Python Sets

What is a set in Python?

A set is an unordered collection of items. Every element is unique (no duplicates) and must be immutable (which cannot be changed).

However, the set itself is mutable. We can add or remove items from it.

Sets can be used to perform mathematical set operations like union, intersection, symmetric difference etc.

How to create a set?

A set is created by placing all the items (elements) inside curly braces {}, separated by comma or by using the built-in function set().

It can have any number of items and they may be of different types (integer, float, tuple, string etc.). But a set cannot have a mutable element, like list, set or dictionary, as its element.

# set of integers
my_set = {1, 2, 3}
print(my_set)
# set of mixed datatypes
my_set = {1.0, "Hello", (1, 2, 3)}
print(my_set)

Try the following examples as well.

# set do not have duplicates
# Output: {1, 2, 3, 4}
my_set = {1,2,3,4,3,2}
print(my_set)
# set cannot have mutable items
# here [3, 4] is a mutable list
# If you uncomment line #12,
# this will cause an error.
# TypeError: unhashable type: 'list'
#my_set = {1, 2, [3, 4]}
# we can make set from a list
# Output: {1, 2, 3}
my_set = set([1,2,3,2])
print(my_set)

Creating an empty set is a bit tricky.

Empty curly braces {} will make an empty dictionary in Python. To make a set without any elements we use the set() function without any argument.

How to change a set in Python?

Sets are mutable. But since they are unordered, indexing have no meaning.

We cannot access or change an element of set using indexing or slicing. Set does not support it.

We can add single element using the add() method and multiple elements using the update() method. The update() method can take tuples, lists, strings or other sets as its argument. In all cases, duplicates are avoided.

# initialize my_set
my_set = {1,3}
print(my_set)
# if you uncomment line 9,
# you will get an error
# TypeError: 'set' object does not support indexing
#my_set[0]
# add an element
# Output: {1, 2, 3}
my_set.add(2)
print(my_set)
# add multiple elements
# Output: {1, 2, 3, 4}
my_set.update([2,3,4])
print(my_set)
# add list and set
# Output: {1, 2, 3, 4, 5, 6, 8}
my_set.update([4,5], {1,6,8})
print(my_set)

When you run the program, the output will be:

{1, 3}
{1, 2, 3}
{1, 2, 3, 4}
{1, 2, 3, 4, 5, 6, 8}

How to remove elements from a set?

A particular item can be removed from set using methods, discard() and remove().

The only difference between the two is that, while using discard() if the item does not exist in the set, it remains unchanged. But remove() will raise an error in such condition.

The following example will illustrate this.

# initialize my_set
my_set = {1, 3, 4, 5, 6}
print(my_set)
# discard an element
# Output: {1, 3, 5, 6}
my_set.discard(4)
print(my_set)
# remove an element
# Output: {1, 3, 5}
my_set.remove(6)
print(my_set)
# discard an element
# not present in my_set
# Output: {1, 3, 5}
my_set.discard(2)
print(my_set)
# remove an element
# not present in my_set
# If you uncomment line 27,
# you will get an error.
# Output: KeyError: 2
#my_set.remove(2)

Similarly, we can remove and return an item using the pop() method.

Set being unordered, there is no way of determining which item will be popped. It is completely arbitrary.

We can also remove all items from a set using clear().

# initialize my_set
# Output: set of unique elements
my_set = set("HelloWorld")
print(my_set)
# pop an element
# Output: random element
print(my_set.pop())
# pop another element
# Output: random element
my_set.pop()
print(my_set)
# clear my_set
#Output: set()
my_set.clear()
print(my_set)

Python Set Operations

Sets can be used to carry out mathematical set operations like union, intersection, difference and symmetric difference. We can do this with operators or methods.

Let us consider the following two sets for the following operations.

>>> A = {1, 2, 3, 4, 5}
>>> B = {4, 5, 6, 7, 8}

Union of A and B is a set of all elements from both sets.

Union is performed using | operator. Same can be accomplished using the method union().

# initialize A and B
A = {1, 2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
# use | operator
# Output: {1, 2, 3, 4, 5, 6, 7, 8}
print(A | B)

Try the following examples on Python shell.


# use union function
>>> A.union(B)
{1, 2, 3, 4, 5, 6, 7, 8}

# use union function on B
>>> B.union(A)
{1, 2, 3, 4, 5, 6, 7, 8}

Set Intersection

Set Intersection in Python

Intersection of A and B is a set of elements that are common in both sets.

