Lecture 239:- Associativity and Unary Operators

In the context of infix to postfix conversion, associativity refers to the rule that determines how operators with the same precedence are evaluated in an expression. There are two types of associativity:

1. Left-Associative: If operators have left-associativity, they are evaluated from left to right. For example, in the expression "3 - 2 - 1," the left-associative "-" operators are evaluated in the order (3 - 2) - 1, resulting in 0.
2. Right-Associative: If operators have right-associativity, they are evaluated from right to left. For example, in the expression "2 ^ 3 ^ 2," the right-associative "^" operators are evaluated in the order 2 ^ (3 ^ 2), resulting in 512.

The associativity of an operator is important during infix to postfix conversion when two operators with the same precedence are encountered. In such cases, the associativity helps determine the order in which the operators should appear in the postfix expression.

Unary operators are operators that act on a single operand. Examples of unary operators include negation (-), logical NOT (!), and increment/decrement (++/--). In an expression like "-3", the "-" is a unary operator applied to the operand 3.

During infix to postfix conversion, it's essential to distinguish between unary and binary operators. Unary operators should have higher precedence than binary operators to ensure they are evaluated first. Additionally, unary operators must be handled differently because they don't have two operands like binary operators.

Here's a modified version of the infix to postfix conversion function to handle unary operators correctly:

cppCopy code

#include <iostream> #include <stack> #include <string> #include <cctype> int precedence(char op) {    if (op == '+' || op == '-')        return 1;    else if (op == '*' || op == '/')        return 2;    return 0; } bool isUnary(char op) {    return op == '+' || op == '-'; } std::string infixToPostfix(const std::string& infix) {    std::stack<char> operatorStack;    std::string postfix;    for (size_t i = 0; i < infix.length(); ++i) {        char c = infix[i];        if (std::isspace(c)) {            continue; // Skip whitespaces        } else if (std::isalnum(c)) {            while (i < infix.length() && std::isalnum(infix[i])) {                postfix += infix[i++];            }            postfix += ' '; // Add a space after each operand            --i; // Decrement i to account for the final ++i in the loop        } 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() && operatorStack.top() != '(' &&                   (isUnary(c) ? precedence(operatorStack.top()) > precedence(c) : 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::getline(std::cin, infix);    postfix = infixToPostfix(infix);    std::cout << "Postfix expression: " << postfix << std::endl;    return 0; }

In this modified implementation, we use the isUnary function to identify unary operators. Unary operators are given higher precedence (greater than the precedence of binary operators) to ensure they are evaluated first. Additionally, the code handles operands that are more than one digit by iterating through the characters and forming complete operands before appending them to the postfix expression.

The main function now uses std::getline to read the entire infix expression, allowing expressions with spaces to be entered. The resulting postfix expression is printed with spaces between operands and operators for better readability.