Transforming Expressions: Infix to Postfix Conversion in C

The world of expressions can take various forms. Infix notation, the familiar format with operators between operands (e.g., "2 + 3 * 5"), is intuitive for humans. However, computers often find it easier to work with postfix notation, where operators come after operands (e.g., "2 3 5 * +"). This blog post delves into how to convert infix expressions to postfix in C programming using the mighty stack data structure.

Why Conversion Matters?

Converting infix to postfix offers several benefits:

• Simplified Evaluation: Postfix expressions have inherent precedence rules, removing the need for complex parsing and handling of parentheses.

• Efficiency: Evaluating postfix expressions with stacks becomes a straightforward process, popping operands and applying operators.

• Applications: Postfix notation plays a crucial role in various areas, including compilers and computer architecture.

Understanding the Algorithm

Here's a simplified breakdown of the infix to postfix conversion algorithm using stacks:

1. Initialization: Create an empty stack.

2. Scan the infix expression:

• Operand: Directly add the operand to the output string.

• Operator:

• If the stack is empty or the operator's precedence is higher than the top element in the stack, push the operator onto the stack.

• Otherwise, pop operators from the stack and add them to the output string until you encounter an operator with lower precedence or an empty stack. Then, push the current operator onto the stack.

• Left Parenthesis: Push it onto the stack.

• Right Parenthesis: Pop operators from the stack and add them to the output string until you encounter the matching left parenthesis. Discard the left parenthesis.

1. Final Steps: Once the entire expression is scanned, pop any remaining operators from the stack and add them to the output string. The resulting string is the postfix expression.

C Code Example:

#include <stdio.h>
#include <stdlib.h>
#include <ctype.h> // for isalpha() function

#define MAX_SIZE 100

char stack[MAX_SIZE];
int top = -1; // Initially, the stack is empty

// Function prototypes
int isEmpty();
int isFull();
char peek();
void push(char data);
char pop();
int precedence(char operator);
void infixToPostfix(char *infix, char *postfix);

int main() {
    char infix[MAX_SIZE], postfix[MAX_SIZE];

    printf("Enter an infix expression: ");
    fgets(infix, sizeof(infix), stdin); // Read the infix expression

    infixToPostfix(infix, postfix);

    printf("Postfix expression: %s\n", postfix);

    return 0;
}

// Check if the stack is empty
int isEmpty() {
    return top == -1;
}

// Check if the stack is full
int isFull() {
    return top == MAX_SIZE - 1;
}

// Get the element at the top of the stack without removing it
char peek() {
    if (isEmpty()) {
        printf("Stack is empty\n");
        exit(1); // Exit the program if stack underflows
    }
    return stack[top];
}

// Push an element onto the stack
void push(char data) {
    if (isFull()) {
        printf("Stack overflow\n");
        exit(1); // Exit the program if stack overflows
    }
    stack[++top] = data;
}

// Pop an element from the stack
char pop() {
    if (isEmpty()) {
        printf("Stack underflow\n");
        exit(1); // Exit the program if stack underflows
    }
    return stack[top--];
}

// Get the precedence of an operator
int precedence(char operator) {
    switch (operator) {
        case '^':
            return 3;
        case '*':
        case '/':
            return 2;
        case '+':
        case '-':
            return 1;
        default:
            return 0; // Consider operands as having precedence 0
    }
}

// Convert infix expression to postfix expression
void infixToPostfix(char *infix, char *postfix) {
    int i, j;
    char ch, temp;

    // Traverse the infix expression
    i = j = 0;
    while ((ch = infix[i++]) != '\0') {
        if (isalnum(ch)) { // If it's an operand, add it to postfix
            postfix[j++] = ch;
        } else if (ch == '(') {
            push(ch);
        } else if (ch == ')') {
            while ((temp = pop()) != '(') {
                postfix[j++] = temp;
            }
        } else { // It's an operator
            while (!isEmpty() && precedence(peek()) >= precedence(ch)) {
                postfix[j++] = pop();
            }
            push(ch);
        }
    }

    // Pop remaining operators from the stack (for expressions like x + y)
    while (!isEmpty()) {
        postfix[j++] = pop();
    }

    postfix[j] = '\0'; // Add null terminator to the postfix string
}

Embrace the Power of Stacks:

By mastering infix to postfix conversion, you unlock a valuable technique in computer science. This blog post provides a starting point, and further exploration can delve into advanced parsing techniques and handling complex expressions. Remember, stacks offer a powerful tool for manipulating data structures and solving various programming challenges.