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]:

    
x









    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]:

    
x









    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.