Lecture 238:- Infix to Postfix Conversion

Infix to Postfix conversion is a common problem in computer science and is often used in compilers and expression evaluation. The goal of this conversion is to take an infix expression as input and convert it to its equivalent postfix expression.

Infix expressions are the standard mathematical expressions we use, where operators are placed between operands. For example, "3 + 4", "5 * (2 + 6)", "a + b * c", etc., are infix expressions.

Postfix expressions, also known as Reverse Polish Notation (RPN), are expressions in which the operators are placed after their operands. For example, "3 4 +" is the postfix equivalent of "3 + 4", "5 2 6 + *" is the postfix equivalent of "5 * (2 + 6)", "a b c * +" is the postfix equivalent of "a + b * c", etc.

To convert an infix expression to a postfix expression, you can use a stack to keep track of operators while scanning the expression from left to right. Here are the steps for the Infix to Postfix conversion algorithm:

1. Initialize an empty stack to hold operators.
2. Initialize an empty string to store the postfix expression.
3. For each character in the infix expression:
   • If the character is an operand (number or variable), append it to the postfix string.
   • If the character is an opening parenthesis '(', push it onto the stack.
   • If the character is a closing parenthesis ')':
     • Pop operators from the stack and append them to the postfix string until an opening parenthesis '(' is encountered on the top of the stack. Pop and discard the opening parenthesis from the stack.
   • If the character is an operator (+, -, *, /, etc.):
     • Pop operators from the stack and append them to the postfix string until either the stack is empty or the operator at the top of the stack has lower precedence than the current operator. Then push the current operator onto the stack.
4. After processing all characters, pop any remaining operators from the stack and append them to the postfix string.

Here's the C++ implementation of Infix to Postfix conversion using a stack:

cppCopy code

#include <iostream> #include <stack> #include <string> int precedence(char op) {    if (op == '+' || op == '-')        return 1;    else if (op == '*' || op == '/')        return 2;    return 0; } std::string infixToPostfix(const std::string& infix) {    std::stack<char> operatorStack;    std::string postfix;    for (char c : infix) {        if (std::isalnum(c)) {            postfix += c; // Operand, append to postfix string        } else if (c == '(') {            operatorStack.push(c);        } else if (c == ')') {            while (!operatorStack.empty() && operatorStack.top() != '(') {                postfix += operatorStack.top();                operatorStack.pop();            }            operatorStack.pop(); // Pop and discard the opening parenthesis        } else { // Operator            while (!operatorStack.empty() && precedence(operatorStack.top()) >= precedence(c)) {                postfix += operatorStack.top();                operatorStack.pop();            }            operatorStack.push(c);        }    }    while (!operatorStack.empty()) {        postfix += operatorStack.top();        operatorStack.pop();    }    return postfix; } int main() {    std::string infix, postfix;    std::cout << "Enter an infix expression: ";    std::cin >> infix;    postfix = infixToPostfix(infix);    std::cout << "Postfix expression: " << postfix << std::endl;    return 0; }

In this implementation, the precedence function assigns a precedence level to each operator, with higher precedence indicating higher priority. The infixToPostfix function converts the infix expression to its postfix equivalent following the steps described earlier.

In the main function, the user is prompted to enter an infix expression. The program then calls the infixToPostfix function to convert the infix expression to postfix and prints the resulting postfix expression.