Have you struggled to analyze complicated mathematical expressions? You're not alone. All of us have struggled to decide which operation to execute first in a lengthy infix expression. What if I told you there is a simpler, quicker way? Reverse Polish Notation (RPN) postfix notation. Many calculators utilize it as their secret weapon to assess mathematical expressions. In this tutorial, I will show you how to develop a stack-based postfix expression calculator. Let's step in! 

 

What is Postfix Notation? 

Regular mathematics uses infix notation: (3 + 5) or {(4 * 2) - 6}. This is how most of us learnt math. However, postfix notation reverses this. Postfix does not use parentheses, and operators always follow operands. (3 + 5) becomes (3 5 +), while {(4 * 2) - 6} becomes (4 2 * 6 -). Sounds odd, right? Postfix is great since it removes parentheses and operator precedence. Stacks simplify expression evaluation. 

Why Stacks? 

Let's swiftly define a stack before evaluating a postfix expression using one. Consider it a stack of plates: Last in, First out (LIFO). Postfix evaluation works well with stacks because we can execute the expression from left to right and organize the operands and operators. 

Step-by-Step Guide to Evaluating Postfix Expressions

Let's get started! We will explain how to analyze a postfix expression step by step using a stack. Look at the postfix expression: "5 3 + 8 *." Here's what we would do: 

1. Start with an empty stack: We start with an empty stack. 
2. Traverse the expression: We will look at each part of the expression one by one. The first token is the number "5". Since it is a number, we add it to the stack. Our stack currently contains: [5]. 
3. Next token: The next token is also a number, "3." We put it back on the stack. Our stack now contains: [5, 3]. 
4. Meet an operator: Next, we come across the "+" operator. We need to take the two numbers (5 and 3) off the stack, add them (5 + 3 = 8), and then put the result back on the stack. Our stack now contains: [8]. 
5. Another number: Next, we look at the number "8". We just add this number to the stack. Our stack is now: [8, 8]. 
6. Final operator: Lastly, we have the "*" operator. We take the two numbers (8 and 8) from the stack, multiply them (8 * 8 = 64), and then place the result back on the stack. Our stack now has one item: 64. 
7. End of the expression: After processing all the tokens, the stack has one item left, which is 64. This is the result of the postfix expression. 

Code Implementation of the Calculator 

Let's put the idea into practice using Python code. Here's an easy way to create a postfix evaluator: 

def evaluate_postfix(expression):
    stack = []
    for token in expression.split():
        if token.isdigit():
           stack.append(int(token))
        else:
            b = stack.pop()
            a = stack.pop()
            if token == '+':
               stack.append(a + b)
            elif token == '-':
               stack.append(a - b)
            elif token == '*':
               stack.append(a * b)
            elif token == '/':
               stack.append(a / b)
    return stack[0]

# Test the function
expression = "5 3 + 8 *"
result = evaluate_postfix(expression)
print("Result:", result)

In this code, evaluate_postfix accepts a postfix expression string. It tokenizes the string and processes each token on the stack. Numbers go on the stack. An operator pops the two highest numbers off the stack, applies the operator, and returns the result to the stack. Only the final result remains in the stack. 

Example Walkthrough 

Use the code to show (5 3 + 8). Start with an empty stack. Push 5 and 3 onto the stack first. We pop the two values, add them to obtain 8, then put 8 back into the stack when we see the "+" operator. Next, we add 8 to the stack. Hit the "" operator to pop the two 8s, multiply them to 64, and put 64 into the stack. Returning 64, the final result. The method is simple! 

Conclusion 

This article explained postfix notation and how stacks may evaluate postfix expressions. We constructed a basic calculator to show the procedure. This simple implementation can handle more complicated expressions and issues like incorrect tokens or division by zero. Postfix evaluation using stacks is a good basis for developing complex calculators or understanding compiler expressions. 

Try creating your own postfix expressions and evaluating them using the code. It helps you learn stacks and postfix evaluation efficiency.