Suppose you're given a string $s$ that consists of lowercase alphabetic letters only. The length of the string is $n$. You are also given $n$ cards, which have lowercase alphabetic letters on the front and back. You want to arrange (shuffle and/or flip each card) the $n$ cards in an order that produces the string. You can use either side of a card, but obviously not both.
I am wondering if this problem can be converted to a Hungarian Algorithm problem? We essentially have a bipartite graph here. The left part consists of $n$ nodes representing each character in $s$. For each character in $s$, there is a subset of the $n$ cards that can can be used to create that character.
Can this be turned into a problem that can be solved with the Hungarian algorithm?