218 - The Skyline Problem.

Hard

A city's skyline 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 the skyline formed by these buildings collectively.

The geometric information of each building is given in the array buildings where <code>buildingsi = left_i, right_i, height_i</code>:

• <code>left_i</code> is the x coordinate of the left edge of the <code>i^th</code> building.

• <code>right_i</code> is the x coordinate of the right edge of the <code>i^th</code> building.

• <code>height_i</code> is the height of the <code>i^th</code> building.

You may assume all buildings are perfect rectangles grounded on an absolutely flat surface at height 0.

The skyline should be represented as a list of "key points" sorted by their x-coordinate in the form <code>[x₁,y₁,x₂,y₂,...]</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 0 and is used to mark the skyline's termination where the rightmost building ends. Any ground between the leftmost and rightmost buildings should be part of the skyline's contour.

Note: There must be no consecutive horizontal lines of equal height in the output skyline. For instance, [...,[2 3],[4 5],[7 5],[11 5],[12 7],...] is not acceptable; the three lines of height 5 should be merged into one in the final output as such: [...,[2 3],[4 5],[12 7],...]

Example 1:

Input: buildings = [2,9,10,3,7,15,5,12,12,15,20,10,19,24,8]

Output: [2,10,3,15,7,12,12,0,15,10,20,8,24,0]

Explanation: 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.

Example 2:

Input: buildings = [0,2,3,2,5,3]

Output: [0,3,5,0]

Constraints:

• <code>1 <= buildings.length <= 10⁴</code>

• <code>0 <= left_i< right_i<= 2³¹ - 1</code>

• <code>1 <= height_i<= 2³¹ - 1</code>

• buildings is sorted by <code>left_i</code> in non-decreasing order.