infix postfix conversion c++, can't seem to get the right answer

Question

so I've working on an assignment converting infix format to postfix format using a stack for the operators, for the digits of the infix notation, the code worked fine, but for the operators, it doesn't work, because the stack is initially empty when I start it, so it can't go into the while loop, but I don't know how to fix this logical error.

void calculator::convertInputIntoPostfix(){
  stack S;
  for(int i=0;i<mInfixInput.length();i++){
    if(mInfixInput[i]>='0' && mInfixInput[i]<='9'){
      mPostfixOutput+=mInfixInput[i];
    }
    else if(isOperator(mInfixInput[i])){                                                                                     
    while
    (!S.isEmpty()
    &&hasHigherPrecedenceThan(S.top(),mInfixInput[i])==true){
        mPostfixOutput += S.top();
        S.pop();
    }
    S.push(mInfixInput[i]);
    }
  }
  while(!S.isEmpty()){
    mPostfixOutput += S.top();
    S.pop();
 }                                                                                                                                                             
}

bool calculator::isOperator(int c) const
{
  return ((c == '+') ||
          (c == '-') ||
          (c == '*') ||
          (c == '/') ||
          (c == '^'));
}
bool calculator::hasHigherPrecedenceThan(int aLHS, int aRHS) const
{
  if ((aRHS == '+' || aRHS == '-') &&
      (aLHS == '*' || aLHS == '/' || aLHS == '^')) {
    return true;
  }
  if ((aRHS == '+' || aRHS == '-' || aRHS == '*' || aRHS == '/') &&
      (aLHS == '^')) {
    return true;
  }
  if (aLHS == '^' && aRHS == '^') {
    return true;
  }
  return false;
}

The cases not given above(like () spaces and commas) can be ignored, and the infix is taken by input in the main. the stack is a linked list stack. with the value being an integer. the outputs for 2+3*3*3(desired answer:233*3*+) I've been getting is 2333**+, as it is not even entering the while loop I've written, it is just storing the values into the stack and at the end outputing it.

Answer 1

2333**+ might be unexpected, but it isn't actually wrong, just wrongly associative.

The way you're computing precedence, you're telling the algorithm that the case where aRHS == '*' && aLHS == '*' is false , ie that the operator isn't left-associative. It is. Ditto for all other cases where the operators are equal, except ^ , which you are wrongly making left-associative when it is right-associative.

It is customary to use a table rather than an if-else chain when determining predence in this algorithm, and to test for >=, not >, in terms of precedence.

The version of the Dijkstra Shunting-yard algorithm given in Wikipedia has this instead of your condition:

while ((there is a function at the top of the operator stack)
    or (there is an operator at the top of the operator stack with greater precedence)
    or (the operator at the top of the operator stack has equal precedence and is left associative))
    and (the operator at the top of the operator stack is not a left bracket):
        pop operators from the operator stack onto the output queue.