Set

Set#

Sets are unordered collections of unique elements in Python. They provide O(1) average time complexity for membership testing and support mathematical set operations like union, intersection, and difference. This cheat sheet covers set comprehensions, common set operations, uniquifying lists, and the immutable frozenset type.

The source code is available on GitHub.

References#

Create a Set#

Create sets using curly braces {} or the set() constructor. Note that empty curly braces {} create a dict, not a set.

>>> s = {1, 2, 3}
>>> s
{1, 2, 3}
>>> s = set([1, 2, 2, 3])
>>> s
{1, 2, 3}
>>> empty = set()  # not {}
>>> type(empty)
<class 'set'>

Create Sets with Set Comprehension#

Like list comprehensions, set comprehensions provide a concise way to create sets. The syntax uses curly braces {} instead of square brackets.

>>> a = [1, 2, 5, 6, 6, 6, 7]
>>> s = {x for x in a}
>>> s
{1, 2, 5, 6, 7}
>>> s = {x for x in a if x > 3}
>>> s
{5, 6, 7}
>>> s = {x ** 2 for x in range(5)}
>>> s
{0, 1, 4, 9, 16}

Remove Duplicates from a List#

Converting a list to a set automatically removes duplicate elements. This is one of the most common use cases for sets.

>>> a = [1, 2, 2, 2, 3, 4, 5, 5]
>>> list(set(a))
[1, 2, 3, 4, 5]

To preserve the original order, use dict.fromkeys() (Python 3.7+):

>>> a = [3, 1, 2, 1, 3, 2]
>>> list(dict.fromkeys(a))
[3, 1, 2]

Add Items to a Set#

Use add() to add a single element, or update() to add multiple elements.

>>> s = {1, 2, 3}
>>> s.add(4)
>>> s
{1, 2, 3, 4}
>>> s.update([5, 6, 7])
>>> s
{1, 2, 3, 4, 5, 6, 7}
>>> s |= {8, 9}  # same as update
>>> s
{1, 2, 3, 4, 5, 6, 7, 8, 9}

Remove Items from a Set#

Use remove() to remove an element (raises KeyError if not found), or discard() to remove without error. Use pop() to remove an arbitrary element.

>>> s = {1, 2, 3, 4, 5}
>>> s.remove(3)
>>> s
{1, 2, 4, 5}
>>> s.discard(10)  # no error if not found
>>> s.pop()  # remove arbitrary element
1
>>> s.clear()  # remove all
>>> s
set()

Union with `|` Operator#

The union of two sets contains all elements from both sets. Use the | operator or the union() method.

>>> a = {1, 2, 3}
>>> b = {3, 4, 5}
>>> a | b
{1, 2, 3, 4, 5}
>>> a.union(b)
{1, 2, 3, 4, 5}
>>> a | b | {6, 7}  # multiple sets
{1, 2, 3, 4, 5, 6, 7}

Intersection with `&` Operator#

The intersection of two sets contains only elements that exist in both sets. Use the & operator or the intersection() method.

>>> a = {1, 2, 3, 4}
>>> b = {3, 4, 5, 6}
>>> a & b
{3, 4}
>>> a.intersection(b)
{3, 4}

Find Common Elements Between Lists#

Finding common items between two lists is a practical application of set intersection.

>>> a = [1, 1, 2, 3]
>>> b = [3, 5, 5, 6]
>>> list(set(a) & set(b))
[3]

Difference with `-` Operator#

The difference of two sets contains elements that are in the first set but not in the second. Use the - operator or the difference() method.

>>> a = {1, 2, 3, 4}
>>> b = {3, 4, 5, 6}
>>> a - b
{1, 2}
>>> b - a
{5, 6}

Symmetric Difference with `^` Operator#

The symmetric difference contains elements that are in either set, but not in both. Use the ^ operator or the symmetric_difference() method.

>>> a = {1, 2, 3}
>>> b = {3, 4, 5}
>>> a ^ b
{1, 2, 4, 5}

Check Subset with `<=` Operator#

Use <= or issubset() to check if all elements of one set are in another. Use < for proper subset (subset but not equal).

>>> a = {1, 2}
>>> b = {1, 2, 3, 4}
>>> a <= b  # a is subset of b
True
>>> a < b   # a is proper subset
True
>>> a <= a  # equal sets
True
>>> a < a   # not proper subset
False

Check Superset with `>=` Operator#

Use >= or issuperset() to check if a set contains all elements of another.

>>> a = {1, 2, 3, 4}
>>> b = {1, 2}
>>> a >= b  # a is superset of b
True
>>> a > b   # a is proper superset
True

Check Disjoint Sets#

Two sets are disjoint if they have no elements in common. Use isdisjoint() to check.

>>> a = {1, 2, 3}
>>> b = {4, 5, 6}
>>> a.isdisjoint(b)
True
>>> c = {3, 4, 5}
>>> a.isdisjoint(c)
False

Membership Testing#

Sets provide O(1) average time complexity for membership testing, making them much faster than lists for this operation.

>>> s = {1, 2, 3, 4, 5}
>>> 3 in s
True
>>> 10 in s
False
>>> 10 not in s
True

Frozenset - Immutable Set#

frozenset is an immutable version of set. It can be used as a dictionary key or as an element of another set.

>>> fs = frozenset([1, 2, 3])
>>> fs
frozenset({1, 2, 3})
>>> fs.add(4)  # raises AttributeError
AttributeError: 'frozenset' object has no attribute 'add'

Use frozenset as dictionary key:

>>> d = {frozenset([1, 2]): "a", frozenset([3, 4]): "b"}
>>> d[frozenset([1, 2])]
'a'

Use frozenset in a set:

>>> s = {frozenset([1, 2]), frozenset([3, 4])}
>>> frozenset([1, 2]) in s
True

Set Operations Summary#

# Creation
s = {1, 2, 3}           # literal
s = set([1, 2, 3])      # from iterable
s = {x for x in range(5)}  # comprehension

# Add/Remove
s.add(x)                # add single element
s.update([x, y])        # add multiple elements
s.remove(x)             # remove (KeyError if missing)
s.discard(x)            # remove (no error if missing)
s.pop()                 # remove arbitrary element
s.clear()               # remove all

# Set Operations
a | b                   # union
a & b                   # intersection
a - b                   # difference
a ^ b                   # symmetric difference

# Comparisons
a <= b                  # subset
a < b                   # proper subset
a >= b                  # superset
a > b                   # proper superset
a.isdisjoint(b)         # no common elements

# Membership
x in s                  # O(1) lookup
x not in s

Set

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