Sets¶

Set is a mutable, unordered collection of unique, hashable elements(may be of same or different types), which is not indexed.

Creating Set¶

Creating an empty set

x = set()

Creating set with some initial elements

x = {2,3,0,'g'}

Creating an empty set with {} is not possible as {} is reserved for dictionary dict objects

In [1]:

x = {1,2,5,3}
x

Out[1]:

{1, 2, 3, 5}

Accessing Set Elements¶

Being an unordered collection, sets do not record element position or order of insertion. Accordingly, sets do not support indexing, slicing, or other sequence-like behavior.

Operations on Set¶

Like any other collection, set supports membership operators in and not in, elements of set can be iterated. If A and B are 2 sets,Following is a list of other operations on set

A.union(B) - returns $A\cup B$
A.union_update(B) - $A= A\cup B$
A.intersection(B) - returns $A\cap B$
A.intersection_update(B) - $A= A\cap B$
A.isdisjoint(B) - returns $A\cap B == \emptyset$
A.issubset(B) - returns $A\subseteq B$
A.issuperset(B) - returns $A\supseteq B$

Other operations like set difference are also supported

In [2]:

Out[2]:

{1, 2, 3, 5}

In [3]:

x.union([2,4,6])

Out[3]:

{1, 2, 3, 4, 5, 6}

In [4]:

x.intersection([2,3])

Out[4]:

{2, 3}

In [5]:

x.intersection_update([1,3,4])

In [6]:

Out[6]:

{1, 3}

Note Graph and Sets

Many Graph Algorithms are modelled using sets. A Graph $G$ is considered as a collection of sets of vertices $V$ and sets of edges $E$

Set of Sets¶

In many cases, it is required to have set of sets as in case of finding subsets of a set. Since set is not hashable, it is not possible to have a ``set`` as an element of ``set``. In this case frozenset comes handy. The only difference between frozenset and a set is that frozenset is immutable. We have to reassign value to it if we want to modify it.