How to determine the FIRST set of E in this grammar?

I wonder how to determine the FIRST set of E with grammar:

E -> XYE | e
X -> x
Y -> y

Ca开发者_如何学编程n anyone give me some direction?

Well, assuming that you're starting with E, then either the first terminal is x via the E→XYE production (since X always produces x) or it is e via the E→e production. So First(E) = {x,e}.

That seems pretty straightforward...

Treat rules of the form A -> ...x... | ...y .... as two rules A -> ...x... and B -> ...y...

Form a set S initially containing rules of form E-> ....

then

Set a set P to empty.
Set a set F to empty.
Repeat until S is empty 
  Choose element of S, and call it R
  If R is in P, remove R from S
  Elsif R is of the form  A -> b ... 
    then { add b to F,
           add R to P,
           remove R from S}
  Else (R is the form A -> B ...)
     then  { place all rules of form B -> ... into S
             remove R from S}
End

WHen the loop terminates, F contains the tokens which are the First(F).

This does not take into account empty productions.