<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:
    vector<vector<int>> getSkyline(vector<vector<int>>& buildings) {
        int n = buildings.size();

        vector<vector<int>> edges;
        vector<vector<int>> ans;
        int heights[n];

        map<int, int> mp;
        for(int i = 0; i < n; i++){
            // add each building's left and right edge and sort according to x coordinate
            edges.push_back({buildings[i][0], i+1});
            edges.push_back({buildings[i][1], -i-1});
            heights[i] = buildings[i][2];
        }
        
        sort(edges.begin(), edges.end());
        
        for(int i = 0; i < 2*n; i++){
            mp[edges[i][1]] = i;
        }
        multiset<vector<int>> mst;

        int currHeight = 0;

       
        int i = 0;
        
        while(i < 2*n) {
            //at ith edge right now
            //is it of type 1 or type 2

            while(i != 2*n) {
                if(edges[i][1] > 0){
                    //addition of an edge to pq
                    mst.insert({heights[edges[i][1] - 1], edges[i][1]});
                }
                else{
                    //remove previosly added 
                    mst.erase(mst.find({heights[-edges[i][1] - 1], -edges[i][1]}));
                }
                if(i == 2*n - 1 || edges[i+1][0] != edges[i][0])
                    break;
                i++;
            }
            
            // do you want to add more to mst?
         
            if(mst.empty()){
                ans.push_back({edges[i][0], 0});
                currHeight= 0;
            }
            else{
                vector<int> largestHeight = *mst.rbegin();
                if(largestHeight[0] != currHeight){
                    // height changes
                    currHeight = largestHeight[0];
                    ans.push_back({edges[i][0], currHeight});
                }
            }
            i++;
        }

        return ans;

    }
};
25191