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The greatest mistake you can make in life is to be continually fearing you will make one

## Monday, 8 February 2010

### Problems based on Expression Evaluation

Problem 1:
Give postfix form of the following expression
1. A*(B+(C+D)*(E+F)/G)*H
2. A+((B+C)*(D+E)*F)/G
3. A*(B+D)/E-F-(G+H/K)
4. ((A-B)*(D/E))/(F*G*H)
Problem 2:
Evaluate the following postfix expression using a stack and show the contents of stack after each step
1. 50 40 +18 14-4*+
2. 100 40 8+20 10 -+*
3. 5 6 9 +80 5*-/
4. 120 45+20 10-15+*
5. 20 45+20 10-15+*
Problem 3:
Simplify the following infix expressions using operator precedence rules
1.  8-2*3-1
2. 12/(6-2)
3. (4+3)*(8-5)
Solution:
(1) A=8-2*3-1
* has higher precedence than -. so 2*3 is executed first
A=8-6-1.both are -.so evaluate from left to right
A=2-1=1
A=1

(2)B=12/(6-2)
operation in parentheses are done first.so 6-2=4
B=12/4=3
B=3
(3)C=(4+3)*(8-5)
operation in parentheses done first
C=7*(8-5)
C=7*3
C=21

Problem 4
Are the following two infix expressions equivalent?
1. A+B*C
2. (A+B)*C
Solution:
The two infix expressions are different.The multiplication is performed first in the first expression while the addition is performed first in the second expression.

1. 2. 3. 