Download presentation

Presentation is loading. Please wait.

Published byMary Oliver Modified over 4 years ago

1
INFIX, PREFIX, & POSTFIX EXPRESSIONS

2
Infix Notation We usually write algebraic expressions like this: a + b This is called infix notation, because the operator (+) is inside the expression A problem is that we need parentheses or precedence rules to handle more complicated expressions: For Example : a + b * c = (a + b) * c ? = a + (b * c) ?

3
Infix, Postfix, & Prefix notation There is no reason we cant place the operator somewhere else. How ? Infix notation : a + b Prefix notation : + a b Postfix notation: a b +

4
Other Names Prefix notation was introduced by the Polish logician Lukasiewicz, and is sometimes called Polish notation. Postfix notation is sometimes calledreverse Polish notation or RPN.

5
Why ? Question: Why would anyone ever want to use anything so unnatural, when infix seems to work just fine? Answer: With postfix and prefix notations, parentheses are no longer needed!

6
Example infix postfix prefix (a + b) * c a b + c * * + a b c a + (b * c) a b c * + + a * b c Infix form : Postfix form : Prefix form :

7
Operator priority

8
Converting Infix to Postfix & Prefix

9
Example

10
Infix to Postfix Conversion Algorithm else // ch must be some other operator { while operator stack not empty and precedence(top(S)) precedence(ch) and top(S) != ( do pop operator; append it to the postfix string; end while; push S } end for; while operator stack is not empty do pop operator; append it to the postfix string; endwhile; given a legal infix string; create an initially empty postfix string; create an initially empty operator stack S; for each symbol ch in the infix string do if ch is an operand then append it to the output postfix string; else if ch == ( then push ch onto stack S; else if S == ) then pop and append operators to output string until the matching ( is encountered; // discard the two parentheses

11
Evaluating Postfix Expression

12
Additional Reading Conversion Algorithm for Prefix Exp.

13
Infix to Prefix Conversion algorithm#1

14
Infix to Prefix Conversion algorithm#1 Example

15
Infix to Prefix Conversion algorithm#2

16
Evaluating Prefix Expression

17
Convert from Infix to Prefix and Postfix (Practice) x x + y (x + y) - z w * ((x + y) - z) (2 * a) / ((a + b) * (a - c))

18
Convert from Postfix to Infix (Practice) 3 r - 1 3 r - + s t * 1 3 r - + + v w x y z * - + *

Similar presentations

Presentation is loading. Please wait....

OK

COSC 2006 Chapter 7 Stacks III

COSC 2006 Chapter 7 Stacks III

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on social contract theory of john Ppt on zener diode characteristics Ppt on private public and global enterprises Ppt on online examination system in php pdf Ppt on personality development for teachers Ppt on tcp/ip protocol and osi model Ppt on bridges in computer networks Ppt on air pollution for students Ppt on data handling for class 7th results Ppt on resistance temperature detector failures