<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) {
        vector<vector<int>> p; // points
        vector<vector<int>> ans;
        for (auto x : buildings) {
            p.push_back({x[0], x[2], 1});
            p.push_back({x[1], x[2], 0});
        }
        sort(p.begin(),p.end());
        int t = 0;       // tallest
        map<int, int> h; // heights
        for (auto x : p) {
            cout << "processing {" << x[0] << ", " << x[1] << ", " << x[2]
                 << "}" << endl;
            if (x[2])
                ++h[x[1]];
            else {
                if (h[x[1]] > 1)
                    --h[x[1]];
                else
                    h.erase(x[1]);
            }
            if (!h.empty()) {
                if (t != h.rbegin()->first) {
                    t = h.rbegin()->first;
                    while (!ans.empty() && ans.back()[0] == x[0]) {
                        cout << "removed {" << ans.back()[0] << ", "
                             << ans.back()[1] << "}" << endl;
                        ans.pop_back();
                    }

                    if (ans.empty() || (!ans.empty() && ans.back()[1] != t)) {
                        ans.push_back({x[0], t});
                        cout << "a inserted {" << x[0] << ", " << t << "}"
                             << endl;
                    }
                }

            } else {
                t = 0;
                if (!ans.empty() && !ans.back()[1]) {
                    cout << "removed {" << ans.back()[0] << ", "
                         << ans.back()[1] << "}" << endl;
                    ans.pop_back();
                }
                ans.push_back({x[0], 0});
                cout << "b inserted {" << x[0] << ", " << t << "}" << endl;
            }
        }

        return ans;
    }
};
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