Sets

A set is an unordered collection of unique items. It can be defined in two different manners:

Taking all the elements from an iterable such as a string, list or tuple using the built-in set() constructor:
```
>>> set('hello')
{'e', 'h', 'l', 'o'}
>>> set([1, 2, 2, 3])
{1, 2, 3}
```
Placing a comma-separated list of elements between curly braces.
```
>>> {2, 2, 3, 5, 7, 7, 7, 11}
{2, 3, 5, 7, 11}
```

As a sidenote, the empty set must be built with set() since Python interprets {} as an empty dictionary.

Operators and methods

Sets support the already familiar x in set, len(set), and for x in set. Since sets are unordered, there is no way to record the position of an element and thus indexing or slicing is not possible.

The set type is mutable in such a way that its contents can be changed using methods like add() and remove().

The Python translation of fundamental operations is pretty undisguised. Let’s consider the following sets,

s1 = {1, 2, 3, 4}
s2 = {3, 4, 5, 6}

and we’ll take a look at some of the most usual. For a complete outlook refer to the Python documentation. In all cases we have an operator and a method available which return a new set and are in essence equivalent.

Union: Items appearing in either

s1 | s2
s1.union(s2)
# {1, 2, 3, 4, 5, 6}

Intersection: Items appearing in both
```
s1 & s2
s1.intersection(s2)
# {3, 4}
```
Difference: Items appearing in s1 but not in s2
```
s1 - s2
s1.difference(s2)
# {1, 2}
```
Symmetric difference: Items appearing in only one set
```
s1 ^ s2
s1.symmetric_difference(s2)
# {1, 2, 5, 6}
```

Lliçons.jutge.org
Víctor Adell
Universitat Politècnica de Catalunya, 2023