The Skyline Problem

Statement

Imagine standing at a distance, viewing the skyline of a city. The skyline is the shape formed by all the buildings in the city when viewed together. Your task is to determine the shape of this skyline, given all the buildings’ position and height. Each building is represented by three values in the array buildings, where $buildings[i] = [left_i,~right_i,~ height_i]$:

1. lefti is the $x$-coordinate where the $i^{th}$ building starts.

2. righti is the $x$-coordinate where the $i^{th}$ building ends.

3. heighti is the height of the $i^{th}$ building.

All buildings are rectangles that sit on flat ground (height $0$). The skyline should be a list of points that define its outline, with each point showing where the height changes as you move from left to right. The final point should have a height of $0$, marking where the last building ends.

Note: The output skyline should not have multiple horizontal lines at the same height in a row. For example, an output like $[...,[1, 4], [3, 6], [5, 6], [7, 6], [8, 3],...]$ is incorrect. The three lines with height $6$ should be combined into one, so the correct version would be $[...,[1, 4], [3, 6], [8, 3],...]$.

Constraints:

• $1 \leq$ buildings.length $\leq 10^3$

• $0 \leq$ lefti $<$ righti $\leq 10^4$

• $0 \leq$ heighti $\leq 10^4$

• buildings is sorted by lefti in ascending order.

Examples