<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 Compare {
public:
    bool operator()(const vector<int>& a, const vector<int>& b) const {
        if (a[0] != b[0]) return a[0] > b[0]; // Sort by x-coordinate (ascending)
        return a[1] > b[1]; // Sort by height (ascending for ties)
    }
};

void printPriorityQueue(priority_queue<vector<int>, vector<vector<int>>, Compare> pq) {
    // Copy the priority_queue to avoid modifying the original
    priority_queue<vector<int>, vector<vector<int>>, Compare> copy = pq;

    // Print elements of the priority_queue
    while (!copy.empty()) {
        vector<int> element = copy.top();
        copy.pop();

        // Print the element (adjust according to your data type)
        cout << "[" << element[0] << ", " << element[1] << "]" << endl;
    }
}

class Solution {
public:
    vector<vector<int>> getSkyline(vector<vector<int>>& buildings) {
        std::priority_queue<vector<int>,vector<vector<int>>,Compare> arr;
        for (const auto& building : buildings) {
            // Push start and end events
            arr.push({building[0], -building[2]}); // Start event (negative x for max-heap)
            arr.push({building[1], building[2]}); // End event (positive x, negative height for end event)
        }
        printPriorityQueue(arr);
        multiset<int> heights;
        vector<vector<int>> skyline;
        int currentMaxHeight = 0;
        while(!arr.empty()){
            vector<int> event=arr.top();
            arr.pop();
            if(event[1]<0){
                heights.insert(-event[1]);
            }
            else { // End event
                heights.erase(heights.find(event[1]));
            }
            int newMaxHeight = heights.empty() ? 0 : *heights.rbegin();
            if (newMaxHeight != currentMaxHeight) {
                skyline.push_back({event[0], newMaxHeight});
                currentMaxHeight = newMaxHeight;
            }
        }
        return skyline;      
    }

};
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