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Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 10

Write a C# program to rotate an n x n 2D matrix (array) by 90 degrees (clockwise). You need to do this in-place, which means you have to modify the input 2D matrix directly. DO NOT allocate another 2D matrix and do the rotation.

Example 1
    
  
  • Input: matrix = [[1,2,3],[4,5,6],[7,8,9]]
    • 
  
  • Output: [[7,4,1],[8,5,2],[9,6,3]]
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  • Explanation:
    
      
      
    • Before rotation:
        
      1 2 3
        
      4 5 6
        
      7 8 9
      • 
      
    • After rotation:
        
      7 4 1
        
      8 5 2
        
      9 6 3
      • 
    
    
  
    •
Example 2
    
  
  • Input: matrix = [[5,1,9,11],[2,4,8,10],[13,3,6,7],[15,14,12,16]]
    • 
  
  • Output: [[15,13,2,5],[14,3,4,1],[12,6,8,9],[16,7,10,11]]
    • 
  
  • Explanation:
    
      
      
    • Before rotation:
        
      5  1  9  11
        
      2  4  8  10
        
      13 3  6  7
        
      15 14 12 16
      • 
      
    • After rotation:
        
      15 13 2  5
        
      14 3  4  1
        
      12 6  8  9
        
      16 7  10 11
      • 
    
    
  
    •
Constraints
    
  
  • n == matrix.length == matrix[i].length
    • 
  
  • 1 <= n <= 20
    • 
  
  • -1000 <= matrix[i][j] <= 1000
    • 
  
  • Time Complexity: O(n²) where n is the matrix dimension
    • 
  
  • Space Complexity: O(1) for in-place rotation
    •
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Hint
Solution

Solution Hints

    
  
  • Rotate the matrix in layers, starting from the outermost layer
    • 
  
  • The rotation can be done in two steps: transpose and then reflect
    • 
  
  • Transpose: swap matrix[i][j] with matrix[j][i]
    • 
  
  • Reflect: reverse each row of the matrix
    • 
  
  • Alternatively, rotate four cells at a time in a single pass
    •

Steps to solve by this approach:

 Step 1: Determine the size of the matrix (n x n).
 Step 2: Transpose the matrix by swapping elements across the main diagonal (i.e., swap matrix[i][j] with matrix[j][i]).
 Step 3: To transpose, iterate through the upper triangular portion of the matrix (where i ≤ j).
 Step 4: After transposing, reverse each row of the matrix.
 Step 5: To reverse each row, swap elements from the beginning and end of each row, moving towards the center.
 Step 6: The result is the original matrix rotated 90 degrees clockwise.

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