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Some more magic and "factorials". solution in Clear category for Reversed Permutation Index by sjosef23
from typing import Iterable
def reversed_permutation_index(length: int, index: int) -> Iterable[int]:
# For a (maybe) better insight in this solution see my solution for "Permutation Index".
from math import factorial
# Fix indexing.
index_temp = index-1
# List of factorials we will need.
facts = [factorial(x) for x in reversed(range(length))]
# Consecutive intiger divisions of the index with the factorials
# gives us the 'order' of the numbers we want to find e.g.:
# In the list [1, 2, 0] the 'order' of the numbers is [1, 1, 0], because:
# a) the 1 is in position 1 in (0, 1, 2)
# b) the 2 is in position 1 in (0, 2) (the 1 is already used)
# c) the 0 is in position 0 in (0) (the 1 and 2 are already used)
nums = []
for fact in facts:
nums.append(index_temp//fact)
index_temp -= nums[-1]*fact
# From the 'order' of the numbers get the numbers.
numbers_range = [x for x in range(length)]
return [numbers_range.pop(num) for num in nums]
if __name__ == '__main__':
assert tuple(reversed_permutation_index(3, 5)) == (2, 0, 1)
assert tuple(reversed_permutation_index(9, 279780)) == (6, 8, 3, 4, 2, 1, 7, 5, 0)
assert tuple(reversed_permutation_index(6, 271)) == (2, 1, 3, 0, 4, 5)
assert tuple(reversed_permutation_index(12, 12843175)) == (0, 4, 7, 5, 8, 2, 10, 6, 3, 1, 9, 11)
assert tuple(reversed_permutation_index(15, 787051783737)) == (9, 0, 6, 2, 5, 7, 12, 10, 3, 8, 11, 4, 13, 1, 14)
assert tuple(reversed_permutation_index(18, 3208987196401056)) == (9, 0, 6, 17, 8, 12, 11, 1, 10, 14, 3, 15, 2, 13, 16, 7, 5, 4)
assert tuple(reversed_permutation_index(21, 38160477453633042937)) == (15, 13, 14, 6, 10, 5, 19, 16, 11, 0, 9, 18, 2, 17, 4, 20, 12, 1, 3, 7, 8)
assert tuple(reversed_permutation_index(24, 238515587608877815254677)) == (9, 5, 4, 12, 13, 17, 7, 0, 23, 16, 11, 8, 15, 21, 2, 3, 22, 1, 10, 19, 6, 20, 14, 18)
assert tuple(reversed_permutation_index(27, 6707569694907742966546817183)) == (16, 17, 10, 23, 4, 22, 7, 18, 2, 21, 13, 6, 9, 8, 19, 3, 25, 12, 26, 24, 14, 1, 0, 20, 15, 5, 11)
Oct. 25, 2019
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