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Skyline Problem

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

Write a C++ program to solve the Skyline Problem. You are given a list of buildings where each building is represented by a triplet [left, right, height], which indicates the left edge position, right edge position, and height of the building. Your task is to output the skyline formed by these buildings collectively.

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: Transform each building into two events: one for the start edge (height increase) and one for the end edge (height decrease).
      • 

    • Step 2: Sort all events by position, with special handling for ties.
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    • Step 3: Process events in order, keeping track of current heights using a priority queue or similar data structure.
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    • Step 4: Record height changes in the skyline when the maximum height changes after processing an event.
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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: Transform each building into two events: one for the start edge (height increase) and one for the end edge (height decrease).
      • 

    • Step 2: Sort all events by position, with special handling for ties.
      • 

    • Step 3: Process events in order, updating current heights.
      • 

    • Step 4: Since the buildings are at the same height and one starts where the other ends, there are only two critical points: the start of the first building (0,3) and the end of the second building (5,0).
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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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  • 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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SetMapTech MahindraSamsung
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Hint
Solution

Solution Hints

    
  
  • Use a priority queue to track the maximum height at each point
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  • Process the buildings by sorting all critical points (both start and end points)
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  • For each critical point, update the maximum height and add it to the result if the height changes
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  • Use a balanced tree data structure like a multiset to efficiently find the maximum height
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  • Handle edge cases like overlapping buildings
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Steps to solve by this approach:

 Step 1: Create an array of "critical points" by adding both the start and end points of all buildings.
 Step 2: For start points, use negative height to distinguish them from end points.
 Step 3: Sort all critical points by their x-coordinate (and by height for tiebreaking).
 Step 4: Iterate through these critical points, maintaining a multiset of current heights.
 Step 5: For a start point, add the height to the multiset; for an end point, remove the corresponding height.
 Step 6: After processing each critical point, check if the maximum height has changed.
 Step 7: If the maximum height changed, add the critical point to the result.

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