Alphabet#

The Alphabet class represents a custom alphabet and allows conversion between words and ordinal numbers, as well as generating ranges of words.

It defines a positional numeral system over an arbitrary user-defined alphabet, and supports:

• Converting words into ordinal numbers (ordinal).
• Converting ordinal numbers back to words (word).
• Generating inclusive ranges of words (range).
• Calculating range lengths (range_length).

Constructor#

__init__#

Alphabet(alphabet: str) -> Alphabet

Creates an alphabet with the given string of characters. Each character must be unique.

Methods#

ordinal#

ordinal(word: str) -> int

Convert a word into its ordinal index within this alphabet. The empty string maps to 0.

Raises ValueError if the word contains characters not in the alphabet.

word#

word(n: int) -> str

Converts an ordinal number back into its corresponding word.

range#

range(start: str, stop: str) -> Iterator[str]

Generates an inclusive sequence of words between start and stop.

• If start <= stop, the range is ascending.
• If start > stop, the range is descending.

range_length#

range_length(start: str, stop: str) -> int:

Returns the number of elements in the inclusive range from start to stop.

Examples#

Constructing an alphabet:

abc = Alphabet("abc")
print(abc.word(5))        # 'ab'
print(abc.ordinal("ab"))  # 5

Iterating over a range:

abc = Alphabet("abc")
for word in abc.range("a", "ba"):
    print(word)

# Output: a, b, c, aa, ab, ac, ba

Range length:

abc = Alphabet("abc")
print(abc.range_length("a", "ba"))  # 7