1. Computer Science 2 5/17/2016 Finish the Queue Program
Postfix/Prefix/Infix
Stack Calculator

2. Learning Objectives
Be able to convert from infix to prefix and postfix notation
Be able to evaluate prefix and post fix expressions
Push: Use stacks in order to evaluate math expressions in postfix

3. 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) ?

4. Infix, Postfix, & Prefix notation
There is no reason we can’t place the operator somewhere else.
How ?
Infix notation : a + b
Prefix notation : + a b
Postfix notation: a b +

5. Prefix/Postfix Other Names
Prefix notation was introduced by the Polish logician Lukasiewicz, and is sometimes called “Polish notation”.
Postfix notation is sometimes called “reverse Polish notation” or RPN.

6. 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!

7. Example infix postfix prefix (a + b) * c a b + c * * + a b c
Infix form : <identifier> <operator> <identifier>
Postfix form : <identifier> <identifier> <operator>
Prefix form : <operator> <identifier> <identifier>

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

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

10. II. Evaluate the following Postfix expressions (Assume A = 7, B = 4, C = 3, D = -2)
b) A B C D + / *
c) A B – C – D –
d) A B C D + + -

11. Postfix Calculator If it’s a digit: If it’s an operation: 853+2-+
Push it on the Digit Stack
If it’s an operation:
Pop two digits from the Digits stack
Perform the operation
Push the result on to the Digit Stack

12. A VALuable Procedure
val(String, RealOrIntegerVariable, IntegerErrorCode);
Converts a String into a real or an integer value
program test;
var
error:integer;
x:real;
number:string;
begin
writeln('Please enter a number (-1 to quit)');
readln(number);
while (number <> '-1') do
val(number, x, error);
if error = 0 then
writeln(x)
else
writeln('Error !!!');
end;
end.

13. Challenge Stack Program
Write a program that will input an addition equation as a string in Postfix notation, and calculate the results.
Start with a simple expression and single digit numbers
52+
63-
Then move to more complex expressions
52+3-