Match words against a letter pattern

Given a pattern string and a list of words, decide for each word whether it follows the pattern.

A word follows the pattern when it has the same length as the pattern and the letters line up through a one-to-one correspondence:

• every occurrence of a given pattern letter lines up with the same word letter, and
• two different pattern letters never line up with the same word letter.

Implement:

def match_words(pattern: str, words: list[str]) -> list[bool]:
    ...

Return a list of booleans, one per word, in input order.

Constraints

• 0 <= len(pattern) <= 10^4, 0 <= len(words) <= 10^4
• Strings may contain any characters; treat each character as a symbol.
• Aim for time linear in the total number of characters.

Example 1

pattern = "abba"
words   = ["xyyx", "xxxx", "qrrq", "xyzx", "xyy"]
output  = [True, False, True, False, False]

"xxxx" fails because a and b would both map to x. "xyy" fails because the lengths differ.

Example 2

pattern = "abc"
words   = ["cab", "dee", "xyz"]
output  = [True, False, True]

Be ready to extend this: patterns whose letters stand for whole words in a sentence, grouping a dictionary by shape, and letters that stand for substrings of unknown length.

Reconstructed from the reported question; details may differ from what interviewers ask.