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Infix to Postfix Conversion
Infix to Postfix Conversion
• Stacks are widely used in the design and implementation of compilers.
• For example, they are used to convert arithmetic expressions from infix notation to postfix notation.
• An infix expression is one in which operators are located between their operands.
• In postfix notation, the operator immediately follows its operands.
Precedence and PriorityToken Operator Precedence1 Associativity
( )
[ ]
-> .
function call
array element
struct or union member
17 left-to-right
-- ++ increment, decrement2 16 left-to-right
-- ++
!
-
- +
& *
sizeof
decrement, increment3
logical not
one’s complement
unary minus or plus
address or indirection
size (in bytes)
15 right-to-left
(type) type cast 14 right-to-left
* / % mutiplicative 13 Left-to-right
+ - binary add or subtract 12 left-to-right
<< >> shift 11 left-to-right
> >=
< <=
relational
10 left-to-right
== != equality 9 left-to-right
& bitwise and 8 left-to-right
^ bitwise exclusive or 7 left-to-right
bitwise or 6 left-to-right
&& logical and 5 left-to-right
logical or 4 left-to-right
?: conditional 3 right-to-left
= += -=
/= *= %=
<<= >>=
&= ^= =
assignment 2 right-to-left
, comma 1 left-to-right
Examples
Infix Postfix
2+3*4
a*b+5
(1+2)*7
a*b/c
(a/(b-c+d))*(e-a)*c
a/b-c+d*e-a*c
234*+
ab*5+
12+7*
ab*c/
abc-d+/ea-*c*
ab/c-de*ac*-
Algorithm
1. Scan the expression from left to right.2. If any operands comes print it simply3. If any operator comes compare the incoming operator with stack
operator. If the incoming operator priority is higher than stackoperator priority push the incoming operator.
4. If the incoming operator has less priority than the operatorinside the stack then go on popping the operator from top of thestack and print them till this condition is true and then push theincoming operator on top of the stack..
5. If both incoming and stack operator priority are equal then popthe stack operator till this condition is true.
6. If the operator is ‘)’ then go on popping the operators from topof the stack and print them till a matching ‘(‘ operator is found.Delete ‘(‘ from top of the stack..
Suppose we want to convert 2*3/(2-1)+5*3 into Postfix form,
So, the Postfix Expression is 23*21-/53*+
2 Empty 2
* * 2
3 * 23
/ / 23*
( /( 23*
2 /( 23*2
- /(- 23*2
1 /(- 23*21
) / 23*21-
+ + 23*21-/
5 + 23*21-/5
3 +* 23*21-/53
Expression Stack Output
* +* 23*21-/53
Empty 23*21-/53*+
13
Postfix Demo: The EquationInfix: (1 + (2 * ((3 + (4 * 5)) * 6)))
Postfix: 1 2 3 4 5 * + 6 * * +
3+1 ( 2 (* ( (+ 4 5* ) *) 6 ) )( )
( 4 5 *)3( +)( *6 )( 2 *) +1( )
3 +1 2 *+4 5 * *6
4 * 5 = 2020 + 3 = 2323 * 6 = 138138 * 2 = 276276 + 1 = 277
= 277
= 277
14
Postfix Demo: The Stack• What is a ‘STACK’?
• At the grocery store, on the canned goods aisle, the cans are STACKED on top of each other.
• Which one do we take to make sure the stack doesn’t fall over?
• How did the store worker put the cans into the stack? Where did he or she place the new can?
• We take the top item and we place new items on the top. So does the computer.
• To evaluate the problem (1 + (2 * ((3 + (4 * 5)) * 6))), the computer uses a stack and postfix notation.
