Let's use these equations to assign values to each of the 17 (French) letters below:

Anywhere the word any appears, a random number can be entered. As a result, infinitely many solutions are possible, for example (for A=20 and N=7):

For all values assigned to the 17-letter alphabet in this way, the following applies:

It can be shown that the above equations are the only ones that result in Z+E+R+O=0, U+N=1, …. Any extension of the French numbers beyond TREIZE is impossible without distinct letters receiving repeated values.

Assignment

We represent an alphabet as a sequence of uppercase letters (str) in which each letter appears at most once.

We represent the values assigned to the letters of an alphabet as a sequence (list or tuple) of integers (int). Each value corresponds to the letter at the corresponding position in the alphabet, so the number of values in the sequence must be equal to the number of letters in the alphabet.

A word is a sequence of uppercase letters (str) in which the same letter may appear more than once. We represent a sequence of words as a string (str) in which the words are separated from each other by commas (,).

Your task:

• Write a function word_value that takes three arguments: i) a word, ii) an alphabet and iii) values assigned to the letters of the alphabet. The function must return the sum (int) of the values assigned to the letters of the given word. This sum is called the word value.

• Write a function word_values that takes three arguments: i) a sequence of words, ii) an alphabet and iii) values assigned to the letters of the alphabet. The function must return a tuple with the values (int) of each word in the given sequence of words.

• Write a function issorted that takes a sequence (list or tuple) of integers (int). The function also has a second optional parameter decreasing that may take a Boolean value (bool, default value: False). The function also has a third optional parameter strict that may take a Boolean value (bool, default value: False). The function must return a Boolean value (bool) that indicates if the given sequence of integers is sorted in increasing (decreasing=False) or decreasing (decreasing=True) order. If the value True is passed to the parameter strict, the same number may not appear more than once in the sequence (so the sequence must be strictly increasing or strictly decreasing).

• Write a function sort that takes three arguments: i) a sequence of words, ii) an alphabet and iii) values assigned to the letters of the alphabet. The function also has a fourth optional parameter decreasing that may take a Boolean value (bool, default value: False). The function must return a list containing the words (str) from the given sequence. These words must be listed according to increasing (decreasing=False) or decreasing (decreasing=True) word value. Words with the same value must be listed in alphabetical (decreasing=False) or reverse alphabetical (decreasing=True) order.

  Tip

  Both the sort¹ method and the built-in function sorted² have a key parameter to specify a function to be called on each element prior to making comparisons. This function takes a single argument and returns a key to use for sorting purposes. More info³.

All of the above functions may assume that the given words only exist of uppercase letters from the given alphabet, without the need to check this explicitly.

Example

>>> french_alphabet = 'ACDEFHINOPQRSTUXZ'
>>> french_values = [20, -19, 14, 16, -8, 17, 18, 7, 0, 2, -1, -4, 10, -21, -6, -22, -12]
>>> french_numbers = 'ZERO,UN,DEUX,TROIS,QUATRE,CINQ,SIX,SEPT,HUIT,NEUF,DIX,ONZE,DOUZE,TREIZE'

>>> english_alphabet = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
>>> english_values = [-10, -14, 17, -6, -14, 17, 17, 5, -12, 6, 7, 18, 3, -6, -3, 15, -16, -15, -10, 11, -12, -13, -7, 20, -16, 17]
>>> english_numbers = 'ZERO,ONE,TWO,THREE,FOUR,FIVE,SIX,SEVEN,EIGHT,NINE,TEN'

>>> word_value('ZERO', french_alphabet, french_values)
0
>>> word_value('UN', french_alphabet, french_values)
1
>>> word_value('DEUX', french_alphabet, french_values)
2
>>> word_value('TROIS', french_alphabet, french_values)
3
>>> word_value('QUATRE', french_alphabet, french_values)
4

>>> word_values(english_numbers, english_alphabet, english_values)
(-15, -23, 1, -27, -13, -22, -2, -57, 7, -38, -9)
>>> word_values(french_numbers, french_alphabet, french_values)
(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13)
>>> word_values(french_numbers, english_alphabet, english_values)
(-15, -18, -12, -29, -56, -17, -2, 2, -8, -15, 2, -6, -18, -27)

>>> issorted((0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13))
True
>>> issorted((0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13), strict=True)
True
>>> issorted((0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13), decreasing=True)
False
>>> issorted((0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13), decreasing=True, strict=True)
False
>>> issorted((13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0), decreasing=True, strict=True)
True

>>> sort(english_numbers, english_alphabet, english_values)
['SEVEN', 'NINE', 'THREE', 'ONE', 'FIVE', 'ZERO', 'FOUR', 'TEN', 'SIX', 'TWO', 'EIGHT']
>>> sort(french_numbers, french_alphabet, french_values, True)
['TREIZE', 'DOUZE', 'ONZE', 'DIX', 'NEUF', 'HUIT', 'SEPT', 'SIX', 'CINQ', 'QUATRE', 'TROIS', 'DEUX', 'UN', 'ZERO']
>>> sort(french_numbers, english_alphabet, english_values, decreasing=True)
['SEPT', 'DIX', 'SIX', 'ONZE', 'HUIT', 'DEUX', 'ZERO', 'NEUF', 'CINQ', 'UN', 'DOUZE', 'TREIZE', 'TROIS', 'QUATRE']