LeetCode-in-All

48. Rotate Image

Medium

You are given an n x n 2D matrix representing an image, rotate the image by 90 degrees (clockwise).

You have to rotate the image 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]]

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]]

Example 3:

Input: matrix = [[1]]

Output: [[1]]

Example 4:

Input: matrix = [[1,2],[3,4]]

Output: [[3,1],[4,2]]

Constraints:

• matrix.length == n
• matrix[i].length == n
• 1 <= n <= 20
• -1000 <= matrix[i][j] <= 1000

To solve the “Rotate Image” problem, you can perform the rotation in-place by swapping elements of the matrix. Here are the steps to solve the problem:

Approach:

1. Transpose the Matrix:
   • Transpose the matrix by swapping matrix[i][j] with matrix[j][i] for all i and j where i < j.
2. Reverse Each Row:
   • Reverse each row of the transposed matrix to get the final rotated matrix.

Python Code:

class Solution:
    def rotate(self, matrix):
        n = len(matrix)
        
        # Transpose the matrix
        for i in range(n):
            for j in range(i + 1, n):
                matrix[i][j], matrix[j][i] = matrix[j][i], matrix[i][j]
        
        # Reverse each row
        for i in range(n):
            matrix[i] = matrix[i][::-1]

# Example Usage:
solution = Solution()

# Example 1:
matrix1 = [
    [1,2,3],
    [4,5,6],
    [7,8,9]
]
solution.rotate(matrix1)
print(matrix1)  # Output: [[7,4,1],[8,5,2],[9,6,3]]

# Example 2:
matrix2 = [
    [5,1,9,11],
    [2,4,8,10],
    [13,3,6,7],
    [15,14,12,16]
]
solution.rotate(matrix2)
print(matrix2)  # Output: [[15,13,2,5],[14,3,4,1],[12,6,8,9],[16,7,10,11]]

# Example 3:
matrix3 = \[\[1]]
solution.rotate(matrix3)
print(matrix3)  # Output: [[1]]

# Example 4:
matrix4 = [
    [1,2],
    [3,4]
]
solution.rotate(matrix4)
print(matrix4)  # Output: [[3,1],[4,2]]

This code defines a Solution class with a rotate method to rotate the given matrix by 90 degrees clockwise. The example usage demonstrates how to create an instance of the Solution class and call the rotate method with different input matrices.

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