This Slides Will Help You About Infix And Postfix Expression.

1. PRESENTATION
OF
DATA STRUCTURE & ALGORITHM
BY
Mohammad Saeed Farooqi

2.  INFIX Notation.
 POSTFIX Notation.
 PREFIX Notation.
 OPERATORS PRECEDENCE.
 Evaluating Of POSTFIX Expression Using Stacks.
 Converting INFIX To POSTFIX Using Stacks.
 ALGORITHMS.

OUTLINES
Mohammad Saeed Farooqi (University Of Swat, Pakistan)

3.  Infix Expression Are Those In Which Operators Are
Written Between Two Operands.
 Infix Expression Is The Common Arithmetic And
Logical Formula Expression.
 Infix Expression Needs Extra Information To Make The
Order Of Evaluation Of The Operators Clear.
 Rules Built Into The Language About Operator
Precedence And Associativity, And Brackets ( ) To Allow
Users To Override These Rules.
 INFIX EXPRESSION
Mohammad Saeed Farooqi (University Of Swat, Pakistan)

4.  EXAMPLE…
 A * ( B + C ) / D…
 This Expression Is Usually Taken To Mean Something
Like: "First Add B And C Together, Then Multiply The
Result By A, Then Divide By D To Give The Final
Answer.
 INFIX EXPRESSION
Mohammad Saeed Farooqi (University Of Swat, Pakistan)

5.  POSTFIX Expression Also Known As “Reverse Polish
Expression”
 In These Expressions Operators Are Written After Their
Operands.
 Operators Act On Values Immediately To The Left Of
Them.
 They Do Not Have (Brackets)
 POSTFIX EXPRESSION
Mohammad Saeed Farooqi (University Of Swat, Pakistan)

6.  EXAMPLE…
 A B C + * D /…
 Operators Act On Values Immediately To The Left Of
Them.
 For Example, The "+" Above Uses The "B" And "C".
 We Can Add (Totally Unnecessary) Brackets To Make
This Easy.
( (A (B C +) *) D /) .
 POSTFIX EXPRESSION
Mohammad Saeed Farooqi (University Of Swat, Pakistan)

7.  Also Known As “Polish Expression”.
 In These Expressions Operators Are Written Before The
Operands.
 We Have To Scan It From Right-To-Left.
 As For Postfix, Operators Are Evaluated Left-To-Right And
Brackets Are Superfluous.
 Operators Act On The Two Nearest Values On The Right.
 I Have Again Added (Totally Unnecessary) Brackets To Make
This Clear.
(/ (* A (+ B C) ) D)
 PREFIX Notation Is Especially Popular With StackBased Operations Due To Its Innate Ability To Easily
Distinguish Order Of Operations Without The Need For
Parentheses.
 PREFIX EXPRESSION
Mohammad Saeed Farooqi (University Of Swat, Pakistan)

8.  We Assume The Following Three Levels Of
PRECEDENCE For The Usual Five Binary Operations.
 Highest
Exponentiation ().
 Next Highest Multiplication (*) And Division (/)
Superfluous
 Lowest
Addition (+) And Subtraction (-)
 Without Understanding Operator Precedence You Can
Not Convert Any Expression.
 OPERATOR PRECEDENCE
Mohammad Saeed Farooqi (University Of Swat, Pakistan)

9.  EVOLUACTION OF POSTFIX EXPRESSION
Mohammad Saeed Farooqi (University Of Swat, Pakistan)

10. • EvaluatePostfix(exp)
• {
• Create A Stack S.
• for I ← 0 to length of the (exp)-1
{
if(exp[i]) // Is An Operand
push(exp[i]);
else if(exp[i])
// Is An Operator
{
op1←pop();
op2← pop();
result←perform(exp[i],op1,op2);
push(result);
}
}
}
 ALGORITHM FOR POSTFIX EVALUATION
Mohammad Saeed Farooqi (University Of Swat, Pakistan)

11. Converting Infix To Postfix
Mohammad Saeed Farooqi (University Of Swat, Pakistan)

12. •
•
•
•
•
•
•
Example: 1*2+3.
Scan: *,+ (Stack) And 12 (Postfix Expression).
Precedence Of * Is Higher Than +.
Thus, Append * to postfix Expression.
+ (Stack) And 12* (Postfix Expression ).
Scan Further, + (Stack ) and 12*3 (Postfix Expression)
There Are No Further Operators, Thus, Postfix Is 12*3+
Converting Infix To Postfix
Mohammad Saeed Farooqi (University Of Swat, Pakistan)

13. Converting Infix To Prefix
Mohammad Saeed Farooqi (University Of Swat, Pakistan)

14. • Step 1. Push “)” onto STACK, and add “(“ to end of the A.
• Step 2. Scan A from right to left and repeat step 3 to 6 for each element of A
until the STACK is empty.
• Step 3. If an operand is encountered add it to B.
• Step 4. If a right parenthesis is encountered push it onto STACK.
• Step 5. If an operator is encountered then: a. Repeatedly pop from STACK
and add to B each operator (on the top of STACK) which has same or higher
precedence than the operator. b. Add operator to STACK.
• Step 6. If left parenthesis is encontered then a. Repeatedly pop from the
STACK and add to B (each operator on top of stack until a left parenthesis is
encounterd) b. Remove the left parenthesis.
• Step 7. Exit
Converting Infix To Postfix
Mohammad Saeed Farooqi (University Of Swat, Pakistan)