<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 Node
{
    public:
    long long int l, r, m, val;
    Node *left, *right;

    Node(long long int x, long long int y, long long int v)
    {
        l=x;
        r=y;
        m=l+(r-l)/2;
        val=v;
        left=right=nullptr;
    }

};

class Solution {
    Node *root;
    void build(Node *root, long long int l, long long int r, long long int v)
    {
        //In range
        if(root->l>=l && root->r<=r && !root->left)
        {
            root->val=max(v, root->val);
            return;
        }
        //Out of range
        if(l>root->r || r<root->l)
            return;
        if((root->r - root->l) < 2)
            return;
        //Overlap
        if(!root->left)
        {
            root->left=new Node(root->l, root->m, root->val);
            root->right=new Node(root->m, root->r, root->val);
        }

        build(root->left, l, r, v);
        build(root->right, l, r, v);
    }

    void sky(Node *root, vector<vector<long long int>> &s)
    {
        if(!root->left)
        {
            s.push_back({root->l, root->r, root->val});
            return;
        }
        sky(root->left, s);
        sky(root->right, s);
    }

    vector<vector<int>> skyline()
    {
        vector<vector<long long int>> s;
        vector<vector<int>>res;
        sky(this->root, s);

        for(int i=0; i<s.size(); i++)
        {
            if(res.empty() && s[i][2]==0)
                continue;
            else if(res.empty() || res.back()[1] != s[i][2])
                res.push_back({(int)s[i][0], (int)s[i][2]});
        }

        return res;
    }
public:
    vector<vector<int>> getSkyline(vector<vector<int>>& buildings) {
        this->root=new Node(0, pow(2, 31), 0);
        for(auto &b: buildings)
            build(this->root, b[0], b[1], b[2]);

        return skyline();
    }
};
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