Description
This assignment will focus on the implementation of a simple binary tree, which will associate variable names with their values. It also involves minor changes to pre-existing functionaltiy to make use of the tree.
Problem Description
The project so far supports calculations on numeric values, but most computational statements (and even most calculators) are not limited to numeric literal values. They usually also include variables.
So this assignment will add the ability to assign to variables, and then to later use their values in further computations. This will require a data structure that will associate variables with values, and to do that efficiently, will use a binary search tree.
Parsing and Interpretation
There will be one additional operator for this homework — the sasignment operator (‘=’). We will support the C++ meaning of this operator, that not only assigns to a variable, but ‘computes’ the assigned value. The assignment operator has the lowest precedence (be aware of what that means for the order of calling functions when parsing.
Here are a few examples:
x = 1 + (y = 4) # assign 4 to y and 5 to x
x = y = z = 4 # assign 4 to z, then y, then x
x = y = z + 4 # add 4 to z, then assign sum to y and x
x = 1 + y = 4 # invalid input: cannot assign 4 to (1+y)
Special Note:
It may be tempting to make the function for assignment operator to be just like the ones for sum and product. That would not be correct, because it would do the operations from left to right. HOWEVER: it can be fixed just by changing the name of one function call within the new while loop. Furthermore, if you do so correctly, the while loop would only repeat 0 or 1 times, so the word ‘while’ could optionally be replaced with a different word.
The postfix forms for the legal expression would be similar to the other operators:
x 1 y 4 = + = # assign 4 to y, add 1 to it, then assign 5 to x
x y z 4 = = = # assign 4 to z, then y, then x
x y z 4 + = = # add 4 to z, then assign sum to y and x
A binary search tree will be used when evaluating the postfix expression. If a variable is the left operand of an assignment, the variable will receive the value. If a variable appears at any other time, its value is retrieved for a computation.
That means that the postfix evaluation function’s stack of ‘values’ will now have a mixture of values and variable names, and will need to be able to know the difference and use the information appropriately.
HINT: The instructor discovered that if value = ‘0.3’, value.isdigit() is False. It is safer to check value[0].isdigit(). That will let you more reliably identify whether the stack element is a variable or a number.
Defining a Binary Tree
There is no need for any self-balancing features in this assignment — just the a simple binary tree supporting the ability to store new variables, to associate values with those variables, and to retrieve the value of a variable.
For consistency, call your file vartree.py
Required Features in Implementation
Nested Node class definition for binary tree node
with __slots__ to save list memory
and __init__ a constructor
__init__() a constructor for an empty tree
_search(here, var) recursively search tree rooted ‘here’ for variable ‘var’
returning correct Node, or None if not found
_insert(here, var, value) return a search tree with variable inserted or updated
this should be a recursive implementation for immutable behavior
assign(var, value) public method to assign to a variable
lookup(var) public method retrieve value of variable<
if the variable does not yet exist, assign it zero
Good functions for Completeness / Practice
is_empty() Identify whether tree is empty
__len__() returns number of elements in list
__iter__() inorder iterator generator(with yield statements)
__str__() represents entire tree as a string
For full credit, this must be no worse than log-linear time and not quadratic
Assignment Specifications
One new file and three modified files are to appear in the solution to this assignment:
vartree.py
Implements the binary tree above as a class
newsplit.py
divides into tokens, generating an iterator, with added support for variable names
infixtoiter.py
given an iterator to an infix expression, produces a linked list for a postfix expression, with added support for variables and =
evalpostfix.py
evaluates a postfix expression, given an iterator, with added support for variables
That module will have its own variable to hold all of those variables
You are also encouraged to insert your own unit testing into each file, but that will not be itself graded.
Testing and Evaluation
Here are a few lines of code from the instructor’s solution and test at this time of writing:
(in the test program)
from infixtoiter import to_postfix
from evalpostfix import eval_postfix
def test(expr):
print (expr, ‘:’, eval_postfix( to_postfix( expr )) )
test(“b=6”) # b=6 : 6
test(“b * 9”) # b * 9 : 54
You may assume that all expressions are legal C expressions with binary operators, but you may NOT assume that:
All numbers are single digits — this assumption was not permitted before either
All variables are single letters — they may include multiple letters (and maye digits)
All variables are assigned before use — if not yet assigned, assign zero.
Extra Credit Option
Support those optional class features listed above, along with suitable unit tests.