Intersection is performed using & operator. Same can be accomplished using the method intersection().

# initialize A and B
A = {1, 2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
# use & operator
# Output: {4, 5}
print(A & B)

Try the following examples on Python shell.


# use intersection function on A
>>> A.intersection(B)
{4, 5}

# use intersection function on B
>>> B.intersection(A)
{4, 5}

Set Difference

Set Difference in Python

Difference of A and B (A - B) is a set of elements that are only in A but not in B. Similarly, B - A is a set of element in B but not in A.

Difference is performed using - operator. Same can be accomplished using the method difference().

# initialize A and B
A = {1, 2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
# use - operator on A
# Output: {1, 2, 3}
print(A - B)

Try the following examples on Python shell.


# use difference function on A
>>> A.difference(B)
{1, 2, 3}

# use - operator on B
>>> B - A
{8, 6, 7}

# use difference function on B
>>> B.difference(A)
{8, 6, 7}

Set Symmetric Difference

Set Symmetric Difference in Python

Symmetric Difference of A and B is a set of elements in both A and B except those that are common in both.

Symmetric difference is performed using ^ operator. Same can be accomplished using the method symmetric_difference().

# initialize A and B
A = {1, 2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
# use ^ operator
# Output: {1, 2, 3, 6, 7, 8}
print(A ^ B)

Try the following examples on Python shell.


# use symmetric_difference function on A
>>> A.symmetric_difference(B)
{1, 2, 3, 6, 7, 8}

# use symmetric_difference function on B
>>> B.symmetric_difference(A)
{1, 2, 3, 6, 7, 8}

Different Python Set Methods

There are many set methods, some of which we have already used above. Here is a list of all the methods that are available with set objects.

Python Set Methods
Method	Description
add()	Adds an element to the set
clear()	Removes all elements from the set
copy()	Returns a copy of the set
difference()	Returns the difference of two or more sets as a new set
difference_update()	Removes all elements of another set from this set
discard()	Removes an element from the set if it is a member. (Do nothing if the element is not in set)
intersection()	Returns the intersection of two sets as a new set
intersection_update()	Updates the set with the intersection of itself and another
isdisjoint()	Returns `True` if two sets have a null intersection
issubset()	Returns `True` if another set contains this set
issuperset()	Returns `True` if this set contains another set
pop()	Removes and returns an arbitary set element. Raise `KeyError` if the set is empty
remove()	Removes an element from the set. If the element is not a member, raise a `KeyError`
symmetric_difference()	Returns the symmetric difference of two sets as a new set
symmetric_difference_update()	Updates a set with the symmetric difference of itself and another
union()	Returns the union of sets in a new set
update()	Updates the set with the union of itself and others

Other Set Operations

Set Membership Test

We can test if an item exists in a set or not, using the keyword in.

# initialize my_set
my_set = set("apple")
# check if 'a' is present
# Output: True
print('a' in my_set)
# check if 'p' is present
# Output: False
print('p' not in my_set)

Iterating Through a Set

Using a for loop, we can iterate though each item in a set.

>>> for letter in set("apple"):
...     print(letter)
...

Built-in Functions with Set

Built-in functions like all(), any(), enumerate(), len(), max(), min(), sorted(), sum() etc. are commonly used with set to perform different tasks.

Built-in Functions with Set
Function	Description
all()	Return `True` if all elements of the set are true (or if the set is empty).
any()	Return `True` if any element of the set is true. If the set is empty, return `False.`
enumerate()	Return an enumerate object. It contains the index and value of all the items of set as a pair.
len()	Return the length (the number of items) in the set.
max()	Return the largest item in the set.
min()	Return the smallest item in the set.
sorted()	Return a new sorted list from elements in the set(does not sort the set itself).
sum()	Retrun the sum of all elements in the set.

Python Frozenset

Frozenset is a new class that has the characteristics of a set, but its elements cannot be changed once assigned. While tuples are immutable lists, frozensets are immutable sets.

Sets being mutable are unhashable, so they can't be used as dictionary keys. On the other hand, frozensets are hashable and can be used as keys to a dictionary.

Frozensets can be created using the function frozenset().

This datatype supports methods like copy(), difference(), intersection(), isdisjoint(), issubset(), issuperset(), symmetric_difference() and union(). Being immutable it does not have method that add or remove elements.

