Lab 9 - Using Stacks

One common use for stacks is to evaluate expressions in Reverse Polish notation(RPN). RPN is another way of expressing a mathematical formula, based on how its "parse tree" looks like. Take the following examples: 
formula: 3 + 4
parse tree:
     +
    / \
   3   4
RPN: 3 4 +
The RPN notation is <left_node> <right_node> <operator>. In this case, the left and right nodes are both numbers, but the nodes may themselves be other formulas. The parse tree is built out of the order of operations, so the operation that takes place last is the root. Take this more complex example: 
formula: (3 + 4) * 2
parse tree:
      *                    * is done last because of the () around 3 + 4
     / \
    +   2                  The left node is 3 + 4 because that has to be
   / \                       evaluated before (3 + 4) * 2 can be evaluated
  3   4
RPN: 3 4 + 2 *
In this case, the "left node" is actually the formula "3 4 +", so that whole formula is put into the left_node portion of the syntax. The "right node" is 2 and the "operator" is *.

Stacks can be used to evaluate a formula that is expressed in RPN notation. The pseudocode is: 

until enter is hit
  read next character from input stream
  if it is a digit
    put character back on the input stream
    extract the number from the input stream
    push the number onto the stack
  else, if it is an operator (+ - * / %)
    pop two values off the stack (two pop calls in a row)
      if stack does not have two values
        issue error (BNF is incorrect) and exit
    compute the operation (a op b)
    push the results of the operation onto the stack
  else
    issue an error about invalid input (not a number or valid operator)
once loop exits, the result is the top value on the stack
  pop the result
  if stack is not empty as a result of a pop
    issue an error (stack should only contain the result at the end)
  else
    print the result
Use the following files to implement the BNF equation evaluator: Email me your completed lab9main.cpp file with those sections filled in.