How to Handle Parentheses in Infix to Postfix Conversions?

Handling Parentheses in Infix to Postfix Conversions

Converting infix expressions to postfix expressions requires careful handling of parentheses. The presence of parentheses poses challenges in determining the correct order of operations. To address this, the following approach can be employed:

Mechanism for Handling Parentheses

Push Left Parentheses: When encountering a left parenthesis, push it onto the operator stack.

Process Right Parentheses: Upon encountering a right parenthesis:

1. Pop operators from the stack and append them to the output string until an opening parenthesis is encountered.
2. If the stack is empty without finding an opening parenthesis, it indicates an unmatched closing parenthesis.
3. If an opening parenthesis is found, pop it from the stack.
4. Pop the right parenthesis from the input stack.

Code Implementation

The following Java code demonstrates how to modify the toPostFix() method to handle parentheses:

public String toPostFix() {
    StringBuilder postfixstr = new StringBuilder();

    Stack<Token> in_fix = new Stack<>();
    Stack<Token> post_fix = new Stack<>();

    for (int i = tokens.length - 1; i >= 0; i--) {
        t = new Token(tokens[i]);
        in_fix.push(t);
    }

    //there are still tokens to process
    while (!in_fix.empty()) {
        // is a number
        if (in_fix.peek().type == 1) {     
            postfixstr.append(in_fix.pop().toString());
        } 

        // is an operator and the stack is empty
        else if (in_fix.peek().type == 3 && post_fix.empty()) {   
            post_fix.push(in_fix.pop());
        } 

        // is an operator that has higher priority than the operator on the stack
        else if (in_fix.peek().type == 3 && in_fix.peek().isOperator() > post_fix.peek().isOperator()) {
            post_fix.push(in_fix.pop());
        } 

        // is an operator that has lower priority than the operator on the stack
        else if (in_fix.peek().type == 3 && in_fix.peek().isOperator() <= post_fix.peek().isOperator()) {
            postfixstr.append(post_fix.pop());
            post_fix.push(in_fix.pop());
        } 

        // opening (
        else if (in_fix.peek().type == 4) {   
            post_fix.push(in_fix.pop());
        }

        // closing )
        else if(in_fix.peek().type == 5){
            while(!(post_fix.isEmpty() || post_fix.peek().type == 4)){
                 postfixstr.append(post_fix.pop());
            }
            if (post_fix.isEmpty())
                ; // ERROR - unmatched )
            else
                post_fix.pop(); // pop the (
            in_fix.pop(); // pop the )
        }

        //puts the rest of the stack onto the output string
        if (in_fix.empty()) {
            while (!post_fix.empty()) {
                postfixstr.append(post_fix.pop());
            }
        }
    }

    return postfixstr.toString();
}

By implementing these steps, the toPostFix() method can effectively handle expressions involving parentheses, ensuring the correct order of operations and producing the desired postfix expressions.

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