Reverse Polish notation (RPN) is a way of writing mathematical expressions without using parentheses. It uses a stack and two rules: 1) if a value appears, push it onto the stack, and 2) if an operator appears, pop two items from the stack and push the result. Examples show RPN expressions for addition, subtraction, multiplication, and division. The shunting yard algorithm can be used to convert infix notation to RPN by reading characters and pushing operands or popping operators based on their precedence.

1. Reverse
Polish
Notation

2. BEDMAS
BIDMAS
BODMAS
PEMDAS

3. 6,2/1,2+*
*
/ +
6 2 1 2
/ 6,2,1,2,+*/
*
+
6 2 1 2

4. Evaluating RPN
• Uses a stack and two simple rules. Reading
left to right …….
• 1. If a value appears next in the
expression, push this value on to the stack.
• 2. If an operator appears next, pop two items
from the top of the stack and push the result
of the operation on to the stack.

5. Reverse Polish Notation Examples
7,4+3- 7+4-3
1,2*3+ 1*2+3
1,2+3* (1+2) *3
5,9,2*+ 5+9*2
1,2*3,4*+ 1*2+3*4

6. Converting from infix to postfix
‘Shunting yard algorithm’
• Read each character • Calculator - another
• If its an operand, add it to
the output
• If it’s an operator then
– If there’s a higher BODMAS
priority operator at the top of
the stack, pop it
– Push it on the stack
• At the end, pop everything
off the operator stack