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Skyline Problem (Building Outline Problem)

Certification: Advanced Level Accuracy: 100% Submissions: 2 Points: 15

Write a Python function get_skyline(buildings) that solves the skyline problem. Each building is represented as [left, right, height], and the function returns the key points that define the skyline.

Example 1
     
  • Input: buildings = [[2,9,10],[3,7,15],[5,12,12],[15,20,10],[19,24,8]]
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  • Output: [[2,10],[3,15],[7,12],[12,0],[15,10],[20,8],[24,0]]
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  • Explanation: 
       
    • Step 1: At x=2, start building height 10 → [2,10]
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    • Step 2: At x=3, taller building 15 starts → [3,15]
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    • Step 3: At x=7, height drops to 12 → [7,12]
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    • Step 4: At x=12, height drops to 0 → [12,0]
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    • Step 5: At x=15, building of height 10 starts → [15,10]
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    • Step 6: At x=20, height drops to 8 → [20,8]
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    • Step 7: At x=24, height drops to 0 → [24,0]
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Example 2
     
  • Input: buildings = [[0,2,3],[2,5,3]]
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  • Output: [[0,3],[5,0]]
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  • Explanation: 
       
    • Step 1: At x=0, height becomes 3 → [0,3]
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    • Step 2: At x=5, all buildings end → [5,0]
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Constraints
     
  • 1 ≤ buildings.length ≤ 104
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  • 0 ≤ left < right ≤ 231 - 1
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  • 1 ≤ height ≤ 231 - 1
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  • Time Complexity: O(n log n), where n is the number of buildings
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  • Space Complexity: O(n)
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Hint
Solution

Solution Hints

    
  
  • Use a sweep line algorithm combined with a priority queue (max heap)
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  • Process all building edges (both left and right) in order of x-coordinate
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  • For left edges, add the height to the max heap; for right edges, remove the height
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  • Record a key point whenever the maximum height changes
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  • Be careful with edge cases such as overlapping buildings and buildings with the same start or end point
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Steps to solve by this approach:

 Step 1: Convert buildings into a list of points, marking start points with negative heights.
 Step 2: Sort all points by x-coordinate (and by height for same x-coordinate).
 Step 3: Process each point in order, keeping track of active building heights in a max heap.
 Step 4: For start points, add the height to the max heap; for end points, remove the corresponding height.
 Step 5: Record a key point whenever the maximum height changes, creating the skyline profile.

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