# initialize A and B
A = frozenset([1, 2, 3, 4])
B = frozenset([3, 4, 5, 6])

Try these examples on Python shell.

>>> A.isdisjoint(B)
False
>>> A.difference(B)
frozenset({1, 2})
>>> A | B
frozenset({1, 2, 3, 4, 5, 6})
>>> A.add(3)
...
AttributeError: 'frozenset' object has no attribute 'add'

Python Sets

Set

A set is a collection which is unordered and unindexed. In Python sets are written with curly brackets.

Example

Create a Set:

thisset = {"apple", "banana", "cherry"}
print(thisset)

Note: Sets are unordered, so you cannot be sure in which order the items will appear.

Access Items

You cannot access items in a set by referring to an index, since sets are unordered the items has no index.

But you can loop through the set items using a for loop, or ask if a specified value is present in a set, by using the in keyword.

Example

Loop through the set, and print the values:

thisset = {"apple", "banana", "cherry"}

for x in thisset:
print(x)

Example

Check if "banana" is present in the set:

thisset = {"apple", "banana", "cherry"}

print("banana" in thisset)

Change Items

Once a set is created, you cannot change its items, but you can add new items.

Add Items

To add one item to a set use the add() method.

To add more than one item to a set use the update() method.

Example

Add an item to a set, using the add() method:

thisset = {"apple", "banana", "cherry"}

thisset.add("orange")

print(thisset)

Example

Add multiple items to a set, using the update() method:

thisset = {"apple", "banana", "cherry"}

thisset.update(["orange", "mango", "grapes"])

print(thisset

Get the Length of a Set

To determine how many items a set has, use the len() method.

Example

Get the number of items in a set:

thisset = {"apple", "banana", "cherry"}

print(len(thisset))

Remove Item

To remove an item in a set, use the remove(), or the discard() method.

Example

Remove "banana" by using the remove() method:

thisset = {"apple", "banana", "cherry"}

thisset.remove("banana")

print(thisset)

Note: If the item to remove does not exist, remove() will raise an error.

Example

Remove "banana" by using the discard() method:

thisset = {"apple", "banana", "cherry"}

thisset.discard("banana")

print(thisset)

Note: If the item to remove does not exist, discard() will NOT raise an error.

You can also use the pop(), method to remove an item, but this method will remove the last item. Remember that sets are unordered, so you will not know what item that gets removed.

The return value of the pop() method is the removed item.

Example

Remove the last item by using the pop() method:

thisset = {"apple", "banana", "cherry"}

x = thisset.pop()

print(x)

print(thisset)

Note: Sets are unordered, so when using the pop() method, you will not know which item that gets removed.

Example

The clear() method empties the set:

thisset = {"apple", "banana", "cherry"}

thisset.clear()

print(thisset)

Example

The del keyword will delete the set completely:

thisset = {"apple", "banana", "cherry"}

del thisset

print(thisset)

The set() Constructor

It is also possible to use the set() constructor to make a set.

Example

Using the set() constructor to make a set:

thisset = set(("apple", "banana", "cherry")) # note the double round-brackets
print(thisset)

Set Methods

Python has a set of built-in methods that you can use on sets.

Method	Description
add()	Adds an element to the set
clear()	Removes all the elements from the set
copy()	Returns a copy of the set
difference()	Returns a set containing the difference between two or more sets
difference_update()	Removes the items in this set that are also included in another, specified set
discard()	Remove the specified item
intersection()	Returns a set, that is the intersection of two other sets
intersection_update()	Removes the items in this set that are not present in other, specified set(s)
isdisjoint()	Returns whether two sets have a intersection or not
issubset()	Returns whether another set contains this set or not
issuperset()	Returns whether this set contains another set or not
pop()	Removes an element from the set
remove()	Removes the specified element
symmetric_difference()	Returns a set with the symmetric differences of two sets
symmetric_difference_update()	inserts the symmetric differences from this set and another
union()	Return a set containing the union of sets
update()	Update the set with the union of this set and others

Sets in Python

Python Sets

What is a set in Python?

How to create a set?

How to change a set in Python?

How to remove elements from a set?

Python Set Operations

Set Intersection

Set Difference

Set Symmetric Difference

Different Python Set Methods

Other Set Operations

Set Membership Test

Iterating Through a Set

Built-in Functions with Set

Python Frozenset

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