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Merge pull request #34 from miguelHx/miguel_1.7_rotate_matrix
Miguel 1.7 - Rotate Matrix [Python]
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‎Python/chapter01/1.7 - Rotate Matrix/miguel_1.7_sol.py

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"""
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Python version 3.7.0
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1.7 - Rotate Matrix
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Given an image represented by an NxN matrix, where each pixel in the image is 4 bytes, write a method to rotate
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the image by 90 degrees. Can you do this in place?
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"""
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import unittest
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from typing import List
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def rotate_matrix(matrix: List[List[int]]) -> List[List[int]]:
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"""
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Rotate matrix will rotate the given matrix by 90 degrees.
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Runtime: O(N^2), asymptotic runtime depends on N
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Space Complexity: O(N^2), creating a new matrix of NxN called 'rotated'
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:param matrix: an NxN matrix
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:param N: the size of the matrix (NxN)
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:return: a newly rotated matrix
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"""
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N = len(matrix)
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rotated = [[0 for i in range(N)] for j in range(N)]
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for i in range(N):
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for j in range(N):
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rotated[j][(N-1)-i] = matrix[i][j]
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return rotated
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def _perform_full_rotation(matrix: List[List[int]], row: int, col: int, M: int):
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"""
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Helper function that performs four 90 degree rotations starting at row, col.
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at a particular row and column from the matrix, there will be 4 rotations.
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visually, the algorithm looks like this:
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[start] (4th swap with original 3rd) - - - - - - - - - - - - - - - - - - -> (1st gets swapped with start)
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| |
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| |
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| |
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| |
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(3rd swap with original 2nd) < - - - - - - - - - - - - - - - - - - - - - - (2nd gets swapped with original 1st)
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this results in a full rotation in-place of a particular row and col coordinate.
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:param matrix: an MxM sub-matrix out of an NxN matrix
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:param row: starting row
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:param col: starting column
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:param M: size of sub-matrix
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:return:
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"""
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num_rotations = 4
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start_row = row
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rotated_row = row
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rotated_col = col
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temp_new = matrix[row][col]
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for _ in range(0, num_rotations):
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# compute new rotated indices
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# (start_row * 2) is an offset to account for reduced M into sub-matrices of matrix
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rotated_col, rotated_row = M - 1 - rotated_row + (start_row * 2), rotated_col
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# store value at newly computed indices
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temp_new, matrix[rotated_row][rotated_col] = matrix[rotated_row][rotated_col], temp_new
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def rotate_matrix_in_place(matrix: List[List[int]]) -> List[List[int]]:
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"""
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Does the same as rotate_matrix, but in place.
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Runtime: O(N^2), asymptotic runtime depends on N. We make N^2 swaps.
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Space Complexity: O(1), constant amount of temp variables that does not depend on N.
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:param matrix: an NxN matrix
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:return: the input matrix, but rotated
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"""
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N = len(matrix)
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# outer loop will keep reducing the matrix size 'n' by 2.
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# For example, a 6x6 matrix contains a 4x4 sub-matrix, we reduce
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# because at first, the values on the perimeter of the matrix will
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# be rotated after the inner for-loop, and we want to start rotating
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# the next sub-matrix perimeter.
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for start_row, n in enumerate(range(N, 1, -2)):
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# rotate along the current row's columns of the current sub-matrix perimeter
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for col in range(start_row, n - 1 + start_row):
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# performs 4 rotations for the current sub-matrix coordinate
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_perform_full_rotation(matrix, start_row, col, n)
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return matrix
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class TestRotateMatrixFunction(unittest.TestCase):
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def setUp(self):
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self.cases = [
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(
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[
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[1, 2, 3, 4],
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[5, 6, 7, 8],
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[9, 10, 11, 12],
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[13, 14, 15, 16]
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],
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[
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[13, 9, 5, 1],
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[14, 10, 6, 2],
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[15, 11, 7, 3],
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[16, 12, 8, 4]
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]
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),
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(
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[
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[1, 2, 3],
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[4, 5, 6],
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[7, 8, 9]
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],
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[
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[7, 4, 1],
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[8, 5, 2],
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[9, 6, 3]
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]
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),
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(
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[
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[1]
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],
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[
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[1]
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]
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),
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(
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[
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[1, 2, 3, 4, 5, 6],
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[7, 8, 9, 10, 11, 12],
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[13, 14, 15, 16, 17, 18],
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[19, 20, 21, 22, 23, 24],
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[25, 26, 27, 28, 29, 30],
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[31, 32, 33, 34, 35, 36]
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],
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[
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[31, 25, 19, 13, 7, 1],
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[32, 26, 20, 14, 8, 2],
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[33, 27, 21, 15, 9, 3],
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[34, 28, 22, 16, 10, 4],
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[35, 29, 23, 17, 11, 5],
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[36, 30, 24, 18, 12, 6]
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]
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),
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(
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[
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[1, 2, 3, 4, 5],
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[6, 7, 8, 9, 10],
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[11, 12, 13, 14, 15],
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[16, 17, 18, 19, 20],
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[21, 22, 23, 24, 25]
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],
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[
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[21, 16, 11, 6, 1],
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[22, 17, 12, 7, 2],
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[23, 18, 13, 8, 3],
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[24, 19, 14, 9, 4],
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[25, 20, 15, 10, 5]
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]
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),
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(
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[
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[1, 2, 3, 4, 5, 6, 7],
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[8, 9, 10, 11, 12, 13, 14],
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[15, 16, 17, 18, 19, 20, 21],
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[22, 23, 24, 25, 26, 27, 28],
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[29, 30, 31, 32, 33, 34, 35],
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[36, 37, 38, 39, 40, 41, 42],
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[43, 44, 45, 46, 47, 48, 49]
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],
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[
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[43, 36, 29, 22, 15, 8, 1],
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[44, 37, 30, 23, 16, 9, 2],
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[45, 38, 31, 24, 17, 10, 3],
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[46, 39, 32, 25, 18, 11, 4],
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[47, 40, 33, 26, 19, 12, 5],
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[48, 41, 34, 27, 20, 13, 6],
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[49, 42, 35, 28, 21, 14, 7]
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]
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)
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]
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def test_rotate_matrix(self):
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for matrix, expected in self.cases:
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self.assertEqual(rotate_matrix(matrix), expected, msg=(matrix, expected))
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def test_rotate_matrix_in_place(self):
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for matrix, expected in self.cases:
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self.assertEqual(rotate_matrix_in_place(matrix), expected, msg=(matrix, expected))
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if __name__ == '__main__':
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unittest.main()

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