Track (min possible open count) and (max possible open count). For '(': both increase by . For ')': both decrease by . For '*': decreases (could be ')'), increases (could be '('). Keep (clamp it).
If , there are too many ')' no matter what. At end, check . The range represents the minimum and maximum possible open parentheses count at each position.
If , there are too many ')' no matter how you assign '*'.
If at the end, some assignment of '*' balances the string. Clamping to handles impossible negative counts.