<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:
    int N = 40001;

    // start, end => start and end of range that needs to be modified
    void ss(vector<int> &tree,int node,int l, int r, int start, int end, int val) {
        int mid = (l + r)/2;
        if(l > r || start > r || end < l) return;
        // cout << node << " " << l << " " << r << " " << start << " " << end << endl;
        if(start <= l && end >= r) {
            tree[node] = max(tree[node], val);
            return;
        }
        ss(tree, node*2, l, mid, start, end, val);
        ss(tree, node*2+1, mid+1, r, start, end, val);
    }

    int q2(vector<int> &tree, int node, int l, int r, int start, int end) {
        if(l > r || start > r || end < l) return 0;
        int mid = (l + r)/2;
        if(start <= l && end >= r) {
            return tree[node];
        }
        return max(
            q2(tree, node*2, l, mid, start, end),
            q2(tree, node*2+1, mid+1, r, start, end)
        );
    }

    void upd(vector<int> &tree, int node, int l, int r, int val) {
        if(l > r) return;
        tree[node] = max(tree[node],val);
        if(l == r) {
            return;
        }
        int mid = (l + r)/2;
        upd(tree, node*2, l, mid, tree[node]);
        upd(tree, node*2+1, mid+1, r, tree[node]);
    }

    int query(vector<int> &tree, int node, int l, int r, int point) {
        if(l > r || point > r || point < l) return 0;

        int mid = (l+r)/2;
        if(l == r && l == point) {
            return tree[node];
        }
        int lq = query(tree, node*2, l, mid, point);
        int rq = query(tree, node*2+1, mid+1, r, point);
        return max(lq,rq);
    }
    vector<vector<int>> getSkyline(vector<vector<int>>& buildings) {
        map<int,int> mp;
        map<int,int> mp2;
        int cnt = 0;
        vector<int> coordinates;
        set<int> temp;
        set<pair<int,int> > s2;
        for(auto b : buildings) {
            temp.insert(b[0]);
            temp.insert(b[1]);
            s2.insert({b[0],b[1]});
        }
        for(auto x : temp) coordinates.push_back(x);
        // sort(coordinates.begin(), coordinates.end());
        for(auto c: coordinates) {
            if(mp.find(c) == mp.end()) {
                mp[c] = cnt;
                mp2[cnt] = c;
                cnt++;
            }
            // cout << c << " " << mp[c] << endl;
        }

        vector<vector<int>> bb;
        vector<int> tree(N);
        int n = mp.size();
        for(int i = 0; i < buildings.size(); i++) {
            int nl = mp[buildings[i][0]];
            int nr = mp[buildings[i][1]];
            bb.push_back({nl, nr, buildings[i][2]});
            ss(tree, 1, 0, n-1, nl, nr-1, buildings[i][2]);
        }
        
        upd(tree, 1, 0, n-1, 0);
        vector<vector<int> > ans;
        // ans.push_back({coordinates[0], query(tree, 1, 0, n-1, mp[coordinates[0]])});
        for(int i = 1; i< mp.size(); i++) {
            int l = coordinates[i-1];
            int r = coordinates[i];
            int ht = 0;
            // if(l+1 == r && s2.find({l,r}) == s2.end()) ht = 0;
            // else 
            ht = q2(tree, 1, 0, n-1, mp[l], mp[r]-1);
            cout << l << " " << r << " " << ht << endl;
            if(ans.size()==0) {
                ans.push_back({l, ht}); continue;
            }
            if(ans[ans.size()-1][1] != ht)
                ans.push_back({l, ht});
        }
        ans.push_back({coordinates[n-1],0});
        return ans;   
    }
};
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