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 mathematical expression:"); var postFix = InfixToPostfix(userInput); var result = EvaluateExpression(postFix);  document.write("Infix: " + userInput + "<br/>"); document.write("Postfix (RPN): " + postFix + "<br/>"); document.write("Result: " + result + "<br/>");   function EvaluateExpression(expression) {     var tokens = expression.split(/([0-9]+|[*+-\/()])/);     var evalStack = [];      while (tokens.length != 0)     {         var currentToken = tokens.shift();          if (isNumber(currentToken))         {             evalStack.push(currentToken);         }         else if (isOperator(currentToken))         {             var operand1 = evalStack.pop();             var operand2 = evalStack.pop();              var result = PerformOperation(parseInt(operand1), parseInt(operand2), currentToken);             evalStack.push(result);         }     }     return evalStack.pop(); }  function PerformOperation(operand1, operand2, operator) {     switch(operator)     {         case '+':              return operand1 + operand2;         case '-':             return operand1 - operand2;         case '*':             return operand1 * operand2;         case '/':             return operand1 / operand2;         default:             return;     }  }  function InfixToPostfix(expression) {     var tokens = expression.split(/([0-9]+|[*+-\/()])/);     var outputQueue = [];     var operatorStack = [];      while (tokens.length != 0)     {         var currentToken = tokens.shift();          if (isNumber(currentToken))          {             outputQueue.push(currentToken);         }         else if (isOperator(currentToken))          {             while ((getAssociativity(currentToken) == 'left' &&                      getPrecedence(currentToken) <= getPrecedence(operatorStack[operatorStack.length-1])) ||                    (getAssociativity(currentToken) == 'right' &&                      getPrecedence(currentToken) < getPrecedence(operatorStack[operatorStack.length-1])))              {                 outputQueue.push(operatorStack.pop())             }              operatorStack.push(currentToken);          }         else if (currentToken == '(')         {                 operatorStack.push(currentToken);         }         else if (currentToken == ')')         {             while (operatorStack[operatorStack.length-1] != '(')             {                 if (operatorStack.length == 0)                     throw("Parenthesis balancing error! Shame on you!");                  outputQueue.push(operatorStack.pop());             }                operatorStack.pop();                 }        }        while (operatorStack.length != 0)     {         if (!operatorStack[operatorStack.length-1].match(/([()])/))             outputQueue.push(operatorStack.pop());         else             throw("Parenthesis balancing error! Shame on you!");              }      return outputQueue.join(" "); }       function isOperator(token) {     if (!token.match(/([*+-\/])/))         return false;     else          return true; }   function isNumber(token) {     if (!token.match(/([0-9]+)/))         return false;     else         return true; }   function getPrecedence(token) {     switch (token)     {         case '^':             return 9;          case '*':                    case '/':         case '%':             return 8;         case '+':         case '-':             return 6;         default:              return -1;     } }  function getAssociativity(token) {     switch(token)     {         case '+':         case '-':         case '*':         case '/':             return 'left';         case '^':             return 'right';     }  } 

It works fine so far. If I give it:

((5+3) * 8)

It will output:

Infix: ((5+3) * 8)
Postfix (RPN): 5 3 + 8 *
Result: 64

However, I'm struggling with implementing the unary operators so I could do something like:

((-5+3) * 8)

What would be the best way to implement unary operators (negation, etc)? Also, does anyone have any suggestions for handling floating point numbers as well?

One last thing, if anyone sees me doing anything weird in JavaScript let me know. This is my first JavaScript program and I'm not used to it yet.

Answer 1

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.