## [f]izzbuzzer

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# Rotate Matrix / Image challenge

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Problem statement
You are given an $n \times n$ 2D matrix / array representing an image. Rotate matrix by 90 degrees (clockwise) in-place.

Solution
We will work through the matrix layers. The layers of a matrix are illustrated below in different colours:

There are a total of $\lfloor\dfrac{n}{2}\rfloor$ layers. We then iterate of the length of each layer and shift our matrix cells, side for side:

for c in range(l, n-l-1):
top = m[l][c]

# left goes to top
m[l][c] = m[n-1-c][l]

# bottom goes to left
m[n-1-c][l] = m[n-l-1][n-c-1]

# right goes to bottom
m[n-l-1][n-c-1] = m[c][n-l-1]

# top goes to right
m[c][n-l-1] = top


We need to temporary store the element of the top side of a layer before we replace it because we are going to need it at the end of the circle top <- left <- bottom <- right <- top. And thats it.

The full code is listed below.

Full code

import numpy as np
class Solution(object):
def rotate(self, m):
"""
:type matrix: List[List[int]]
:rtype: void Do not return anything, modify matrix in-place instead.
"""
n = len(m)
for l in range(0,n//2):
for c in range(l, n-l-1):
top = m[l][c]

# left goes to top
m[l][c] = m[n-1-c][l]

# bottom goes to left
m[n-1-c][l] = m[n-l-1][n-c-1]

# right goes to bottom
m[n-l-1][n-c-1] = m[c][n-l-1]

# top goes to right
m[c][n-l-1] = top

print(np.matrix(m))

def main():
solution = Solution()
solution.rotate([[1]])
solution.rotate([[1,2],[3,4]])
solution.rotate([[1,2,3],[4,5,6],[7,8,9]])
solution.rotate([[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]])
solution.rotate([[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15],[16,17,18,19,20],[21,22,23,24,25]])

if __name__ == "__main__": main()