<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:
    def getSkyline(self, buildings: List[List[int]]) -> List[List[int]]:
        # Iterate over all buildings, for each building i,
        # add (position, i) to edges.
        edges = []
        for i, build in enumerate(buildings):
            edges.append([build[0], i])
            edges.append([build[1], i])

        # Sort edges by non-decreasing order.
        edges.sort()
     
        # Initailize an empty Priority Queue 'live' to store all the 
        # newly added buildings, an empty list answer to store the skyline key points.
        live, answer = [], []
        idx = 0
        
        # Iterate over all the sorted edges.
        while idx < len(edges):
            
            # Since we might have multiple edges at same x,
            # Let the 'curr_x' be the current position.
            curr_x = edges[idx][0]
            
            # While we are handling the edges at 'curr_x':
            while idx < len(edges) and edges[idx][0] == curr_x:
                # The index 'b' of this building in 'buildings'
                b = edges[idx][1]
                
                # If this is a left edge of building 'b', we
                # add (height, right) of building 'b' to 'live'.
                if buildings[b][0] == curr_x:
                    right = buildings[b][1]
                    height = buildings[b][2]
                    heapq.heappush(live, [-height, right])
                    
                # If the tallest live building has been passed,
                # we remove it from 'live'.
                while live and live[0][1] <= curr_x:
                    heapq.heappop(live)
                idx += 1
            
            # Get the maximum height from 'live'.
            max_height = -live[0][0] if live else 0
            
            # If the height changes at this curr_x, we add this
            # skyline key point [curr_x, max_height] to 'answer'.
            if not answer or max_height != answer[-1][1]:
                answer.append([curr_x, max_height])
        
        # Return 'answer' as the skyline.
        return answer
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