<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 SegTreeNode
{
    public:
    SegTreeNode* left = NULL;
    SegTreeNode* right = NULL;
    int start, end;
    int info;  // the maximum value of the range
    bool tag; 
        
    SegTreeNode(int a, int b, int val) { // init for range [a,b] with val                 
        tag = 0;
        start = a, end = b;
        if (a == b) {
            info = val;
            return;
        }        
        int mid = (a+b)/2;
        if (left == NULL) {
            left = new SegTreeNode(a, mid, val);
            right = new SegTreeNode(mid+1, b, val);            
            info = max(left->info, right->info);  // check with your own logic
        }        
    }    
    
    void pushDown() {
        if (tag == 1 && left) {
            left->info = info;
            right->info = info;
            left->tag = 1;
            right->tag = 1;
            tag = 0;
        }        
    } 
    
    void updateRange(int a, int b, int val)     // set range [a,b] with val
    {        
        if (b < start || a > end ) // not covered by [a,b] at all
            return;        
        if (a <= start && end <=b) { // completely covered within [a,b]
            info = val;
            tag = 1;
            return;
        }

        if (left) {
            pushDown();        
            left->updateRange(a, b, val);
            right->updateRange(a, b, val);
            info = max(left->info, right->info);  // write your own logic            
        }        
    }

};

class Solution {    
    vector<pair<int, int>> heights; // {idx, h}
public:
    vector<vector<int>> getSkyline(vector<vector<int>>& buildings) {
        set<int> Set;
        for (auto & building : buildings) {
            Set.insert(building[0]);
            Set.insert(building[1]);
        }
        int id = 0;
        unordered_map<int,int> pos2idx;
        unordered_map<int,int> idx2pos;
        for (auto x : Set) {
            pos2idx[x] = id;
            idx2pos[id] = x;
            ++id;
        }
        
        int n = pos2idx.size();
        SegTreeNode* root = new SegTreeNode(0, n-1, 0);        
        
        sort(buildings.begin(), buildings.end(), [](vector<int> &a, vector<int> &b) {
            return a[2]<b[2];
        });
        
        for (auto & building: buildings)
            root->updateRange(pos2idx[building[0]], pos2idx[building[1]]-1, building[2]); 
        
        DFS(root);
                
        vector<vector<int>> res;
        for (int i = 0; i < heights.size(); i++) {
            auto [idx, h] = heights[i];
            res.push_back({idx2pos[idx], h});
            while (i+1 < heights.size() && heights[i+1].second == heights[i].second)
                i++;
        }
        return res;
    }
    
    void DFS(SegTreeNode* node) {
        if (node->start == node->end || node->tag == 1) {
            heights.push_back({node->start, node->info});
            return;
        }
        DFS(node->left);
        DFS(node->right);
    }
};
28664