Expression Tree ( Due 31 Jul 2020 )

For this assignment you will read a file expression.txt and create an expression tree. The expression will be a valid infix expression with the all the necessary parentheses so that there is no ambiguity in the order of the expression. You will evaluate the expression and print the result. You will also write the prefix and postfix versions of the same expression without any parentheses.

In an expression tree the nodes are either operators or operands. The operators will be in the set ['+', '-', '*', '/', '//', '%', '**']. The operands will be either integers or floating point numbers. All the operand nodes will be leaves of the expression tree. All the operator nodes will have exactly two children.

The outline of your program will be as follows: 

class Stack (object):

class Node (object):

class Tree (object):
  def __init__ (self):

  def create_tree (self, expr):

  def evaluate (self, aNode):

  def pre_order (self, aNode):

  def post_order (self, aNode):

def main():

main()

The function create_tree() will take as input parameter an infix expression with parentheses as a String and create an Expression Tree from it. Assume that the expression string is valid.

You will take the expression string and break it into tokens. There are four different kinds of tokens - left parenthesis, right parenthesis, operator, and operand. When we read a left parenthesis we are starting a new expression and when we read a right parenthesis we are ending an expression. Here is the algorithm that you will use. Start with an empty node that is going to be your root node. Call it the current node. Then start parsing the expression.

  1. If the current token is a left parenthesis add a new node as the left child of the current node. Push current node on the stack and make current node equal to the left child.
  2. If the current token is an operator set the current node's data value to the operator. Push current node on the stack. Add a new node as the right child of the current node and make the current node equal to the right child.
  3. If the current token is an operand, set the current node's data value to the operand and make the current node equal to the parent by popping the stack.
  4. If the current token is a right parenthesis make the current node equal to the parent node by popping the stack if it is not empty.

For the input expression, this is what your program will output: 

( ( 8 + 3 ) * ( 7 - 2 ) ) = 55.0

Prefix Expression: * + 8 3 - 7 2

Postfix Expression: 8 3 + 7 2 - *

You may work with a partner on this assignment. Both of you must read the paper on Pair Programming and abide by the ground rules as stated in that paper. Only one of you will submit the code. Make sure that you have your partner's name and UT EID in the header.

Use the HackerRank system to submit your code by 11 PM on Friday, 31 Jul 2020. There will be substantial penalties if you do not adhere to the guidelines. HackerRank will not assign late penalties (if any), we will make those adjustments.

References