first state of clr 1 parser

Question

I have doubts regarding first state clr1 parser of below grammer

A→ Au | At | w

Select the correct option which represent initial state in LR(1) state diagram.

i think it should be

S –> .A , $

A –> . Au , u|$

A –> . At , t|$

A →  .w , u|t|$

but i am not sure.

Comments

except the augmented production, all production will contain $, u, t as lookahead

Answer 1

All the productions will be having $\$$ as the lookahead in the initial state.
S->.A, $\$$

A->.Au, $\$$

A->.At, $\$$

A->.w,$\$$