Python 3 function to rotate an image 90° A coding challenge that rotates an image 90 degrees counterclockwise. The image is represented as an array matrix. I believe the time complexity is O(n2), but I'd like to know for sure, as well as any other feedback.

def rotate_image(img):
    rotated_image = [[] for x in range(len(img))]
    for i in range(len(img)):
        for j in range(len(img[i])):
          rotated_image[len(img) - j - 1].append(img[i][j])
    return rotated_image


Example usage:

image = [
  [1, 1, 5, 9, 9],
  [2, 2, 6, 0, 0],
  [3, 3, 7, 1, 1],
  [4, 4, 8, 2, 2],
  [5, 5, 9, 3, 3]
]

rotated_img = rotate_image(image)
for i in rotated_img:
    print(i)


Outputs:

[9, 0, 1, 2, 3]
[9, 0, 1, 2, 3]
[5, 6, 7, 8, 9]
[1, 2, 3, 4, 5]
[1, 2, 3, 4, 5]
You can use NumPy module that's good with arrays and matrices. It has a built-in for exactly that purpose -

import numpy as np

np.rot90(image).tolist()


With array manipulations, that's essentially same as performing matrix/array transpose and then flipping the rows -

np.asarray(image).T[::-1].tolist()


If the input is already an array, we can skip the array-conversion. Also, if the output as an array is okay, it would be simply a view into the input and as such the entire operation would be virtually-free.

Thus, with image_arr as the input array, it would be -

np.rot90(image_arr)


With transpose and flipping rows -

image_arr.T[::-1]


Let's take the provided sample and check out outputs on an IPython console -

In [48]: image
Out[48]: 
[[1, 1, 5, 9, 9],
 [2, 2, 6, 0, 0],
 [3, 3, 7, 1, 1],
 [4, 4, 8, 2, 2],
 [5, 5, 9, 3, 3]]

In [50]: np.asarray(image).T[::-1].tolist()
Out[50]: 
[[9, 0, 1, 2, 3],
 [9, 0, 1, 2, 3],
 [5, 6, 7, 8, 9],
 [1, 2, 3, 4, 5],
 [1, 2, 3, 4, 5]]


Timings on a large 5000 x 5000 sized image

1) Image as a list :

In [53]: image = np.random.randint(0,256,(5000,5000)).tolist()

# @Dima Tisnek's soln
In [54]: %timeit list(reversed(list(zip(*image))))
1 loop, best of 3: 1.09 s per loop

In [55]: %timeit np.array(image).T[::-1].tolist()
1 loop, best of 3: 1.06 s per loop


Time-complexity

There's no time-complexity involved here (not on computation anyway) and the entire play is about array and list conversion, as shown below when we break down the steps -

In [72]: image_arr = np.array(image)

In [71]: %timeit np.array(image) # convert to array
1 loop, best of 3: 771 ms per loop

In [73]: %timeit image_arr.T[::-1] # perform 90deg rotation
1000000 loops, best of 3: 372 ns per loop

In [74]: %timeit image_arr.T[::-1].tolist() # convert back to list
1 loop, best of 3: 296 ms per loop


2) Image and output as arrays :

In [56]: image = np.random.randint(0,256,(5000,5000))

# @Dima Tisnek's soln
In [57]: %timeit list(reversed(list(zip(*image))))
1 loop, best of 3: 1.34 s per loop

In [58]: %timeit image.T[::-1]
1000000 loops, best of 3: 363 ns per loop

In [59]: %timeit np.rot90(image)
100000 loops, best of 3: 9.05 µs per loop


The last two NumPy based ones are virtually free as discussed earlier.  This is because internally image.T[::-1] is same as input image, but with different stride pattern representation. Let's verify that they are same by checking their memory occupancy -

In [60]: np.shares_memory(image, image.T[::-1])
Out[60]: True


Conversion to list on own-data for slight perf. boost

Closer inspection on list conversion reveals that converting to list when the strided pattern isn't regular (row-order) might not be the most optimal scenario. So, one way would be create a copy of array data once we have the rotated one and then convert. This seems to give around 10% improvement -

In [2]: image = np.random.randint(0,256,(5000,5000)).tolist()

In [8]: %timeit list(reversed(list(zip(*image))))
1 loop, best of 3: 1.12 s per loop

In [9]: %timeit np.asarray(image).T[::-1].tolist()
1 loop, best of 3: 1.11 s per loop

# Have own-data (copy) and then convert to list
In [10]: %timeit np.asarray(image).T[::-1].copy().tolist()
1 loop, best of 3: 1.01 s per loop