#Conversion-of-Infix-Expressions--Postfix-Expressions-Data-Structures

Conversion of Infix Expressions to Postfix: A Comprehensive Guide

In programming and data structures, understanding how to convert infix expressions to postfix notation is essential for implementing efficient algorithms. This article delves into the conversion process, providing code examples, explanations, and insights into why postfix expressions are valuable.

What is an Infix Expression?

An infix expression is the standard mathematical notation where operators are placed between operands, like A + B. For example, the expression A + B * C explicitly shows that multiplication has precedence over addition, which can also be written as (A + (B * C)).

While infix notation is easier for humans to read, it requires additional computational effort to evaluate. This is where postfix notation comes in handy.

What is a Postfix Expression?

A postfix expression (also known as Reverse Polish Notation) places operators after their operands. For example, the infix expression A + B * C converts to A B C * +. In this format:

• Operands maintain their original order.
• Operators are placed based on precedence and associativity.

By converting infix expressions to postfix, we eliminate the need for parentheses and simplify the evaluation process using stacks.

Example of Conversion

Let’s consider converting the infix expression A + B * (C - D) to postfix.

1. Start with ( to define operator precedence explicitly.
2. Identify precedence and associativity of operators (e.g., * has higher precedence than +).
3. Rearrange the operators in reverse order for postfix.

The result will be: A B C D - * +.

Code for Conversion of Infix to Postfix

Here is the C program to convert infix expressions to postfix:

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

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

void push(char ch) {
    if (top == MAX - 1) {
        return;
    }
    stack[++top] = ch;
}

char pop() {
    if (top == -1) {
        return '\0';
    }
    return stack[top--];
}

int precedence(char ch) {
    if (ch == '/' || ch == '*') {
        return 2;
    }
    if (ch == '+' || ch == '-') {
        return 1;
    }
    return 0;
}

void main() {
    char in[50], post[50], ch;
    int i = 0, j = 0, len;

    printf("\n Enter any expression in infix notation:");
    scanf("%s", in);

    len = strlen(in);
    push('(');
    in[len] = ')';
    in[len + 1] = '\0';

    while (in[i] != '\0') {
        if (isalpha(in[i])) {
            post[j++] = in[i];
        } else if (in[i] == '(') {
            push('(');
        } else if (in[i] == ')') {
            while ((ch = pop()) != '(') {
                post[j++] = ch;
            }
        } else if (in[i] != ' ') {
            while (precedence(ch = pop()) >= precedence(in[i])) {
                post[j++] = ch;
            }
            push(ch);
            push(in[i]);
        }
        i++;
    }
    post[j] = '\0';
    printf("\n Postfix Expression = %s", post);
    getch();
}

Explanation of the Code

1. Stack Initialization:

   • A stack is used to store operators and manage their precedence.
   • The stack ensures proper order when building the postfix expression.

2. Precedence Function:

   • The function precedence assigns a numerical priority to operators. For instance, * and / have higher precedence than + and -.

3. Conversion Logic:

   • Operands are added directly to the postfix expression.
   • Operators are pushed to the stack and popped based on precedence rules.
   • Parentheses are used to manage precedence and are removed in the final postfix expression.

Advantages of Postfix Notation

1. No Parentheses Required: Postfix expressions eliminate the need for parentheses, simplifying parsing and evaluation.

2. Stack-Based Evaluation:

   • Postfix expressions can be evaluated efficiently using a stack.
   • Each operator applies to the last two operands on the stack.

3. Simplifies Compiler Design: Many compilers convert expressions to postfix for easier syntax tree construction and code generation.

Conclusion

In this article, we explored how to convert infix expressions to postfix notation, the associated C code, and its advantages. By understanding this conversion, developers can implement efficient algorithms for expression evaluation in data structures.

Whether you’re designing a calculator, compiler, or another system that relies on mathematical expressions, mastering postfix notation is a valuable skill.