rotate matrix Algorithm
The rotate matrix algorithm is an efficient method used in computer science and mathematics to perform rotation operations on a matrix, typically a two-dimensional square matrix. This algorithm is often used in image processing, computer graphics, and linear algebra for rotating an image or a set of data points by a specific angle. The main goal of this algorithm is to transpose the matrix and then reverse either its rows or columns, resulting in the rotated matrix. The algorithm can be applied to rotate the matrix by 90, 180, or 270 degrees, either clockwise or counterclockwise.
To illustrate the rotate matrix algorithm, let's consider rotating a square matrix by 90 degrees clockwise. The first step is to transpose the matrix, which means swapping the rows and columns - elements on the main diagonal remain the same, while the other elements are interchanged accordingly. After transposing, the next step is to reverse the order of the columns. This results in a matrix that has been rotated by 90 degrees clockwise. To rotate the matrix by 90 degrees counterclockwise, the order of operations would be to transpose the matrix and then reverse the rows. For 180-degree rotation, the algorithm can be applied twice for a 90-degree rotation, or simply reverse both the rows and columns of the matrix. The rotate matrix algorithm is highly useful in practice due to its simplicity and efficiency in performing matrix rotations.
"""
In this problem, we want to rotate the matrix elements by 90, 180, 270 (counterclockwise)
Discussion in stackoverflow:
https://stackoverflow.com/questions/42519/how-do-you-rotate-a-two-dimensional-array
"""
def make_matrix(row_size: int = 4) -> [[int]]:
"""
>>> make_matrix()
[[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]]
>>> make_matrix(1)
[[1]]
>>> make_matrix(-2)
[[1, 2], [3, 4]]
>>> make_matrix(3)
[[1, 2, 3], [4, 5, 6], [7, 8, 9]]
>>> make_matrix() == make_matrix(4)
True
"""
row_size = abs(row_size) or 4
return [[1 + x + y * row_size for x in range(row_size)] for y in range(row_size)]
def rotate_90(matrix: [[]]) -> [[]]:
"""
>>> rotate_90(make_matrix())
[[4, 8, 12, 16], [3, 7, 11, 15], [2, 6, 10, 14], [1, 5, 9, 13]]
>>> rotate_90(make_matrix()) == transpose(reverse_column(make_matrix()))
True
"""
return reverse_row(transpose(matrix))
# OR.. transpose(reverse_column(matrix))
def rotate_180(matrix: [[]]) -> [[]]:
"""
>>> rotate_180(make_matrix())
[[16, 15, 14, 13], [12, 11, 10, 9], [8, 7, 6, 5], [4, 3, 2, 1]]
>>> rotate_180(make_matrix()) == reverse_column(reverse_row(make_matrix()))
True
"""
return reverse_row(reverse_column(matrix))
# OR.. reverse_column(reverse_row(matrix))
def rotate_270(matrix: [[]]) -> [[]]:
"""
>>> rotate_270(make_matrix())
[[13, 9, 5, 1], [14, 10, 6, 2], [15, 11, 7, 3], [16, 12, 8, 4]]
>>> rotate_270(make_matrix()) == transpose(reverse_row(make_matrix()))
True
"""
return reverse_column(transpose(matrix))
# OR.. transpose(reverse_row(matrix))
def transpose(matrix: [[]]) -> [[]]:
matrix[:] = [list(x) for x in zip(*matrix)]
return matrix
def reverse_row(matrix: [[]]) -> [[]]:
matrix[:] = matrix[::-1]
return matrix
def reverse_column(matrix: [[]]) -> [[]]:
matrix[:] = [x[::-1] for x in matrix]
return matrix
def print_matrix(matrix: [[]]) -> [[]]:
for i in matrix:
print(*i)
if __name__ == "__main__":
matrix = make_matrix()
print("\norigin:\n")
print_matrix(matrix)
print("\nrotate 90 counterclockwise:\n")
print_matrix(rotate_90(matrix))
matrix = make_matrix()
print("\norigin:\n")
print_matrix(matrix)
print("\nrotate 180:\n")
print_matrix(rotate_180(matrix))
matrix = make_matrix()
print("\norigin:\n")
print_matrix(matrix)
print("\nrotate 270 counterclockwise:\n")
print_matrix(rotate_270(matrix))
