Tutorialspoint
Problem
Solution
Submissions
Back

The Skyline Problem

Certification: Advanced Level Accuracy: 100% Submissions: 1 Points: 15

Write a Java program to solve the skyline 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.

Each building is represented by a triplet of integers [left, right, height], where:

  • left is the x coordinate of the left edge of the building.
  • right is the x coordinate of the right edge of the building.
  • height is the height of the building.

The skyline should be represented as a list of "key points" sorted by their x-coordinate in ascending order. Each key point is a pair of integers [x, height], where:

  • x is the x-coordinate of a key point.
  • height is the height of the skyline at that point.
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: 
    • At x=2, the first building starts with height 10, so we have point [2,10]. 
    • At x=3, the second building starts with height 15, so the maximum height becomes 15, giving us [3,15]. 
    • At x=7, the second building ends, leaving the third building with height 12, so we have [7,12]. 
    • At x=12, the third building ends, and there's no building, so the height becomes 0, giving us [12,0]. 
    • At x=15, the fourth building starts with height 10, so we have [15,10]. 
    • At x=20, the fourth building ends and the fifth building is still present with height 8, so we have [20,8]. 
    • At x=24, the fifth building ends, making the height 0, so we have [24,0].
    •
Example 2
    
  
  • Input: buildings = [[0,2,3],[2,5,3]]
    • 
  
  • Output: [[0,3],[5,0]]
    • 
  
  • Explanation:
    •  At x=0, the first building starts with height 3, so we have point [0,3]. 
    • At x=2, the first building ends and the second building starts, but both have the same height of 3, so there's no change in skyline. 
    • At x=5, the second building ends, making the height 0, so we have [5,0].
    •
Constraints
    
  
  • 1 ≤ buildings.length ≤ 10^4
    • 
  
  • 0 ≤ left < right ≤ 2^31 - 1
    • 
  
  • 1 ≤ height ≤ 2^31 - 1
    • 
  
  • buildings is sorted by left in ascending order
    • 
  
  • Time Complexity: O(n log n) where n is the number of buildings
    • 
  
  • Space Complexity: O(n)
    •
Priority QueueDropboxApple
Editorial

Login to view the detailed solution and explanation for this problem.

My Submissions
All Solutions
Refresh
Lang Status Date Code
You do not have any submissions for this problem.
Refresh
User Lang Status Date Code
No submissions found.

Please Login to continue
Solve Problems

 
 
 
Output Window
Clear All Apply Filters

Trending

Others

SIGN IN

Don't have an account? Register

Hint
Solution

Solution Hints

    
  
  • Use a priority queue to keep track of the highest building at each point
    • 
  
  • Process building edges (start and end) in ascending order of x-coordinate
    • 
  
  • Use a height map to keep track of building heights for each start and end point
    • 
  
  • For each critical point (where a building starts or ends), recalculate the maximum height
    • 
  
  • Only add a point to the result when there's a change in the maximum height
    •

Steps to solve by this approach:

 Step 1: Create a list of critical points by processing each building and adding two entries: one for the start and one for the end.

 Step 2: For start points, negate the height to distinguish them from end points when sorting.

 Step 3: Sort all critical points by x-coordinate. If two points have the same x-coordinate, sort them by height (start points before end points).

 Step 4: Use a TreeMap (ordered by height in descending order) to keep track of active building heights and their frequencies.

 Step 5: Process each critical point in order, updating the height map: add heights for start points and remove heights for end points.

 Step 6: After processing each point, check if the maximum height has changed. If it has, add a new skyline point.

 Step 7: Return the list of skyline points, each representing a change in the maximum height of the skyline.

Submitted Code :