Rotate Matrix in Python

Rotating a matrix in python, can be done by utilizing various approaches like Transpose and Reverse method which is commonly used in rotating a matrix by converting the rows to columns and columns to rows.

Common Approaches

Some of the common methods, we can use to rotate a matrix by 90 degress clockwise are as follows.

• Layer by Layer Rotation

• Temp Matrix Method

• Transpose and reverse

2D Matrix

Let us consider an n x n 2D matrix, whic we have to rotate this matrix 90 degress clockwise.

1	5	7
9	6	3
2	1	3

Using Layer by Layer Rotation

This method includes rotating the matrix layer by layer, which doesn't require extra space for another matrix. The process of rotating a 2D matrix starts from the outermost layer and moving towards the inner layers. After it rotates the four corners of each layer.

Example

In the below example code the matrix is divided into four concentric layers, for each layer as follows:

• Top row is moved to the right

• Right column is moved to the bottom

• Bottom row is moved to the left

• Left column is moved to the top

class Solution:
    def rotate(self, matrix):
        n = len(matrix)
        
        for i in range(n // 2):
            for j in range(i, n - i - 1):
                # Save the top element
                temp = matrix[i][j]
                
                # Move left to top
                matrix[i][j] = matrix[n - j - 1][i]
                
                # Move bottom to left
                matrix[n - j - 1][i] = matrix[n - i - 1][n - j - 1]
                
                # Move right to bottom
                matrix[n - i - 1][n - j - 1] = matrix[j][n - i - 1]
                
                # Move top to right
                matrix[j][n - i - 1] = temp
        
        return matrix

ob1 = Solution()
print(ob1.rotate([[1, 5, 7], [9, 6, 3], [2, 1, 3]]))

Input

[[1,5,7],[9,6,3],[2,1,3]]

Output

[[2, 9, 1], [1, 6, 5], [3, 3, 7]]

Rotated Matrix

2	9	1
1	6	5
3	3	7

Using Temp Matrix Method

As the name Implies this method creates a temporary matrix to store the rotated matrix. The original matrix is updated with rotated elements after creating the temporary matrix.

Example

In the below example code the 'temp_matrix' initialize a temporary matrix, which stores the rotated elements. populating the temporary matrix by extracting the elements from top to bottom and placing them as a row.

class Solution:
    def rotate(self, matrix):
        temp_matrix = []
        column = len(matrix) - 1
        
        # Create the rotated matrix
        for column in range(len(matrix)):
            temp = []
            for row in range(len(matrix) - 1, -1, -1):
                temp.append(matrix[row][column])
            temp_matrix.append(temp)
        
        # Copy the rotated matrix back to the original matrix
        for i in range(len(matrix)):
            for j in range(len(matrix)):
                matrix[i][j] = temp_matrix[i][j]
        
        return matrix

ob1 = Solution()
print(ob1.rotate([[10, 15, 27], [11, 16, 8], [43, 17, 35]]))

Input

[[10, 15, 27], [11, 16, 8], [43, 17, 35]]

Output

[[43, 11, 10], [17, 16, 15], [35, 8, 27]]

Rotated Matrix

43	11	10
17	16	15
35	8	27

Using Transpose and reverse

This method is efficient and commonly used and the proces of rotating matrix involves two main steps are as follows below.

• Transpose the matrix : Converting all the rows to columns and columns to rows of the matrix.

• Reversing each row(elements) : In the next step Reversing the elements in each row to get our required rotation.

Example

In the below example code, the element at position '(i,j)' is swapped with the elements at position '(j,i)' and each row is reversed to get the required rotation of the matrix.

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

ob1 = Solution()
print(ob1.rotate([[1, 5, 7], [9, 6, 3], [2, 1, 3]]))

Input

[[1,5,7],[9,6,3],[2,1,3]]

Output

[[2, 9, 1], [1, 6, 5], [3, 3, 7]]

Rotated Matrix

2	9	1
1	6	5
3	3	7