Superpermutations Paradotea

from itertools import permutations

n = int(input("Enter n: "))
Permutations = list(permutations(range(1,n+1)))             # Permutations: list of tuples (each tuple contain a combination)
#print("Initial List: " + str(Permutations))


from itertools import permutations

# 1st function (Paragontiko)
def factorial(x):
    if x== 0:
        return 1;
    else:
        return x*factorial(x-1);

# 2nd function (Synartisi pou antigrafei olo to string/arithmo ektos tou teleutaiou grammatos)
def copyPartOfTuple(myTuple):                    # Argument myTuple = Tuple like one of each unique combinations in Permutations
    newList = list(myTuple)                      # Make typecast to the tuple ---> becomes list
    size = len(newList)
    newList += newList
    del newList[2*size-1]                       # Delete to stoixeio se index = 2*size-1
    return newList

# 3rd funtion (Synartisi pou sou anapodogyrizei to string kai sto kollaei sto arxiko ---> Symmetria)
def reverseAndExtendList(list):
    initialList = list.copy()                   # Copy the list to variable initialList
    list.reverse()                              # EINAI VOID !!!! Den epistrefei lista h synartisi list.reverse() ---> Exei allaxei pleon h list kai egine anapodi
    initialList.extend(list)                    # Enwnei tin arxiki list (initialList) me tin allagmeni/reversed lista (list)
    return initialList


'''
# 4th funtion (Kanei n=4 swsta)
def makeNCorrectChoices(n, list):          # Synithws nCorrect = 4
    newList = []
    for i in range(nCorrect):                                       # Kanw n loops
        for j in range(nCorrect-1):                                 # Gia kathe loop koitw ta n-1 teleytaia grammata
            newList.append(list[(len)list -1 -j])                   # kai ta vazw mesa se 1 alli lista
        # H newList exei n-1=3 grammata k psaxnw poio leipei
'''




# * * * * M A I N * * * *
print("All the permutations from 1 to " + str(n) + " is the following list: ")
print(Permutations);                                                                 # Swsto ws edw
print();


# CASE 1
if n ==1:
    print("The shortest permutation has length " + str(factorial(n)))
    print("This permutation is: 1");

# CASE 2
elif n == 2:
    print("The shortest permutation has length " + str(factorial(n) + factorial(n-1)))
    print("Found 2 permutations/solutions is: 121 or 212")

# CASE 3
elif n == 3:
    print("**** All the solutions for n = 3 are the following: :****")
    size = 0
    for i in range(len(Permutations)):
        print(str(i+1) + ") When tuple is: " + str(Permutations[i]) + ", solution is: ");
        plusList = copyPartOfTuple(Permutations[i])          # [1,2,3] ---> [1,2,3,1,2]
        result = reverseAndExtendList(plusList)              # To exw kanei symmetriko (tin plusList)
        del result[ int(len(result)/2) ]                     # TELOS DIADIKASIAS ---> To result einai LISTA
        size = len(result)
        print(''.join(map(str, result)))
        print()

    print("So,all of these results (found 6 solutions) have the minimum length which is: " + str(size))
    print("*****************************************")
    print("*****************************************")

# CASE 4
elif n==4:
    print("**** All the solutions for n = 4 are the following: :****")
    for i in range(len(Permutations)):
        print(str(i + 1) + ") When tuple is: " + str(Permutations[i]) + ", solution is: ");
        size = 0
        myList = copyPartOfTuple(Permutations[i])  # Make 4 correct
        myList.append(Permutations[i][0])  # Stin for tha allaksei mono to 1o kai tha ginei i to 2o 0 meneiiiii
        myList.append(myList[len(myList) - (n + 1)])
        myList.append(myList[len(myList) - n])
        myList.append(myList[len(myList) - n])
        myList.append(myList[len(myList) - n])
        myList.append(Permutations[i][1])
        myList.append(myList[len(myList) - (n + 1)])
        myList.append(myList[len(myList) - n])
        myList.append(myList[len(myList) - n])
        myList.append(myList[len(myList) - n])  # Swsto to miso akrivws string
        result = reverseAndExtendList(myList)  # To exw kanei symmetriko (tin myList)
        del result[int(len(result) / 2)]  # TELOS DIADIKASIAS ---> To result einai LISTA
        size = len(result)
        print(''.join(map(str, result)))
        print()

    print("So,all of these results (found 24 solutions) have the minimum length which is: " + str(size))
    print("*****************************************")
    print("*****************************************")


else:

    # 1) Beginning: Result = 1st element of Pemrutations
    result = ""
    flag = False

    #print(str(Permutations[0][0]))
    for i in range(n):                                          # Scanning n times
        result += str(Permutations[0][i])                       # Result = "123" for example
    del Permutations[0]
    print("Initial List: " + str(Permutations))


    # 2) Continue
    depth = n-1                                                  # In which depth are we searching for same strings
    # Loop: Ends when depth = 0 (when Permutations has no elements)
    while len(Permutations) > 0:

        if flag:
            depth -= 1
        else:
            depth = n-1

        flag = True


        for i in range (len(Permutations)):                  # Sarwnei olon ton pinaka (n! fores osa kai ta diafora tuples = permutations)
            eystoxies = 0
            for j in range (depth):                   # Sarwnei tin apantisi mou = result
                if result[len(result)-1-j] == str(Permutations[i][depth-1-j]):   # !!!! (AAAA)
                    eystoxies += 1

            if eystoxies == depth:                   # An oses fores epsaksa (depth), toses fores eixa epityxia se "taytisi string"
                for k in range(n - depth):            # Iterations = n - depth: depth epityxies ---> prepei na balw n-depth grammata akoma
                    result += str(Permutations[i][depth+k])       # !!!! (AAAA)

                del Permutations[i]
                flag = False
                break

    print("Result: " + result)
    print("Length: " + str(len(result)))