Operator- Precedence With Parser Problem

Operator Precedence (Order of Operation):

Precedence	Operator	Description	Associativity
1	::	Scope resolution	Left-to-right
2	++   --	Suffix/postfix increment and decrement
	()	Function call
	[]	Array subscripting
	.	Element selection by reference
	−>	Element selection through pointer
3	++   --	Prefix increment and decrement	Right-to-left
	+   −	Unary plus and minus
	!   ~	Logical NOT and bitwise NOT
	(type)	Type cast
	*	Indirection (dereference)
	&	Address-of
	sizeof	Size-of
	new, new[]	Dynamic memory allocation
	delete, delete[]	Dynamic memory reallocation
4	.*   ->*	Pointer to member	Left-to-right
5	*   /   %	Multiplication, division, and remainder
6	+   −	Addition and subtraction
7	<<   >>	Bitwise left shift and right shift
8	<   <=	For relational operators < and ≤ respectively
	>   >=	For relational operators > and ≥ respectively
9	==   !=	For relational = and ≠ respectively
10	&	Bitwise AND
11	^	Bitwise XOR (exclusive or)
12	|	Bitwise OR (inclusive or)
13	&&	Logical AND
14	||	Logical OR
15	?:	Ternary conditional	Right-to-left
	=	Direct assignment (provided by default for C++ classes)
	+=   −=	Assignment by sum and difference
	*=   /=   %=	Assignment by product, quotient, and remainder
	<<=   >>=	Assignment by bitwise left shift and right shift
	&=   ^=   |=	Assignment by bitwise AND, XOR, and OR
16	throw	Throw operator (for exceptions)
17	,	Comma	Left-to-right

Operator- Precedence Parser Problem:

Grammar:

List              list + list

          |         list – list

          |         digit

digit            0|1|2|-------------|9

Problem:      9-5+4

Proposed Solution (1):

                                     

                                    

                                               

Proposed Solution (2):

                                      

Answer:   Solution 2 is correct. As the operators of given problem are not unary, their associativity is left to right. So, plus (+) operator precedence is high than minus (-) operator. Again, operator precedence parser in a bottom-up parser so minus (-) operator operation will be done before plus (+) operator operation.

              

References:

1.     http://en.cppreference.com/w/cpp/language/operator_precedence

2.     http://en.wikipedia.org/wiki/Operator-precedence_parser