How do parentheses impact the conversion of infix expressions to postfix?

Handling Parentheses in Infix-to-Postfix Expression Conversion

While converting infix expressions to postfix, parentheses play a pivotal role in determining the order of precedence. Here's how you can handle parentheses and multiple layers of parentheses in your code:

In the toPostFix() method, when you encounter a left parenthesis (:

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

When you encounter a right parenthesis ):

//closing )
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 )
} 

This code ensures that:

• When you encounter a left parenthesis (, it is pushed onto the stack post_fix.
• When you encounter a right parenthesis ), you pop elements from the stack and append them to the output string postfixstr until you either reach an empty stack or encounter a left parenthesis ( again.
• If, during this process, the stack is empty, it means there's an unmatched right parenthesis; however, if the stack contains a left parenthesis, it is popped.
• Finally, the right parenthesis itself is popped from the input stack in_fix.

By implementing this logic, your code will be able to handle multiple layers of parentheses and correctly convert infix expressions that contain parentheses to postfix expressions.

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