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Skyline Problem

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C program to find the skyline formed by a set of rectangular buildings. Given an array of buildings where buildings[i] = [left, right, height], return the skyline formed by these buildings. The skyline should be represented as a list of "key points" sorted by their x-coordinate in the form [[x1,h1],[x2,h2],...] where each key point is the left endpoint of some horizontal segment in the skyline except the last point which marks the end.

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: 
    • Building [2,9,10] creates skyline from x=2 to x=9 with height 10. 
    • Building [3,7,15] overlaps and has greater height, creating key point [3,15]. 
    • At x=7, height drops back to 12, then to 0 at x=12. 
    • Subsequent buildings create more key points as heights change.
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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: 
    • First building creates skyline from x=0 to x=2 with height 3. 
    • Second building continues the same height from x=2 to x=5. 
    • Since heights are same, no key point needed at x=2. 
    • Final key point at x=5 marks end with height 0.
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Constraints
    
      
  • 1 ≤ buildings.length ≤ 10^4
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  • 0 ≤ left < right ≤ 2^31 - 1
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  • 1 ≤ height ≤ 2^31 - 1
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  • Buildings are sorted by left coordinate
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  • Time Complexity: O(n^2)
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  • Space Complexity: O(n)
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Hint
Solution

Solution Hints

    
      
  • Use a sweep line algorithm to process building start and end events
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  • Create events for building starts (negative height) and ends (positive height)
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  • Sort events by x-coordinate, handling ties appropriately
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  • Use a data structure to track active building heights at each x-coordinate
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  • When height changes, add a key point to the result
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Steps to solve by this approach:

 Step 1: Create events for each building - start event (x, height, 0) and end event (x, height, 1).
 Step 2: Sort events by x-coordinate with proper tie-breaking rules for overlapping events.
 Step 3: Process events in order, maintaining a list of active building heights.
 Step 4: For start events, add the building height to active heights list.
 Step 5: For end events, remove the corresponding height from active heights list.
 Step 6: After each event, find the maximum height among active buildings.
 Step 7: If maximum height changes, add a key point [x, newMaxHeight] to the result.

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