Calculator Enactment
Continue with Classes, Queues, performing Sorts and BigO analysis on your algorithm(s).
Reverse Polish Notation (RPN) & Postfix Evaluation
Understanding Stacks and Queues
- Stack (LIFO - Last In, First Out): Think of stacking cards. The last one placed is the first one removed.
- Queue (FIFO - First In, First Out): Think of a line at a store. The first one in is the first one out.
What is Reverse Polish Notation (RPN)?
- Infix Notation: Standard mathematical notation where operators are between operands. (e.g.,
3 + 5 * 8
) - Postfix Notation (RPN): Operators come after the operands. (e.g.,
35+8*
instead of(3+5)*8
)
Example Conversions:
3 * 5
→35*
(3 + 5) * 8
→35+8*
Postfix Expression Evaluation
Example: Solve 8 9 + 10 3 * 8 *
Step-by-Step Calculation:
8 9 +
→17
10 3 *
→30
30 8 *
→240
- Final result:
17 240
(Not combined yet, needs more context)
Try this: Solve 8 2 ^ 8 8 * +
Step-by-Step Calculation:
8 2 ^
→64
(Exponentiation:8^2 = 64
)8 8 *
→64
64 64 +
→128
(Final result)
Why Use Postfix Notation?
- Follows PEMDAS naturally (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
- Operators go into a stack, while numerals go into a queue.
- Easier to evaluate expressions using stacks, reducing complexity in parsing.
Popcorn Hack - Convert to Infix!
Convert the following postfix expressions into infix notation:
6 3 * 4 +
10 2 8 * + 3 -
15 3 / 4 2 * +
7 3 2 * + 5 -
9 3 + 2 ^
Answers Here for Popcorn Hack
Infix to RPN
- For every “token” in infix
- If token is number: push into queue
- Else if token is operator
- While the stack isn’t empty, and the operator at the top of the stack has greater or equal “precedence” to the current token, pop values from stack into the queue.
- Then push the “token” into the stack.
- Else if token is “(“
- Push token into stack
- Else if token is “)”
Evaluate the RPN
- Make new stack
- For every token in queue
- If token is number: push into stack
- If token is operator:
- Take 2 nums from top of the stack
- Use the operator: [num1] (operator) [num2]
- Put result into stack
- When stack only has 1 element, you have your answer!
Homework:
- Instead of making a calculator using postfix, make a calculator that uses prefix (the operation goes before the numerals)
- Prefix: 35 becomes *35, (7-5)2 becomes *2-75