<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>

auto hcmp = [](const vector<int>& a, const vector<int> b) {
    return a[1] < b[1];
};

bool pcmp (const vector<int>& a, const vector<int> b) {
    if ( a[0] == b[0]) {
        return a[2] > b[2];
    } else {
        return a[0] < b[0];
    }
};

class Solution {
public:
    vector<vector<int>> getSkyline(vector<vector<int>>& buildings) {
        priority_queue<vector<int>, vector<vector<int> >, decltype(hcmp) > pq{hcmp};
        sort(buildings.begin(), buildings.end(), pcmp);
        vector< vector<int> > ans;
        //int scan = b[0][0];
        priority_queue<int, vector<int>, greater<int> > exit_pq;
        vector<int> ans_back = {-1, -1}; // double check
        for (auto& b : buildings) {
            b[0] -= 100;
            b[1] -=100;
        }
        buildings.push_back({INT_MAX-1, INT_MAX, 0});
        for (auto& b : buildings) {
            vector<int> back = {b[1], b[2]};
            exit_pq.push(b[1]);

            cout << "b[0]: " << b[0] <<endl;
            // handle all area: end
            while (exit_pq.size() && exit_pq.top() <b[0]) { // double check <=?
                cout<< "handle exit: " << exit_pq.top()
                <<". pqsize:" << pq.size() << endl;
                while (pq.size() && pq.top()[0] <= exit_pq.top()) { // dc <?
                    cout<< "handle pop before exit" << pq.top()[0]<<endl;
                    pq.pop();
                }
                cout << "pqtop:"  << (pq.size() ? pq.top()[1] : 0) <<endl;
                vector<int> t = {exit_pq.top(), pq.size() ? pq.top()[1] : 0};
                if (t[1] < ans_back[1]) {
                    ans.push_back(t);
                    ans_back = t;

                    cout << format("end point x: {}, y: {}", t[0], t[1]) <<endl;
                } else if (t[1] == ans_back[1]){
                    //ans.back()[0] = t[0];
                }

                exit_pq.pop();
            }
            pq.push(back);
            cout<< "pushed:" << back[0] << ", " << back[1] 
            << " new_top: " << pq.top()[0] << " , " << pq.top()[1]<<endl;

            // cur new area: start
            while (pq.size() && pq.top()[0] <= b[0]) { // dc <?
                cout <<"pop b[0]:" << b[0] 
                << " pq.top[0]: " << pq.top()[0] <<endl;
                pq.pop();
            }
            vector<int> t = {b[0], pq.size() ? pq.top()[1] : 0};
            
            if (t[1] > ans_back[1]) {
                ans.push_back(t);
                ans_back = t;
                cout << format("new point x: {}, y: {}", t[0], t[1]) <<endl;
            }else if (t[1] == ans_back[1]) {
                //ans.back()[0] = t[0];
                cout << format("skip new point= x: {}, y: {}", t[0], t[1]) <<endl;
            } else {
                cout << format("skip new point< x: {}, y: {}", t[0], t[1]) <<endl;

            }
            //pq.pop();
        }
        for (auto & a : ans) {
            a[0]+=100;
        }
        return ans;

        
    }
};
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