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How do Parenthesis Affect Infix to Postfix Expression Conversion?

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2024-11-10 18:05:02197browse

How do Parenthesis Affect Infix to Postfix Expression Conversion?

Handling Parenthesis in Infixed to Postfix Expression Conversion

Converting infixed expressions to postfix expressions involves handling parenthesis. Parenthesis can introduce multiple layers of precedence considerations, which must be addressed to ensure correct evaluation.

In an infixed expression, parenthesis can act as grouping elements that alter the order of operations. For instance, while the expression "2 3 4" evaluates to 14, the expression "(2 3) 4" evaluates to 20 because the parenthesis forces the addition to occur before the multiplication.

To handle parenthesis in the conversion, we need to adjust the logic as follows:

// 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 )
} 

When encountering an opening parenthesis, it's pushed onto the stack. When a closing parenthesis is encountered, the stack is processed as long as it contains elements that are not opening parenthesis. These elements are appended to the postfix string. Once the stack is empty or the current element is an open parenthesis, the closing parenthesis and its corresponding open parenthesis are popped from the stack and the infixed stack, ensuring that the precedence of expressions within parenthesis is maintained.

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