Clockwise matrix rotation

rotate.py

def cycles(size, depth=0):
    # we use (x,y) notation
    if size < 2:
        return iter([])

    not_aware_of_depth = (cycle(offset, size) for offset in range(0, size - 1))
    cycles_at_current_depth = (
        (go_right(go_down(p, depth), depth) for p in cycle)
        for cycle in not_aware_of_depth
    )
    for x in cycles_at_current_depth:
        yield x
    for x in cycles(size - 2, depth + 1):
        yield x

def go_right(point, distance):
    x,y = point
    return (x + distance, y)

def go_down(point, distance):
    x,y = point
    return (x, y + distance)

def go_left(point, distance):
    x,y = point
    return (x - distance, y)

def go_up(point, distance):
    x,y = point
    return (x, y - distance)

def cycle(offset, size):
    # we use (x,y) notation
    upper_left = (0,0)
    upper_right = (size - 1, 0)
    lower_right = (size - 1, size - 1)
    lower_left = (0, size - 1)
    return [
        go_right(upper_left, offset),
        go_down(upper_right, offset),
        go_left(lower_right, offset),
        go_up(lower_left, offset)
    ]

def perform_cycle(matrix, cycle):
    # rotate.perform_cycle([[0,1,2,3,4]], [(0,0), (1,0), (2,0), (3,0), (4,0)])
    # ---->   [[4, 0, 1, 2, 3]]

    first, *rest = cycle
    x,y = first
    return iterate_cycle(matrix, rest + [first], matrix[y][x])

def iterate_cycle(matrix, cycle, swap):
    # a 'cycle' of (a,b,c) means,
    # 'put a where b was, then put b where c was, then put c where a was'
    # so at any moment you have just put an item down, but you've displaced a new item
    # and this code says, "put one thing down, and pick up a new one"
    first, *rest = cycle
    x,y = first
    new_swap = matrix[y][x]
    matrix[y][x] = swap
    if len(rest) == 0:
        return matrix
    else:
      return iterate_cycle(matrix, rest, new_swap)

def rotate_clockwise(m):
    for c in cycles(len(m)):
        perform_cycle(m,c)
    return m

def make_square_matrix(size):
    return [list(range(size* x, (size*x)+size)) for x in range(size)]

def main():
    m = make_square_matrix(1000)
    print('starting')
    rotate_clockwise(m)
    print('done')
#abc
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