1. Data Structures and Algorithms
Prof. Ajit A. Diwan
Prof. Ganesh Ramakrishnan
Prof. Deepak B. Phatak
Department of Computer Science and Engineering
IIT Bombay
Session: Infix to Postfix
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

2. Infix to Postfix Expressions
Operator is placed after all its operands
No need of parentheses
Examples
Infix Expressions
Postfix Expressions
a + b
a b +
(a + b) * (a - b)
a b + a b - *
(a ^ b * (c + (d * e) - f ) ) / g
a b ^ c d e * + f - * g /
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

3. Infix to Postfix using Stack
Consider infix expression
a+b (Input string)
Postfix expression will be
ab+ (Output string)
We have 2 operands (a, b) and 1 operator (+)
Use stack to facilitate the process
Push operators on the stack based on some conditions
Output String: Assemble operands and operators
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

4. Example 1: Implementation
Infix Expression: a+b
Push operator on stack
Append operands and operator to the string
Infix element
Operator Stack
Postfix String
Comments a
Append ‘a’ +
Push ‘+’ b ab
Append ‘b’
ab+
Append ‘+’
Note: Operator in red color denotes the element at the top of the stack
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

5. Example 2: Implementation
Infix Expression: a+b*c
Infix element
Operator Stack
Postfix String
Comments a
Append ‘a’ +
Push ‘+’ b ab
Append ‘b’ * +*
Push ‘*’ c
abc
Append ‘c’
abc*
Append ‘*’
abc*+
Append ‘+’
‘*’ has higher precedence than ‘+’
Note: Operator in red color denotes the element at the top of the stack
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

6. Example 3: Implementation
Infix Expression: a*b+c
Infix element
Operator Stack
Postfix String
Comments a
Append ‘a’ *
Push ‘*’ b ab
Append ‘b’ +
ab*
Append ‘*’
Push ‘+’ c
ab*c
Append ‘c’
ab*c+
Append ‘+’
‘+’ has lower precedence than ‘*’
Note: Operator in red color denotes the element at the top of the stack
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

7. Example 4: Implementation
Infix Expression: (a^b*(c+(d*e-f)))
Infix String
Operator Stack
Postfix String
Comments (
Push ‘(‘ a
Append ‘a’ ^ (^
Push ‘^’ b ab
Append ‘b’ *
ab^
Append ‘^’ (*
Push ‘*’
(*( c
ab^c
Append ‘c’
Note: Operator in red color denotes the element at the top of the stack
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

8. Example 4: Implementation
Infix Expression: (a^b*(c+(d*e-f)))
Infix String
Operator Stack
Postfix String
Comments +
(*(+
ab^c
Push ‘+’ (
(*(+(
Push ‘(‘ d
ab^cd
Append ‘d’ *
(*(+(*
Push ‘*‘ e
ab^cde
Append ‘e’ -
ab^cde*
Append ‘*’
(*(+(-
Push ‘-’
Note: Operator in red color denotes the element at the top of the stack
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

9. Example 4: Implementation
Infix Expression: (a^b*(c+(d*e-f)))
Infix String
Operator Stack
Postfix String
Comments f
(*(+(-
ab^cde*f
Append ‘f’ )
(*(+(
ab^cde*f-
Append ‘-’
(*(+
Pop ‘(‘
(*(
ab^cde*f-+
Append ‘+’ (* (
ab^cde*f-+*
Append ‘*’
Note: Operator in red color denotes the element at the top of the stack
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

10. References https://en.wikipedia.org/wiki/Stack_(abstract_data_type)
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

11. Thank you
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay