How to Rotate a Matrix 270 Degrees in Java?

To rotate a matrix 270 degrees clockwise in Java, the most straightforward and commonly used method is to perform a 90-degree clockwise rotation three consecutive times.

Rotating a matrix 270 degrees clockwise is mathematically equivalent to rotating it 90 degrees counter-clockwise. However, if you have an implementation for 90 degrees clockwise rotation, simply repeating that process three times achieves the desired 270-degree clockwise result. As noted in the provided reference, "And you repeat it three times. And hence you will get the 270 degrees clockwise rotation."

The Process: 90-Degree Rotation Three Times

The core idea is to apply a 90-degree clockwise rotation algorithm to your matrix, then apply it again to the result, and a third time to that result.

Here's a breakdown of the steps:

1. Perform 90° Clockwise Rotation (1st time): Apply your method for rotating the original matrix 90 degrees clockwise. This typically involves two main steps:
   • Transpose the matrix: Swap the rows and columns. The element at matrix[i][j] moves to matrix[j][i].
   • Reverse each row: After transposing, reverse the elements in each row. This completes the 90-degree clockwise rotation.
2. Perform 90° Clockwise Rotation (2nd time): Take the matrix resulting from step 1 and apply the same 90-degree clockwise rotation method to it.
3. Perform 90° Clockwise Rotation (3rd time): Take the matrix resulting from step 2 and apply the 90-degree clockwise rotation method one final time.

The matrix after the third rotation will be the original matrix rotated 270 degrees clockwise.

Understanding 90-Degree Rotation Steps

Let's elaborate on a common technique for a single 90-degree clockwise rotation for a square matrix for simplicity (though it can be adapted for rectangular matrices):

• Step A: Transpose

  • Iterate through the matrix from i = 0 to n-1 and j = i to n-1.
  • Swap matrix[i][j] with matrix[j][i].

  Original Matrix:
  1 2 3
  4 5 6
  7 8 9
  
  After Transpose:
  1 4 7
  2 5 8
  3 6 9

• Step B: Reverse Rows

  • Iterate through each row of the transposed matrix.
  • Reverse the elements in that row.

  After Transpose:
  1 4 7
  2 5 8
  3 6 9
  
  After Reversing Rows (90 deg clockwise):
  7 4 1
  8 5 2
  9 6 3

Repeat this two-step process (Transpose then Reverse Rows) a total of three times on the matrix, updating the matrix after each rotation.

Time Complexity

The time complexity for a single 90-degree clockwise rotation of an M x N matrix is Order of O(MN), as mentioned in the reference. Since you perform this operation three times, the total time complexity for a 270-degree rotation is 3 * O(MN), which simplifies to O(MN). This is generally efficient as you must process each element of the matrix.

Alternative Perspective

Rotating 270 degrees clockwise is also equivalent to rotating 90 degrees counter-clockwise. A 90-degree counter-clockwise rotation can be achieved by:

1. Transposing the matrix.
2. Reversing each column (instead of each row).

So, another way to perform a 270-degree clockwise rotation is to perform a single 90-degree counter-clockwise rotation using the Transpose and Reverse Columns method. However, the reference explicitly suggests repeating the 90-degree clockwise rotation three times.

By implementing the 90-degree clockwise rotation and calling that function three times, you can effectively rotate your matrix 270 degrees clockwise in Java.