BUSINESS_MATH

# FORWARDS PERMUTATION (FIRST TO LAST)
# FOR: WHOEVER
# FROM: NICHOLAS STEVEN DAVILA (Imk0tter/LiTHiuM)
def INFINITY_UNIQUE_NUMBER_SERIES(x, *args):
    if (len(args) > 0): return INFINITY_UNIQUE_NUMBER_SERIES(((x + 0) * 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 tuple(results)

def DECIMAL_TO_PERMUTATION(number, factorial_list):
    current_permutation = FACTORIAL_BASE(number)
    new_factorial_list = list(reversed(tuple(factorial_list)))

    permutation = []
    permutation2 = []

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

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

def PERMUTATION_TO_FACTORIAL_BASE(business_slot_list, static_business_slot_list):
    current_static_business_slot_list = list(reversed(tuple(static_business_slot_list)))
    current_business_slot_list = list(reversed(tuple(business_slot_list)))

    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", "ART", "WAR", "MARTIAL ART", "MARTIAL WAR", "BIOLOGY", "PSYCHOLOGY", "PRODUCTION", "COMPUTING"]

for permutation_number in range(0, PERMUTATION_MAX(6)):
    permutation = DECIMAL_TO_PERMUTATION(permutation_number, business_slots)
    print(str(permutation))