CS132 HW1 LL(1) Parsing Solution

Grammar
-------
S->E$    (this is very important)
E->TE'
E'->+TE'
E'->-TE'
E'->e    (e is epsilon)
T->FT'
T'->*FT'
T'->/FT'
T'->e
F->num   (where num->0...9)
F->(E)

Note that 0..9, +, -, *, /, (, and ) are terminals
and that everything else is non-terminal.

First Set
---------
First(S)=First(E)
First(E)={num, (}
First(E')={+,-,e}
First(T)={num, (}
First(T')={*, /, e}
First(F)={num, (}

Follow Set
----------
Follow(S)={}
Follow(E)={), $}
Follow(E')={), $}
Follow(T)={+, -, ), $}
Follow(T')={+,-,),$}
Follow(F)={*, /, +, -, ), $}

Parsing Table
-------------
	+	-	*	/	(	)	num	$
E	!	!	!	!	->TE'	!	->TE'	!
E'	->+TE	->-TE	!	!	!	->e	!	->e
T	!	!	!	!	->FT'	!	->FT'	!
T'	->e	->e	->*FT'	/FT'	!	T'->e	!	T'->e
F	!	!	!	!	->(E)	!	F->num	!
Where the character ! denotes error.

Explanation of LL(1)
--------------------
No conflict/duplicates in the entry.
Lookahead is one symbol.
No left recursion in the grammar.
Factored grammar.

==============================================
Grading Criteria for 10 points

up to -2 points for incorrect grammar/typo/symbol
  Additional -2 points for no precedence in the grammar.
up to -2 points for incorrect symbol in the first set
  -1 if no epsilon or didn't say which symbols are nullable
  -1 if no start state
up to -2 points for incorrect symbol in the follow set
  -1 each mistake
  -1 if no $ or EOF
up to -2 points for the table
  -1 each mistake
up to -2 for incorrect or incomplete explanation of
why the grammar is LL(1).
  -1 each missing explanation
  -2 if didn't explain at all