import math

EVAL_FUN = {**math.__dict__}

def extract_letters(words: list[str]) -> set[str]:
    """Extracts unique letters from a list of words

    :param words: list of leafs
    :return: set of letters

    :example:
    >>> leafs = ["a", "a*k"]
    >>> extract_letters(leafs) == {'a', 'k'}
    True
    """
    letters = set()
    for word in words:
        for c in word:
            if c.isalpha():
                letters.add(c)
    return letters


def eval_words(words: list[str], values: dict[str, int]) -> dict[str, int]:
    """Evaluate words replacing letters with values

    :param words: list of words
    :param values: Dictionary of letters:value
    :return: Dictionary of evaluated words from generated values

    In words, you have access to all math module functions

    :example:
    >>> leafs = ["a", "a*k"]
    >>> generated_values = {"a":2, "k":3}
    >>> eval_words(leafs, generated_values)
    {'a': 2, 'a*k': 6}
    >>> leafs = ["exp(a)", "gcd(a, k)"]
    >>> generated_values = {"a":2, "k":3}
    >>> eval_words(leafs, generated_values)
    {'exp(a)': 7.38905609893065, 'gcd(a, k)': 1}
    """
    return {word: eval(word, EVAL_FUN, values) for word in words}