3 +1 2 *+4 5 * *6
15
Postfix Demo: The Evaluation
3 +1 2 *+4 5 * *6
3
+
1
2
*
+
4
5
*
*4 5 = 2020
203 = 2323
6
623 = 138
138
1382 = 276
276
2761 = 277
277
The Stack
The Answer
FPE Infix to Postfix
( ( ( A + B ) * ( C - E ) ) / ( F + G ) )
• stack: <empty>
• output: []
FPE Infix to Postfix
( ( A + B ) * ( C - E ) ) / ( F + G ) )
• stack: (
• output: []
FPE Infix to Postfix
( A + B ) * ( C - E ) ) / ( F + G ) )
• stack: ( (
• output: []
FPE Infix to Postfix
A + B ) * ( C - E ) ) / ( F + G ) )
• stack: ( ( (
• output: []
FPE Infix to Postfix
+ B ) * ( C - E ) ) / ( F + G ) )
• stack: ( ( (
• output: [A]
FPE Infix to Postfix
B ) * ( C - E ) ) / ( F + G ) )
• stack: ( ( ( +
• output: [A]
FPE Infix to Postfix
) * ( C - E ) ) / ( F + G ) )
• stack: ( ( ( +
• output: [A B]
FPE Infix to Postfix
* ( C - E ) ) / ( F + G ) )
• stack: ( (
• output: [A B + ]
FPE Infix to Postfix
( C - E ) ) / ( F + G ) )
• stack: ( ( *
• output: [A B + ]
FPE Infix to Postfix
C - E ) ) / ( F + G ) )
• stack: ( ( * (
• output: [A B + ]
FPE Infix to Postfix
- E ) ) / ( F + G ) )
• stack: ( ( * (
• output: [A B + C ]
FPE Infix to Postfix
E ) ) / ( F + G ) )
• stack: ( ( * ( -
• output: [A B + C ]
FPE Infix to Postfix
) ) / ( F + G ) )
• stack: ( ( * ( -
• output: [A B + C E ]
FPE Infix to Postfix
) / ( F + G ) )
• stack: ( ( *
• output: [A B + C E - ]
FPE Infix to Postfix
/ ( F + G ) )
• stack: (
• output: [A B + C E - * ]
FPE Infix to Postfix
( F + G ) )
• stack: ( /
• output: [A B + C E - * ]
FPE Infix to Postfix
F + G ) )
• stack: ( / (
• output: [A B + C E - * ]
FPE Infix to Postfix
+ G ) )
• stack: ( / (
• output: [A B + C E - * F ]
FPE Infix to Postfix
G ) )
• stack: ( / ( +
• output: [A B + C E - * F ]
FPE Infix to Postfix
) )
• stack: ( / ( +
• output: [A B + C E - * F G ]
FPE Infix to Postfix
)
• stack: ( /
• output: [A B + C E - * F G + ]
FPE Infix to Postfix
• stack: <empty>
• output: [A B + C E - * F G + / ]
• void infix :: convert( ) • { • char opr ;• while ( *s ) {• if ( *s == ' ' || *s == '\t' ) { • s++ ; • continue ; • }• if ( isdigit ( *s ) || isalpha ( *s ) ) • {• while ( isdigit ( *s ) || isalpha ( *s ) )• {• *t = *s ; s++ ; t-- ;• }• } • if ( *s == ')' ) • {• push ( *s ) ; • s++ ; • }• if ( *s == '*' || *s == '+' || *s == '/' || *s == '%' || *s == '-' || *s == '$' )• {• if ( top != -1 ) • { • opr = pop( ) ;• while ( priority ( opr ) > priority ( *s ) )• {• *t = opr ; • t-- ; • opr = pop( ) ;• } • push ( opr ) ;• push ( *s ) ;• }• else • push ( *s ) ;• s++ ; • } • if ( *s == '(' ) • {• opr = pop( ) ;• while ( ( opr ) != ')' )• {• *t = opr ; • t-- ;• opr = pop ( ) ; • }• s++ ; • }• } • while ( top != -1 ) { opr = pop( ) ; *t = opr ; t-- ; } t++ ; } - See more at: http://electrofriends.com/source-codes/software-programs/cpp-programs/cpp-data-structure/c-program-
to-convert-an-expression-from-infix-expression-to-prefix-form/#sthash.eCuEQFN6.dpuf
