Download presentation

Presentation is loading. Please wait.

Published byGretchen Sumler Modified over 2 years ago

1
Arithmetic Expressions Infix form –operand operator operand 2+3 or a+b –Need precedence rules –May use parentheses 4*(3+5) or a*(b+c)

2
Arithmetic Expressions Postfix form –Operator appears after the operands (4+3)*5 : 4 3 + 5 * 4+(3*5) : 4 3 5 * + –No precedence rules or parentheses! Input expression given in postfix form –How to evaluate it?

3
Evaluating Postfix Expressions Use a stack, assume binary operators +,* Input: postfix expression Scan the input –If operand, push to stack –If operator pop the stack twice apply operator push result back to stack

4
Example Input 5 9 8 + 4 6 * * 7 + * Evaluation push(5) push(9) push(8) push(pop() + pop()) /* be careful for ‘-’ */ push(4) push(6) push(pop() * pop()) push(7) push(pop() + pop()) push(pop() * pop()) print(pop()) What is the answer?

5
Exercise Input 6 5 2 3 + 8 * + 3 + * Input a b c * + d e * f + g * + For each of the previous inputs –Find the infix expression

6
Infix to Postfix Conversion Observation –Operands appear in the same order in both –Output operands as we scan the input –Must put operators somewhere use a stack to hold pending operators –‘)’ indicates both operands have been seen Will allow only +, *, ‘(‘, and ‘)’, and use standard precedence rules Assume legal (valid) expression

7
Conversion Algorithm Output operands as encountered Stack left parentheses When ‘)’ –repeat pop stack, output symbol –until ‘(‘ ‘(‘ is poped but not output If symbol +, *, or ‘(‘ –pop stack until entry of lower priority or ‘(‘ ‘(‘ removed only when matching ‘)’ is processed –push symbol into stack At end of input, pop stack until empty

8
Exercises (5 * (((9 + 8) * (4 * 6)) + 7)) 6 * (5 + (2 + 3) * 8 + 3) a + b * c + (d * e + f) * g

Similar presentations

Presentation is loading. Please wait....

OK

Stack Applications.

Stack Applications.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

View my ppt online maker Ppt on role of foreign institutional investment in india Ppt on recent mergers and acquisitions in india Ppt on types of parallelograms pictures Download ppt on nationalism in indochina Ppt on next generation 2-stroke engine stops Mp ppt online viewer Ppt on active directory services Ppt online examination project in java Ppt on service oriented architecture in healthcare