factorial encoder

factorial.py

ordered = ["A", "B", "C", "D", "E", "F"]

def encode_permutation(permutation, ordered):
    ordered = ordered.copy()
    size = len(ordered)
    encoded = 0
    for (i, value) in enumerate(permutation):
        fact = factorial(size - i - 1)
        idx = ordered.index(value)
        ordered.remove(value)
        encoded += fact * idx
    return encoded

def decode_permutation(encoded, ordered):
    ordered = ordered.copy()
    size = len(ordered)
    permutation = []
    for i in range(len(ordered)):
        divisor = factorial(size - i - 1)
        idx = encoded // divisor
        permutation.append(ordered[idx])
        del ordered[idx]
        encoded = encoded % divisor
    return permutation

def factorial(n):
    if n == 0:
        return 1
    return n * factorial(n - 1)

for encoded in range(factorial(len(ordered))):
    roundtripped = encode_permutation(decode_permutation(encoded, ordered), ordered)
    if roundtripped != encoded:
        print("bad")

permutation = ["D", "C", "A", "B", "F", "E"]
print("Permutation", permutation)
encoded = encode_permutation(permutation, ordered)
print("Encoded", encoded) # Prints '409' 
decoded = decode_permutation(encoded, ordered)
print("Decoded    ", decoded)