How can I modify my Shunting-Yard Algorithm so it accepts unary operators?

Question

I\'ve been working on implementing the Shunting-Yard Algorithm in JavaScript for class.

Here is my work so far:

var userInput = prompt(\"Enter in a m         


        

Answer 1

In my Java implementation I did it in next way:

expression = expression.replace(" ", "").replace("(-", "(0-")
                .replace(",-", ",0-");
        if (expression.charAt(0) == '-') {
            expression = "0" + expression;
        }

Answer 2

When I needed to support this, I did this in an intermediate stage. I started by generating a list of all expression lexemes, then used helper functions to extract operators and operands and the "get operand" function simply consumed two lexemes whenever it saw a unary operator.

It really helps if you use another character to signify "unary minus", though.

Answer 3

The easiest thing would be to make isNumber match /-?[0-9]+(\.[0-9]+)?/, handling both floating points and negative numbers.

If you really need to handle unary operators (say, unary negation of parenthesized expressions), then you have to:

• Make them right-associative.
• Make them higher precedence than any of the infix operators.
• Handle them separately in EvaluateExpression (make a separate PerformUnaryExpression function which only takes one operand).
• Distinguish between unary and binary minus in InfixToPostfix by keeping track of some kind of state. See how '-' is turned into '-u' in this Python example.

I wrote up a more thorough explanation of handling unary minus on another SO question.

Answer 4

I could solve this problem by modifying unary operators('+' and '-') to distinguish them from the binary ones.

For example, I called the unary minus 'm' and unary plus 'p', making them right-assocative and their precedence equal to the exponent operator('^').

To detect if the operator is unary I simply had to check if the token before the operator was an operator or an opening bracket.

This is my implementation in C++:

        if (isOperator(*token))
        {
            if (!isdigit(*(token - 1)) && *(token - 1) != ')')   // Unary check
            {
                if (*token == '+')
                    *token = 'p';        // To distinguish from the binary ones
                else if (*token == '-')
                    *token = 'm';
                else
                    throw;
            }

            short prec = precedence(*token);
            bool rightAssociative = (*token == '^' || *token == 'm' || *token == 'p');

            if (!operators.empty())
            {
                while (prec < precedence(operators.top()) || (prec == precedence(operators.top()) && !rightAssociative))
                {
                    rpn += operators.top();
                    operators.pop();

                    if (operators.empty())
                        break;
                }
            }
            operators.push(*token);
        }

Here operators is a stack and token is an iterator to the infix expression string

(This just the operator handling part)

Answer 5

my suggestion is this. don't handle the '-' as an arithmetic operator. treat it as a 'sign' operator. or treat it as if it's a part of the whole operand (i.e. its sign). what i mean is that everytime you encounter '-', you just have to multiply the operand after it by -1, then proceed to read the next token. :) i hope that helps. just a simple thought...

Answer 6

To handle floating point numbers you can change your (number part of) regex to:

/([0-9]+\.?[0-9]*)/

so the final regex would be:

/([0-9]+\.?[0-9]*|[*+-\/()])/

And for handling unary minus operator, you can change it to another character like 'u'. (As it is explained here by -TGO)

The javascript code that i wrote for handling unary minus operator based on the link given is:

// expr is the given infix expression from which, all the white spaces has been
// removed.(trailing and leading and in between white space characters)
const operators = ['+', '*', '-', '/', '^'];
const openingBrackets = ['(', '[', '{'];
let exprArr = Array.from(expr);
// Since strings are immutable in js, I am converting it to an array for changing 
// unary minus to 'u'
for (let i = 0; i < expr.length; i++) {
    if (expr[i] === '-') {
        if (i === 0) {
            exprArr[i] = 'u';
        } else if (operators.includes(expr[i - 1])) {
            exprArr[i] = 'u';
        } else if (openingBrackets.includes(expr[i - 1])) {
            exprArr[i] = 'u';
        } else {
            // '-' is not a unary operator
            // it is a binary operator or we have the wrong expression, so...
            if (!openingBrackets.includes(expr[i + 1]) && !/[0-9]/.test(expr[i + 1])) {
                throw new Error("Invalid Expression...");
            }
        }
    }
}
// And finally converting back to a string.
let expr2 = exprArr.join('');