Question

1. Given the following grammar and LR Parser table, trace the parse of “id+id*id” and draw the parse tree.

(1) E -> E + T

(2) E -> E – T

(3) E -> T

(4) T -> T * F

(5) T -> T / F

(6) T -> F

(7) F -> (E)

(8) F -> id

State	id	+	-	*	/	(	)	$	E	T	F
0	S5					S4			1	2	3
1		S6	S7					Acc
2		R3	R3	S8	S9		R3	R3
3		R6	R6	R6	R6		R6	R6
4	S5					S4			10	2	3
5		R8	R8	R8	R8		R8	R8
6	S5					S4				11	3
7	S5					S4				12	3
8	S5					S4					13
9	S5					S4					14
10		S6	S7				S15
11		R1	R1	S8	S9		R1	R1
12		R2	R2	S8	S9		R2	R2
13		R4	R4	R4	R4		R4	R4
14		R5	R5	R5	R5		R5	R5
15		R7	R7	R7	R7		R7	R7

Stack                                                   Input                Entry               Action/Production

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Answer 1

The trace for the string id + id * id is :

Stack	Input Entry	Actions
$	id+id*id $	Shift id
$id	+id*id $	Reduce F -> id
$F	+id*id $	Reduce T -> F
$T	+id*id $	Reduce E -> T
$E	+id*id $	Shift +
$E+	id*id $	Shift id
$E+id	*id $	Reduce F -> id
$E+F	*id $	Reduce T -> F
$E+T	*id $	Shift *
$E+T *	id $	Shift id
$E+T*id	$	Reduce F -> id
$E+T*F	$	Reduce T -> T*F
$E+T	$	Reduce E -> E+T
$E	$	accept

The parse tree for the string is :