The Skyline Problem Python Solution with Tests

Tested Python solution for LeetCode 218 with 19 pytest cases. Generate a practice environment with lcpy.

LeetCode 218, Hard. Topics: Array, Divide and Conquer, Binary Indexed Tree, Segment Tree, Sweep Line, Sorting, Heap (Priority Queue), Ordered Set. View on LeetCode.

Generate this problem as a practice environment: tested reference solution, 19 parametrized pytest cases, and a playground notebook:

lcpy gen -n 218   # by problem number
lcpy gen -s the_skyline_problem   # by problem name

​

Problem

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 buildings[i] = [lefti, righti, heighti]:

• lefti is the x coordinate of the left edge of the ith building.
• righti is the x coordinate of the right edge of the ith building.
• heighti is the height of the ith 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 [[x1,y1],[x2,y2],...]. 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],...]

​

Examples

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.

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

​

Constraints

• 1 <= buildings.length <= 10^4
• 0 <= lefti < righti <= 2^31 - 1
• 1 <= heighti <= 2^31 - 1
• buildings is sorted by lefti in non-decreasing order.

​

Solution

Reference implementation from solution.py on GitHub, full suite in test_solution.py:

import heapq


class Solution:
    # Time: O(n log n)
    # Space: O(n)
    def get_skyline(self, buildings: list[list[int]]) -> list[list[int]]:
        events: list[tuple[int, int, int]] = []
        for left, right, height in buildings:
            events.append((left, -height, right))
            events.append((right, 0, 0))
        events.sort()

        heap: list[tuple[int, int]] = [(0, 2**31)]
        result: list[list[int]] = []
        for x, neg_height, right in events:
            while heap[0][1] <= x:
                heapq.heappop(heap)
            if neg_height < 0:
                heapq.heappush(heap, (neg_height, right))
            height = -heap[0][0]
            if not result or result[-1][1] != height:
                result.append([x, height])
        return result

​

Complexity

Time	Space
O(n log n)	O(n)

​

Tags