Cryptarithmetic Puzzle

'''
Good morning! Here's your coding interview problem for today.
This problem was asked by Google.
A cryptarithmetic puzzle is a mathematical game where the digits of some numbers are represented by letters.
Each letter represents a unique digit.
For example, a puzzle of the form:
  SEND
+ MORE
--------
 MONEY
may have the solution:
{'S': 9, 'E': 5, 'N': 6, 'D': 7, 'M': 1, 'O', 0, 'R': 8, 'Y': 2}
Given a three-word puzzle like the one above, create an algorithm that finds a solution.
'''
from itertools import permutations
from timeit import default_timer as timer

# FUNCTION 1
def breakMessage(message):
    # First, I have to find the '+' and '=' characters
    plusIndex = message.index('+')
    equalsIndex = message.index('=')
    word1 = message[0 : plusIndex-1]
    word2 = message[plusIndex+2 : equalsIndex-1]
    word3 = message[equalsIndex+2:]
    return word1, word2, word3

# FUNCTION 2
def uniqueLetters(word1, word2, word3):
    words = word1 + word2 + word3
    unique = list()
    for letter in words:
        isUnique = True
        for un in unique:
            if letter == un:
                isUnique = False
                break
        if isUnique == True:
            unique.append(letter)
    return unique

# FUNCTION 3
def matchLists(list1, list2):
    if len(list1) != len(list2):
        print("Error while using function " + matchLists.__name__)
    dictionary = dict()
    for i in range(len(list1)):
        dictionary[list1[i]] = list2[i]
    return dictionary


# FUNCTION 4
def match(message):
    word1, word2, word3 = breakMessage(message)
    unique = uniqueLetters(word1, word2, word3)
    # Now, we have a list with unique letters. Let's suppose N unique letters
    # Each unique letter can take values from 0 to 9, so there are
    # 10 ^ N possible arrangements. So I will create all the 10^N possible
    # permutations. Each index of permutation can be from 0 to 9.
    # I will equalise each permutation with the letters
    N = len(unique)
    perms = permutations(list(range(10)), N)
    N1 = len(word1)
    N2 = len(word2)
    N3 = len(word3)
    solutionLetters = dict()
    solutionNumbers = list()

    for perm in perms:
        dictionary = matchLists(unique, perm)
        # print(dictionary)
        number1 = 0
        number2 = 0
        number3 = 0
        # ===============================================================================
        # ===============================================================================
        # Word 1 ----> Number 1
        for i in range(N1):
            letter = word1[i]
            digit = -1
            for key in dictionary:
                if letter == key:
                    digit = dictionary[key]
                    break
            number1 += digit * (10**(N1-1-i))
        # Word 2 ----> Number 2
        for i in range(N2):
            letter = word2[i]
            digit = -1
            for key in dictionary:
                if letter == key:
                    digit = dictionary[key]
                    break
            number2 += digit * (10**(N2-1-i))
        # Word 3 ----> Number 3
        for i in range(N3):
            letter = word3[i]
            digit = -1
            for key in dictionary:
                if letter == key:
                    digit = dictionary[key]
                    break
            number3 += digit * (10**(N3-1-i))
        # ===============================================================================
        # ===============================================================================
        # Now, I have all the 3 numbers I want
        perm = [number1, number2, number3]
        # print(perm)
        if number1 + number2 == number3:
            # print("YES, WE FOUND A SOLUTION TO THIS PROBLEM")
            solutionLetters = dictionary
            solutionNumbers = perm
            break

    if len(solutionLetters) != 0:
        # We have found a solution
        return solutionLetters, solutionNumbers
    else:
        # There is no solution
        return {}, []


# FUNCTION 5
def prettyPrint(message):
    start = timer()
    print("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")
    solutionLetters, solutionNumbers = match(message)
    print(message)
    if len(solutionLetters) != 0:
        result = ""
        M = len(solutionLetters)
        counter = 0
        for key in solutionLetters:
            if counter != M - 1:
                result += key + " = " + str(solutionLetters[key]) + ", "
            else:
                result += key + " = " + str(solutionLetters[key])
        print("Solution for: " + result)
        print(str(solutionNumbers[0]) + " + " + str(solutionNumbers[1]) + " = " + str(solutionNumbers[2]))
        end = timer()
        elapsed = end - start
        print()
        print("Execution time: " + str(round(elapsed, 4)) + " seconds.")
        print("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")
        print()
    else:
        print("There is no solution for this problem")
        print("Next time")


# MAIN FUNCTION
# RULES
print("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")
print("We are trying to match letters with numbers, so we can have an acceptable addition")
print("But, the user has to leave blank space between and after the symbols '+' and '='")
print("One good example is: send + more = money")
print("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")
print()
message1 = "ab + ba = cc"
prettyPrint(message1)
message2 = "send + more = money"
prettyPrint(message2)
message3 = input("Message: ")
prettyPrint(message3)