What could be possible NFA for the RegEx "a?"

Question

I am trying to use the Thompson's method to draw an NFA for a RegEx given by: $(a+b|c?)c$

I am wondering if I should deconstruct the RegEx as -

1. Concatenation of $a+$, $(b|c?)$ together with $c$ OR
2. Union of $a$ and $(b|c?)$ concatenated with $c$

In either case, I would the need the atomic NFA construction for the $c?$. I am unable to figure it out.

Please help.

Answer 1

I would assume that $+$ and $|$ do not both mean union, so the regex is actually (assuming POSIX syntax) $$a^+ (b + c + \varepsilon) c \equiv aa^\ast (b + c + \varepsilon) c.$$ You should be able to figure out the NFA if you know the Thompson construction.