#evaluation-implementation-of-postfix-notation-Data-Structure

Evaluation and Implementation of Postfix Notation in Data Structures

Postfix notation, also known as Reverse Polish Notation (RPN), is a mathematical notation where operators follow their operands. Unlike infix notation (e.g., 4 + 5), postfix notation eliminates the need for parentheses to define order of operations. This makes it especially useful for computer systems and programming languages that work with stacks to evaluate expressions efficiently.

In this article, we explore how to evaluate and implement postfix notation in C programming with a focus on data structures. We’ll also discuss its practical applications and provide code examples to help you understand its implementation.

What Is Postfix Notation?

In postfix notation:

• Operands (numbers or variables) appear before their corresponding operators.
• Operators are evaluated only when sufficient operands are available.

For example, the postfix expression 4 5 6 * + translates to:

1. Multiply 5 and 6 → 30
2. Add 4 → 34

This sequence eliminates the ambiguity of operator precedence found in infix notation.

Evaluating Postfix Expressions Using a Stack

Postfix expressions are evaluated using a stack:

1. Push operands onto the stack.
2. When an operator is encountered, pop the top two operands.
3. Perform the operation and push the result back onto the stack.
4. Continue until the expression is fully evaluated, with the result being the only item left on the stack.

Implementation in C

Here’s how you can implement postfix evaluation in C using a stack:

#include <stdio.h>
#include <conio.h>
#include <ctype.h>
#define MAX 50

float stack[MAX];
int top = -1;

// Function to push a value onto the stack
void push(float val) {
    if (top == MAX - 1) {
        printf("\nStack Overflow");
        return;
    }
    stack[++top] = val;
}

// Function to pop a value from the stack
float pop() {
    if (top == -1) {
        printf("\nStack Underflow");
        return -0.0;
    }
    return stack[top--];
}

void main() {
    char post[50];
    int i = 0;
    float A, B, C;
    
    clrscr(); // Clears the screen (specific to Turbo C; replace for other compilers)
    printf("\nEnter any expression in postfix notation (in Numeric Form): ");
    scanf("%s", post);

    while (post[i] != '\0') {
        if (isdigit(post[i])) {  // If the character is a digit
            push(post[i] - '0'); // Convert character to number
        } else if (post[i] != ' ') {  // If it's an operator
            A = pop();
            B = pop();
            
            switch (post[i]) {
                case '+': C = B + A; break;
                case '-': C = B - A; break;
                case '*': C = B * A; break;
                case '/': C = B / A; break;
                default: printf("\nInvalid operator"); return;
            }
            push(C); // Push the result back onto the stack
        }
        i++;
    }
    printf("\nAnswer of Postfix Expression = %f", pop());
}

Example: Evaluating 23*5+

Let’s evaluate the postfix expression 23*5+ step by step:

1. Push 2 and 3 onto the stack.
2. Encounter *: Pop 3 and 2, calculate 2 * 3 = 6, and push 6 back.
3. Push 5 onto the stack.
4. Encounter +: Pop 5 and 6, calculate 6 + 5 = 11.
5. Final result: 11.

Why Use Postfix Notation?

Advantages:

1. Eliminates Parentheses: No need for additional rules to determine operator precedence.
2. Simplifies Evaluation: Particularly useful for stack-based systems and calculators.
3. Efficient Parsing: Easier for computers to evaluate compared to infix notation.

Applications:

• Expression evaluation in programming languages.
• Compilers and interpreters.
• Reverse Polish calculators.

Key Takeaways from the Code

1. Stack-Based Evaluation: A stack simplifies the process by ensuring the operands are readily available for evaluation.
2. Dynamic Operand Handling: The code dynamically handles multiple operations in sequence, making it flexible for various postfix expressions.
3. Error Handling: Proper checks for stack overflow and underflow ensure robustness.

Conclusion

In this article, we discussed the evaluation and implementation of postfix notation in data structures using C. By leveraging stacks, postfix expressions can be evaluated efficiently and without ambiguity. The provided code demonstrates how to handle operands and operators dynamically, ensuring a clear and effective solution.

Whether you're working on compilers, calculators, or learning advanced data structures, mastering postfix notation is a valuable skill. Try implementing the code with different expressions to deepen your understanding!