Updated (12 Feb 2023)

Postfix & Prefix Evaluator

This is a simple Prefix or Postfix Evaluator.

Enter the Postfix or Prefix expression below in box and press Evaluate
Note: Enter the number and operators seperated with space " "

Type the Expression below
prefix : + - 2 7 * 8 / 4 12
postfix: 4 55 + 62 23 - *
(seperated with space)

Postfix Evaluate Prefix Evaluate

< Convert

Evaluated :

By Raj

Sr. no.	Expression	Stack

Algorithm used

Postfix Evaluation

Step 1: Add a ")" at the end of the postfix expression
Step 2: Scan every character of the postfix expression and repeat Step 3 and 4 until ")" is encountered.
Step 3: IF an operand is encountered, Push it on the stack
IF an operator O is encountered, then
- a: Pop the top two elements from the stack as A and B
- b: Evaluate B O A, where A is the topmost element and B is the element below A.
- c: Push the result of evaluation on the stack
  [END OF IF]
Step 4: Set result = stack's top elements
Step 5: Exit

Prefix Evaluation

Step 1: Get Prefix expression as it is
Step 2: Repeat untill all the characters in prefix
expression have been scanned

a: Read the prefix expression from right to left one at a time
b: If the readed character is an operand, push it on the stack
c: If the readed character is an operator, then
- i: pop two values from the stack.
- ii: Apply the operation on the operands.
- iii: Push the result onto the stack.

Step 3: Exit

Understanding the Postfix & Prefix Evaluator

Our Postfix & Prefix Evaluator is a powerful tool designed to calculate the result of mathematical expressions written in postfix (Reverse Polish Notation) or prefix (Polish Notation) formats. This evaluator is particularly useful for students, programmers, and anyone working with these alternative mathematical notations.

What are Postfix and Prefix Notations?

Postfix Notation (Reverse Polish Notation): In this notation, operators follow their operands. Example: 4 5 + 6 2 - *
Prefix Notation (Polish Notation): Here, operators precede their operands. Example: + - 2 7 * 8 / 4 12

How to Use the Evaluator

Enter your postfix or prefix expression in the input box.
Ensure that numbers and operators are separated by spaces.
Choose the appropriate evaluation mode (Postfix or Prefix) using the respective buttons.
Click the "Evaluate" button to see the result.
Review the evaluation process in the table below the result.

Features of Our Evaluator

Dual Evaluation: Supports both postfix and prefix notations.
Step-by-Step Breakdown: Displays the evaluation process in detail, helping users understand the algorithm.
Support for Complex Expressions: Handles multiple operators and operands.
Easy Conversion: Includes a link to convert between infix, postfix, and prefix notations.

Why Use Postfix and Prefix Notations?

While less intuitive for humans, postfix and prefix notations have several advantages:

They eliminate the need for parentheses and operator precedence rules.
They are easier for computers to parse and evaluate.
They are used in many programming languages and in some calculators.

Applications

This evaluator is valuable for:

Students learning about expression evaluation and stack-based algorithms.
Programmers implementing calculators or expression parsers.
Anyone looking to understand or work with postfix and prefix notations.

Understanding the Evaluation Process

The evaluator uses a stack-based algorithm:

For postfix: It scans from left to right, pushing operands onto a stack and applying operators to the top stack elements.
For prefix: It scans from right to left, following a similar process but with reversed order of operations.

By using this tool and studying the evaluation process, you can gain a deeper understanding of how these notations work and how stack-based algorithms can efficiently evaluate complex expressions. This knowledge is fundamental in various areas of computer science, particularly in compiler design and expression parsing.