Lecture Notes on 26 Oct 2020

* Evaluate the following RPN expressions:
4 8 7 + 2 * 3 1 - * +
3 4 + 5 *
3 4 5 + *
7 4 + 3 - 2 5 * /

* Reverse Polish Notation Revisited
  Some definitions
  operator: + - * / // % **

  operand: 2 (integers) or 3.4 (floating point numbers)

  Infix: 2 + 3

  Postfix: 2 3 +
  
  Prefix: + 2 3

* There is an inherent ambiguity in infix expressions.
  What does 2 + 3 * 5 mean? Is it (2 + 3) * 5 or 2 + (3 * 5)?

* There is no ambiguity using either postfix or prefix notation.
  (2 + 3) * 5 = 2 3 + 5 *

  2 + (3 * 5) = 2 3 5 * +

  As you can see the two expressions are different in postfix.

* Given a valid RPN expression how do you evaluate it

* Parse the RPN expression (go through the expression token by token)

* If the token is an operand push the operand on the stack

* If the token is an operator 
  - pop the stack twice
  - apply the operator to those operands 
  - push the result on the stack

* When you finish parsing there should be only one number in the stack. 
  Pop the stack. That is your answer.

* Code to evaluate RPN expressions stored in a file called rpn.txt

class Stack (object):
  def __init__ (self):
    self.stack = []

  # add an item on the top of the stack
  def push (self, item):
    self.stack.append (item)

  # remove an item from the top of the stack
  def pop (self):
    return self.stack.pop()

  # check the item on the top of the stack
  def peek (self):
    return self.stack[-1]

  # check if the stack is empty
  def is_empty (self):
    return (len(self.stack) == 0)

  # return the number of elements in the stack
  def size (self):
    return (len(self.stack))

def operate (oper1, oper2, token):
  expr = str(oper1) + token + str(oper2)
  return eval (expr)

def rpn (s):
  theStack = Stack()

  operators = ['+', '-', '*', '/', '//', '%', '**']

  tokens = s.split()

  for item in tokens:
    if (item in operators):
      oper2 = theStack.pop()
      oper1 = theStack.pop()
      theStack.push (operate (oper1, oper2, item))
    else:
      theStack.push (item)

  return theStack.pop()

  
def main():
  in_file = open ("rpn.txt", "r")
  for line in in_file:
    line = line.strip()
    value = rpn (line)
    print (line, " = ", value)
  in_file.close()

main()