rearrange the items on the shelf by decreasing popularity rating such that the rating for the i item is always greater than the popularity rating of the (i + 1) item.

minimal_swaps.py

"""
Question:
Mary can perform the following minimal sequence of swap operations to 
successfully sort all 3 items by decreasing popularity rating: [3, 1, 2] → [3, 2, 1].

Solution:
1. The swap always compares the last element in the array with
 the least element in the remaining list e.g.  
 in the case  of [3, 1, 2, 4]...we compare 4 with the minimum value in [3,1,2]
  and swap the two if the minimum value is less
2. Repeat 1 until the the list is sorted in descending order
3. Do the above while counting the swaps"""

def minimum_swaps(ratings):
    if sorted(ratings, reverse=True) == ratings:
       return 0
    swaps = 1
    while sorted(ratings, reverse=True) != sorter(ratings):
        swaps += 1
    return swaps

def sorter(array):

    for i in sorted(range(len(array)), reverse=True):    
        comp = array[:i]
        if len(comp) > 0:
            mini = min(comp)

        if mini < array[i]:
            index = array.index(mini)

            array[i], array[index] = array[index], array[i]
            return array

    return array

test_minimum_swaps.py

import unittest
from minimum_swaps import minimum_swaps

class Test(unittest.TestCase):
    def test_cases(self):
        self.assertEqual(minimum_swaps([3, 2, 1]), 0) 
        self.assertEqual(minimum_swaps([3, 1, 2]), 1) 
        self.assertEqual(minimum_swaps([3, 1, 2, 4]), 2)

if __name__ == '__main__':
    unittest.main()