Rotate the Matrix

This article will see the code that will rotate the given matrix elements clockwise. To visualize the problem, let us first look at some examples of matrix rotation.

Examples of rotation of matrix:

For 3 * 3 matrix

Input

  4    7
  5    8
  6    9

Output:

2    1    4
3    5    7
6    9    8

For 4 * 4 matrix

Input:

  5    9   13
  6   10   14
  7   11   15
  8   12   16

Output:

2    1    5    9
3    7    6   13
4   11   10   14
8   12   16   15

Approach - 1

This question is similar to another question about the matrix where we have to print the spiral form of the matrix. We will use similar loops, but we have to do it according to the rings this time. We have to rotate all the rings of the elements one by one, starting from the ring that makes the border of the matrix.

We will follow the following steps to rotate a ring of the matrix:

First, we will move forward with the elements in the top row of the matrix.
Then we will move the elements of the last column or the right part of the ring.
Next, we will go to the bottom row or the bottom part of the ring and move them from the last column to the first column.
Lastly, we will move forward with the elements in the first column of the matrix.
We will repeat these steps for each ring of the matrix until the rings are complete or we are left with a single element in the middle of the matrix.

Below is the Python code that uses the abovementioned approach to solve the problem and rotate the given matrix.

Code

# Python program which will rotate the given matrix

# Defining a function that will take the matrix and return the rotated matrix
def rotateMatrix(matrix):

  # First, check if the matrix is not empty. If yes, return the function
  if not len(matrix):
    return
   
  """
    Let us look at the indexing rules to be followed
    the top row is the first row index
    the bottom row is the last row index 
    the leftmost column is the last column index 
    the rightmost column is the first column index 
  """

  top_row = 0
  bottom_row = len(matrix)-1

  left_col = 0
  right_col = len(matrix[0])-1

  # Starting a while loop which will run until the top and left indices of the matrix are less than the bottom and right indices
  while left_col < right_col and top_row < bottom_row:

    # We need to store the first element of the following row
    # This is because while moving the elements forward, the current rotated row's first element will be the next row's first element.
    first = matrix[top_row + 1][left_col]

    # Starting a for loop to move the elements of the top row one step forward or toward the right
    for i in range(left_col, right_col + 1):
      c = matrix[top_row][i]
      matrix[top_row][i] = first
      first = c
    
    # Updating the top row to the next row or moving to the inner ring
    top_row += 1

    # Starting a for loop to move the elements of the right column one step forward or downward 
    for i in range(top_row, bottom_row + 1):
      c = matrix[i][right_col]
      matrix[i][right_col] = first
      first = c

    # Updating the right column to the next column 
    right_col -= 1

    # Starting a for loop to move the elements of the bottom row one step forward or toward the left 
    for i in range(right_col, left_col - 1, -1):
      c = matrix[bottom_row][i]
      matrix[bottom_row][i] = first
      first = c
    # Updating the bottom row to the inner row
    bottom_row -= 1

    # Starting a for loop to move the elements of the left column one step forward or upward
    for i in range(bottom_row, top_row - 1, -1):
      c = matrix[i][left_col]
      matrix[i][left_col] = first
      first = c

    left_col += 1

  return matrix

# Creating a function to print the matrix in the matrix form
def printMatrix(matrix):
  for row in matrix:
    print(row)


# Test case 1
matrix1 =[
     [1, 4, 7],
     [2, 5, 8],
     [3, 6, 9]
    ]

# Test case 2
matrix2 =[
     [1, 5, 9, 13], 
     [2, 6, 10, 14],
     [3, 7, 11, 15],
     [4, 8, 12, 16]
    ]
print("Rotated matrix1:")
matrix1 = rotateMatrix(matrix1)
printMatrix(matrix1)

print("Rotated matrix2:")
matrix2 = rotateMatrix(matrix2)
printMatrix(matrix2) 

Output:

Rotated matrix1:
[2, 1, 4]
[3, 5, 7]
[6, 9, 8]
Rotated matrix2:
[2, 1, 5, 9]
[3, 7, 6, 13]
[4, 11, 10, 14]
[8, 12, 16, 15]

Time Complexity: O(max(m, n) * max(m, n)) is the time complexity of this program where m is the number of rows and n is the number of columns in the matrix

Auxiliary Space: This program will take O(m * n) extra memory space

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