<sub>i</sub> &lt;= 2<sup>31</sup> - 1</code></li>
	<li><code>buildings</code> is sorted by <code>left<sub>i</sub></code> in&nbsp;non-decreasing order.</li>
</ul>

class Solution {
public:
    void update(vector<int>& tree,int n,int pos,int val){
        pos+=n;
        tree[pos]=val;
        pos/=2;
        while(pos){
            tree[pos]=max(tree[pos*2],tree[pos*2+1]);
            pos/=2;
        }
    }
    int querry(vector<int>& tree){
        return tree[1];
    }
    struct Compare {
        bool operator()(const tuple<int,int,int>& a, const tuple<int,int,int>& b) {
            if(get<0>(a)==get<0>(b)){
                return get<2>(a)>get<2>(b);
            }else{
                return get<0>(a)>get<0>(b);
            }
        }
    };
    vector<vector<int>> getSkyline(vector<vector<int>>& b) {
        sort(b.begin(),b.end(),[](const vector<int>& l,const vector<int>& r){
            if(l[0]==r[0]){
                return l[2]>r[2];
            }else{
                return l[0]<r[0];
            }
        });
        priority_queue<tuple<int,int,int>,vector<tuple<int,int,int>>,Compare> q;
        int n=16384;
        vector<int> tree(2*n,0);
        vector<vector<int>> res;

        for(int i=0;i<b.size();i++){
            int cx=b[i][0];
            while(!q.empty()&&get<0>(q.top())<cx){
                int j=get<1>(q.top());
                update(tree,n,j,0);
                int h=querry(tree);
                if(b[j][2]>h){
                  //  cout<<get<0>(q.top())<<" "<<b[j][2]<<" "<<h<<'\n';
                    res.push_back({get<0>(q.top()),h});
                }
                q.pop();
            }
            int mh=querry(tree);
            if(b[i][2]>mh){
                res.push_back({b[i][0],b[i][2]});
            }
            update(tree,n,i,b[i][2]);
            q.push({b[i][1],i,b[i][2]});
        }
        while(!q.empty()){
            int j=get<1>(q.top());
            update(tree,n,j,0);
            int h=querry(tree);
            if(b[j][2]>h){
               // cout<<get<0>(q.top())<<" "<<b[j][2]<<" "<<h<<'\n';
                res.push_back({get<0>(q.top()),h});
            }
            q.pop();
        }
        return res;
    }
};
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