1. Fundamentals of Programming II What Is Equality?
Computer Science 112
Fundamentals of Programming II
What Is Equality?

2. What Is Equality?
For collections, the == operator is syntactic sugar for a call of the __eq__ method on the left operand, with the right operand as an argument
Thus,
>>> "Hi" == "hi"
False
>>> "Hi".__eq__("hi")
>>>

3. Python’s Two Equality Operators
The is operator tests two objects for identity (same address in memory)
The == operator has a default implementation (__eq__ method) in the object class
This implementation uses is

4. Identity vs Structural Equivalence
numbers = Array(4) # Then put 3, 2, 6, and 4 in there
numbers 3 2 6 4

5. Identity vs Structural Equivalence
numbers = Array(4) # Then put 3, 2, 6, and 4 in there
alias = numbers # An alias
numbers and alias refer to the same object in memory
numbers 3 2 6 4
alias

6. Identity vs Structural Equivalence
numbers = Array(4) # Then put 3, 2, 6, and 4 in there
alias = numbers # An alias
copy = resize(numbers, 1) # A real copy
numbers and alias refer to the same object in memory
numbers and copy refer to distinct objects whose contents are the same
numbers 3 2 6 4
alias
copy 3 2 6 4

7. Identity vs Structural Equivalence
>>> numbers == alias
True
numbers and alias refer to the same object in memory
numbers and copy refer to distinct objects whose contents are the same
numbers 3 2 6 4
alias
copy 3 2 6 4

8. Identity vs Structural Equivalence
>>> numbers == alias
True
>>> numbers is alias
numbers and alias refer to the same object in memory
numbers and copy refer to distinct objects whose contents are the same
numbers 3 2 6 4
alias
copy 3 2 6 4

9. Identity vs Structural Equivalence
>>> numbers == alias
True
>>> numbers is alias
>>> numbers is copy # Right, they are not identical
False
numbers and alias refer to the same object in memory
numbers and copy refer to distinct objects whose contents are the same
numbers 3 2 6 4
alias
copy 3 2 6 4

10. Identity vs Structural Equivalence
>>> numbers == alias
True
>>> numbers is alias
>>> numbers is copy # Right, they are not identical
False
>>> numbers == copy
False # Counterintuitive: why not True?
numbers and alias refer to the same object in memory
numbers and copy refer to distinct objects whose contents are the same
numbers 3 2 6 4
alias
copy 3 2 6 4

11. Equality for Linear Collections
The __eq__ method is redefined in the list, tuple, and str classes
This method first checks for object identity (using is)
It then checks for equality of type, and then for equality of length, and finally for equality of pairs of elements at each position

12. Default Pattern for Equality Test
def __eq__(self, other)
if self is other: return True
if type(self) != type(other): return False
if len(self) != len(other): return False
otherIter = iter(other)
for item in self:
if item != next(otherIter)
return False
return True
Works for linear and sorted collections, but not for unordered collections. Why not?

13. Equality for Sets Two sets are equal if they are identical
Or they are of the same type and length and contain exactly the same elements (if everything in set A is also in set B)

14. Equality Test for Sets Works for sets. Why won’t it work for bags?
def __eq__(self, other):
"""Returns True if self equals other, or False otherwise."""
if self is other: return True
if type(self) != type(other) or len(self) != len(other):
return False
for item in self:
if not item in other:
return True
Works for sets. Why won’t it work for bags?

15. A Counterexample
>>> s1 = ArraySet([1, 1, 2, 2, 2])
>>> s2 = ArraySet([1, 1, 1, 2, 2])
>>> s1 == s2
True
>>> b1 = ArrayBag([1, 1, 2, 2, 2])
>>> b2 = ArrayBag([1, 1, 1, 2, 2])
>>> b1 == b2 # Should be False
Two bags are equal if and only if the number of instances of each item in one is the same as the number of instances of the same item in the other

16. What is the Big-O? == for linear and sorted collections == for sets
== for bags

17. Best Case, Worst Case, Average Case: Linear and Sorted Collections
def __eq__(self, other):
if self is other: return True
if type(self) != type(other): return False
if len(self) != len(other): return False
otherIter = iter(other)
for item in self:
if item != next(otherIter)
return False
return True

18. Best Case, Worst Case, Average Case: Sets
def __eq__(self, other):
"""Returns True if self equals other, or False otherwise."""
if self is other: return True
if type(self) != type(other) or len(self) != len(other):
return False
for item in self:
if not item in other:
return True

19. Best Case, Worst Case, Average Case: Bags
def __eq__(self, other):
"""Returns True if self equals other, or False otherwise."""
if self is other: return True
if type(self) != type(other) or len(self) != len(other):
return False
for item in self:
if ???????:
return True

20. How Many __eq__s Can There Be?
BagInterface
LinkedBag
ArrayBag
ArraySortedBag
Interface polymorphism:
== always looks the same from the clients’ side, but __eq__ can be implemented differently to provide optimal performance

21. Inheritance and abstract classes Chapter 6
For Wednesday
Inheritance and abstract classes
Chapter 6