How do you solve The Skyline Problem on LeetCode?

The Skyline Problem (LeetCode #218) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: The skyline problem requires understanding how to manage overlapping intervals efficiently.

What is the brute force solution for The Skyline Problem?

The brute force approach for The Skyline Problem is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves checking each x-coordinate to determine the maximum height of buildings at that point. This is simple but inefficient, as it requires examining all buildings for each x-coordinate. The optimal Optimal Solution approach improves this to O(n log n).

What are the interview tips for The Skyline Problem?

Clearly explain your thought process and how you plan to handle overlapping buildings. Discuss edge cases, such as buildings that start and end at the same x-coordinate. Practice drawing the skyline to visualize how buildings interact.

What are common mistakes when solving The Skyline Problem?

Failing to handle the end of buildings properly, leading to incorrect heights. Not merging consecutive horizontal lines of the same height in the output.

#218

The Skyline Problem

Hard

ArrayDivide and ConquerBinary Indexed TreeSegment TreeSweep LineSortingHeap (Priority Queue)Ordered SetSweep LinePriority QueueSorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(n)

💡

Intuition

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

The optimal solution uses a sweep line algorithm with a priority queue to efficiently track the heights of buildings as we process events (start and end of buildings). This allows us to dynamically update the maximum height at each x-coordinate.

⚙️

Algorithm

4 steps

1Step 1: Create a list of all start and end points of buildings, marking starts with negative heights.
2Step 2: Sort the points by x-coordinate, and by height for ties.
3Step 3: Use a max-heap (priority queue) to keep track of current building heights.
4Step 4: Iterate through the sorted points, updating the heap and recording changes in height.

solution.py26 lines

1# Full working Python code
2from collections import defaultdict
3import heapq
4
5def getSkyline(buildings):
6    points = []
7    for left, right, height in buildings:
8        points.append((left, -height))  # Start of a building
9        points.append((right, height))   # End of a building
10    points.sort()
11    result = []
12    heights = [(0, 1)]  # (height, count)
13    prev_height = 0
14
15    for x, h in points:
16        if h < 0:
17            heapq.heappush(heights, (h, 1))
18        else:
19            heights.remove((h, 1))
20            heapq.heapify(heights)
21        current_height = -heights[0][0]
22        if current_height != prev_height:
23            result.append([x, current_height])
24            prev_height = current_height
25    return result
26

ℹ

Complexity note: The sorting of points takes O(n log n) time, and maintaining the max-heap for heights takes O(log n) for each insertion/removal, leading to an overall efficient solution.

1The skyline problem requires understanding how to manage overlapping intervals efficiently.
2Using a max-heap allows for dynamic height tracking as buildings start and end.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.