# Infix to Postfix Conversion

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1 Infix to Postfix Conversion

2 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.

3 Precedence and Priority Token Operator Precedence 1 Associativity ( ) [ ] ->. function call array element struct or union member 17 left-to-right increment, decrement 2 16 left-to-right -- ++! & * sizeof decrement, increment 3 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

4 + - 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

5 ?: conditional 3 right-to-left = += -= /= *= %= <<= >>= &= ^= = assignment 2 right-to-left, comma 1 left-to-right

6 Examples Infix 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 Postfix 234*+ ab* * ab*c/ abc-d+/ea-*c* ab/c-de*ac*-

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9 Algorithm 1. Scan the expression from left to right. 2. If any operands comes print it simply 3. If any operator comes compare the incoming operator with stack operator. If the incoming operator priority is higher than stack operator priority push the incoming operator. 4. If the incoming operator has less priority than the operator inside the stack then go on popping the operator from top of the stack and print them till this condition is true and then push the incoming operator on top of the stack.. 5. If both incoming and stack operator priority are equal then pop the stack operator till this condition is true. 6. If the operator is ) then go on popping the operators from top of the stack and print them till a matching ( operator is found. Delete ( from top of the stack..

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12 Suppose we want to convert 2*3/(2-1)+5*3 into Postfix form, Expression Stack Output 2 Empty 2 * * 2 3 * 23 / / 23* ( /( 23* 2 /( 23*2 - /(- 23*2 1 /(- 23*21 ) / 23* *21-/ *21-/5 * +* 23*21-/53 3 +* 23*21-/53 Empty 23*21-/53*+ So, the Postfix Expression is 23*21-/53*+

13 Postfix Demo: The Equation Infix: (1 + (2 * ((3 + (4 * 5)) * 6))) = 277 Postfix: * + 6 * * + = 277 ( 1 + ( 2 * ( ( 3 + ( 4 * 5 ) ) * 6 ) ) ) ( 1 ( 2 ( ( 3 ( 4 5 ) * ) + 6 ) * ) * ) * + * 5 * + 36 = 21 = 20 = * + 6 * * + 13

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 * + 6 * * + 14

15 Postfix Demo: The Evaluation * + 6 * * + The Stack * 5 = = * 6 = 138 The Answer 2 * 138 = =

16 ( ( ( A + B ) * ( C - E ) ) / ( F + G ) ) stack: <empty> output: []

17 ( ( A + B ) * ( C - E ) ) / ( F + G ) ) stack: ( output: []

18 ( A + B ) * ( C - E ) ) / ( F + G ) ) stack: ( ( output: []

19 A + B ) * ( C - E ) ) / ( F + G ) ) stack: ( ( ( output: []

20 + B ) * ( C - E ) ) / ( F + G ) ) stack: ( ( ( output: [A]

21 B ) * ( C - E ) ) / ( F + G ) ) stack: ( ( ( + output: [A]

22 ) * ( C - E ) ) / ( F + G ) ) stack: ( ( ( + output: [A B]

23 * ( C - E ) ) / ( F + G ) ) stack: ( ( output: [A B + ]

24 ( C - E ) ) / ( F + G ) ) stack: ( ( * output: [A B + ]

25 C - E ) ) / ( F + G ) ) stack: ( ( * ( output: [A B + ]

26 - E ) ) / ( F + G ) ) stack: ( ( * ( output: [A B + C ]

27 E ) ) / ( F + G ) ) stack: ( ( * ( - output: [A B + C ]

28 ) ) / ( F + G ) ) stack: ( ( * ( - output: [A B + C E ]

29 ) / ( F + G ) ) stack: ( ( * output: [A B + C E - ]

30 / ( F + G ) ) stack: ( output: [A B + C E - * ]

31 ( F + G ) ) stack: ( / output: [A B + C E - * ]

32 F + G ) ) stack: ( / ( output: [A B + C E - * ]

33 + G ) ) stack: ( / ( output: [A B + C E - * F ]

34 G ) ) stack: ( / ( + output: [A B + C E - * F ]

35 ) ) stack: ( / ( + output: [A B + C E - * F G ]

36 ) stack: ( / output: [A B + C E - * F G + ]

37 stack: <empty> output: [A B + C E - * F G + / ]

38 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:

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