The first step in parsing a language often involves matching an input string against a set of a patterns.

In this problem, we allow a pattern to be any sequence of alphabetic letters $($e$.$g$.,\text{'}$a$\text{'},\text{'}$b$\text{'},...,\text{'}$z$\text{'})$ and the special character $\text{'}?\text{'}($which can be any single alphabetic character$).$ For example, the pattern ab$?$d$?$f would match the inputs $$abcdef$,$abbddf$,$ and $$abzdzf$,$ but it would not match $$bbbbbb$$ or $$abc$.$

We call a set of patterns unambiguous if no input string can be matched by two or more patterns in the set. For example, the set of patterns $\{$a$,$ bc$,?$a$\}$ is unambiguous, but the set of patterns $\{$a$,$ bc$,?$c$\}$ is ambiguous because the patterns bc and $?$c both match the input string $$bc$.$

Given a set of patterns, briefly describe an efficient algorithm that determines whether the set is ambiguous. You may use one of the following data structures to help you: BST$,$ AVL Tree, Trie, LLRB Tree.

Your description should take $1-2$ sentences. Be sure to also justify the efficiency of your answer by providing the worst case running time of your algorithm in O$()$ notation. Use the variable n to represent the number of patterns in your set.