FACTORIAL MATH

from random import randint

def INFINITY_UNIQUE_NUMBER_SERIES(x, *args):
    if (len(args) > 0): return INFINITY_UNIQUE_NUMBER_SERIES((x * 2 - 1) * (2 ** args[0]), *args[1:])
    return x


def FACTORIAL(x):
    result = 1
    for i in range(0, x):
        result = result * (i + 1)
    return result

def FACTORIAL_BASE(x):
    results = []
    radix = 1
    while x > 0:
        current = x % radix
        results = [int(current)] + results
        x = (x - current) / radix
        radix += 1
    return results

def DECIMAL_TO_PERMUTATION(decimal, factorial_list, factorial_list_count = 0):
    if (factorial_list_count == 0):
        factorial_list_count = len(factorial_list)
    current_permutation = FACTORIAL_BASE(decimal)
    new_factorial_list = factorial_list.copy()

    permutation = []
    permutation2 = []
    for i in range(0, len(new_factorial_list) - len(current_permutation) - 0):
        permutation2 = permutation2 + [new_factorial_list.pop(0)]
    for element in current_permutation:
        current_factorial = new_factorial_list.pop(element)
        permutation = permutation + [current_factorial]
    while len(new_factorial_list) > 0:
        permutation2 = permutation2 + [new_factorial_list.pop(0)]
    return permutation2, permutation, current_permutation

def FACTORIAL_BASE_TO_DECIMAL(factorial_base, padding = 0):
    current_radix = len(factorial_base) - 1
    decimal = 0
    for current_number in factorial_base:
        decimal = current_number * FACTORIAL(current_radix) + decimal
        current_radix = current_radix - 1
    return decimal

def PERMUTATION_TO_FACTORIAL_BASE(current_business_slot_list, static_business_slot_list):
    current_static_business_slot_list = static_business_slot_list.copy()
    factorial_base = []

    while len(current_static_business_slot_list) > len(current_business_slot_list):
        current_static_business_slot_list.pop(0)

    for current_business_slot in current_business_slot_list:
        current_index = current_static_business_slot_list.index(current_business_slot)
        current_static_business_slot_list.pop(current_index)
        factorial_base = factorial_base + [current_index]
    return factorial_base

def PERMUTATION_TO_DECIMAL(permutation, static_business_slots):
    return FACTORIAL_BASE_TO_DECIMAL(PERMUTATION_TO_FACTORIAL_BASE(permutation, static_business_slots))


def PERMUTATION_MAX(slots):
    return FACTORIAL(slots)

# EXAMPLE:
#business_slots = ["MATH", "SCIENCE", "WAR", "ART", "PSYCHOLOGY", "BIOLOGY", "ELECTRICITY", "BUSINESS", "RELIGION", "MARTIAL ART", "MARTIAL WAR", "PRODUCTION"]

business_slots = ["PRODUCTION", "MARTIAL WAR", "MARTIAL ART", "RELIGION", "BUSINESS", "ELECTRICITY", "BIOLOGY", "PSYCHOLOGY", "ART", "WAR", "SCIENCE", "MATH"]

for permutation_number in range(0, PERMUTATION_MAX(6)):
    permutation = DECIMAL_TO_PERMUTATION(permutation_number, business_slots)
    print("CURRENT_ITERATION: " + str(permutation_number) + ", " + str(permutation))
    print("DECIMAL: " + str(PERMUTATION_TO_DECIMAL(permutation[1], business_slots)))
    print("\n")

print(str(PERMUTATION_TO_DECIMAL(["MATH", "WAR", "SCIENCE", "PSYCHOLOGY", "ART"], business_slots)))
print(str(DECIMAL_TO_PERMUTATION(112, business_slots)))