<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>

struct compare{
    bool operator()(vector<int> lhs, vector<int> rhs) {
        if (lhs[2] < rhs[2])
            return true;
        return false;
    }
};

class Solution {
public:
    vector<vector<int>> getSkyline(vector<vector<int>>& buildings) {
        sort(buildings.begin(), buildings.end(), [](vector<int> lhs, vector<int> rhs) {
            if (lhs[0] < rhs[0])
                return 1;
            return 0;
        });
        map<int, int> m;
        priority_queue<vector<int>, vector<vector<int>>, compare> pq;
        pq.push(buildings[0]);
        m[buildings[0][0]] = buildings[0][2];
        for (int i = 1; i < buildings.size(); i++) {
            int cur_start = buildings[i][0];
            int cur_end = buildings[i][1];
            int cur_value = buildings[i][2];
            int key = pq.top()[1];
            int value = pq.top()[2];
            while (!pq.empty() && cur_start > pq.top()[1]) {
                pq.pop();
                if (pq.empty()) {
                    break;
                }
                int v = pq.top()[2];
                if (pq.top()[1] > key) {
                    if (value != v) {
                        m[key] = v;
                        value = v;
                    }
                    key = pq.top()[1];
                }
            }
            if (pq.empty()) {
                m[key] = 0;
                m[cur_start] = cur_value;
            } else if (pq.top()[2] < cur_value) {
                m[cur_start] = cur_value;
            }
            pq.push(buildings[i]);
        }

        int key = pq.top()[1];
        int value = pq.top()[2];
        while (!pq.empty()) {
            pq.pop();
            if (pq.empty()) {
                break;
            }
            int v = pq.top()[2];
            if (pq.top()[1] > key) {
                if (value != v) {
                    m[key] = v;
                    value = v;
                }
                key = pq.top()[1];
            }
        }
        m[key] = 0;

        vector<vector<int>> ans;
        for (map<int,int>::iterator it = m.begin(); it != m.end(); it++) {
            ans.push_back({it->first, it->second});
        }
        return ans;
    }
};
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