Sets

Sets are a very robust data structure that are mostly useful in situations where the order of elements is not as important as their uniqueness. They are also useful if you need to efficiently check efficiency if the element is contained in a collection. Sets in Python are generalizations of mathematic sets, and are provided as built-in types in two flavors:

• set(): This is a mutable, non-ordered, finite collection of unique, immutable (hashable) objects
• frozenset(): This is an immutable, hashable, non-ordered collection of unique, immutable (hashable) objects

The immutability of frozenset() objects makes it possible for them to be included as dictionary keys and also other set() and frozenset() elements. A plain mutable set() object cannot be used within another set() or frozenset(). Attempting to do so will raise a TypeError exception, as in the following example:

>>> set([set([1,2,3]), set([2,3,4])])
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: unhashable type: 'set'

On the other hand, the following set initializations are completely correct, and do not raise exceptions:

>>> set([frozenset([1,2,3]), frozenset([2,3,4])])
{frozenset({1, 2, 3}), frozenset({2, 3, 4})}
>>> frozenset([frozenset([1,2,3]), frozenset([2,3,4])])
frozenset({frozenset({1, 2, 3}), frozenset({2, 3, 4})})

Mutable sets can be created in three ways:

• Using a set() call that accepts optional iterables as the initialization argument, such as set([0, 1, 2])
• Using a set comprehension such as {element for element in range(3)}
• Using set literals such as {1, 2, 3}

Note that using literals and comprehensions for sets requires extra caution, because they are very similar in form to dictionary literals and comprehensions. Also, there is no literal for empty set objects – empty curly brackets {} are reserved for empty dictionary literals.