example2.py

#!/usr/bin/python


def combinations(digits):
    keys = {
        "2": "abc",
        "3": "def",
        "4": "ghi",
        "5": "jkl",
        "6": "mno",
        "7": "pqrs",
        "8": "tuv",
        "9": "wxyz",
    }

    def backtrack(combination, next_digits):
        if len(next_digits) == 0:
            result.append(combination)
        else:
            letters = keys[next_digits[0]]
            for letter in letters:
                backtrack(combination + letter, next_digits[1:])

    result = []
    if digits:
        backtrack("", digits)
    return result


print(combinations("23")) # ['ad', 'ae', 'af', 'bd', 'be', 'bf', 'cd', 'ce', 'cf']
print(combinations("")) # []
print(combinations("2")) # ['a', 'b', 'c']