Changing Infix To Postfix Notation Using Stacks - How To Utilize Hash Maps

So I am supposed to be changing infix notation to postfix notation using stacks. This is simply taking a string "3 + 5 * 6" (infix) and turning it into (3 5 6 * +" (postfix).

To do this, we are to scan the string from left to right and when we encounter a number, we just add it to the final string, but when we encounter an operand, we throw it on the stack. Then if the next operand has a higher input precedence than the stack precedence of the operator on the top of the stack, we add that operator to the stack too, otherwise we pop from the stack THEN add the new operator.

I am supposed to be utilizing a hash map but I don't see how you would go about doing this. We are supposed to store operators on the hash map but operators need their own character, input precedence, stack precedence, and rank. How do you use a hash map when you need to tie a character to 3 values instead of just 1? I just don't get it.

The following is our Operator class that we are to use. Another problem is this isn't really supposed to be modified, yet we were given two important variables (inputPrecedence and outputPrecedence) that we can't have nothing to be initialized to and no way of accessing? So that might be where a hash map comes in but I am not sure. I am not very sure on how they exactly work anyway...

public class Operator implements Comparable<Operator>
{
public char operator; // operator
privateint inputPrecedence; // input precedence of operator in the range [0, 5]
privateint stackPrecedence; // stack precedence of operator in the range [-1, 3]

[Code] ....

So my question mostly revolves around how I tie an Operator character to its required values, so I can use it in my code to test two operators precedence values.

My original thought was turn string into character array, but then I would need nested for/while loops to check if it is a number or letter, or if it is an operator and thus result in O(n^2) time