How do you handle parentheses in infix to postfix conversion?

Handling Parentheses in Infix to Postfix Conversion

Introduction:
When converting an infix expression to a postfix expression, one needs to consider how to handle the presence of parenthesis. Parentheses dictate the order of operations, and ignoring their significance can lead to incorrect results.

Handling Parentheses:
To handle parentheses effectively, we employ a stack-based approach. When an opening parenthesis '(' is encountered in the infix expression, it is pushed onto the stack. When a closing parenthesis ')' is encountered, we process the stack as follows:

1. While the stack is not empty and the top of the stack is not an opening parenthesis '(', pop the top of the stack and append it to the output string.
2. If the stack is empty, the parentheses are mismatched, indicating an error.
3. If the top of the stack is an opening parenthesis '(', pop it from the stack.
4. Pop the closing parenthesis ')' from the input infix expression.

Multiple Layers of Parentheses:
Our algorithm can handle multiple layers of parentheses recursively. When an opening parenthesis is reached, the process continues as described above. When a closing parenthesis is encountered, it will trigger the same process, effectively resolving each level of parentheses.

Example Implementation:

In Java, the following code snippet demonstrates how to incorporate parenthesis handling into the infix to postfix conversion method:

// ... Existing code for infix to postfix conversion ...

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

// 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 )
}

// ... Existing code for the rest of the algorithm ...

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