# 8.7. `sets` — Unordered collections of unique elements

New in version 2.3.

Deprecated since version 2.6: The built-in `set`/`frozenset` types replace this module.

The `sets` module provides classes for constructing and manipulating unordered collections of unique elements. Common uses include membership testing, removing duplicates from a sequence, and computing standard math operations on sets such as intersection, union, difference, and symmetric difference.

Like other collections, sets support `x in set`, `len(set)`, and `for x in set`. 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.

Most set applications use the `Set` class which provides every set method except for `__hash__()`. For advanced applications requiring a hash method, the `ImmutableSet` class adds a `__hash__()` method but omits methods which alter the contents of the set. Both `Set` and `ImmutableSet` derive from `BaseSet`, an abstract class useful for determining whether something is a set: `isinstance(obj, BaseSet)`.

The set classes are implemented using dictionaries. Accordingly, the requirements for set elements are the same as those for dictionary keys; namely, that the element defines both `__eq__()` and `__hash__()`. As a result, sets cannot contain mutable elements such as lists or dictionaries. However, they can contain immutable collections such as tuples or instances of `ImmutableSet`. For convenience in implementing sets of sets, inner sets are automatically converted to immutable form, for example, `Set([Set(['dog'])])` is transformed to `Set([ImmutableSet(['dog'])])`.

class `sets.``Set`([iterable])

  Constructs a new empty `Set` object. If the optional iterable parameter is supplied, updates the set with elements obtained from iteration. All of the elements in iterable should be immutable or be transformable to an immutable using the protocol described in section Protocol for automatic conversion to immutable.

class `sets.``ImmutableSet`([iterable])

  Constructs a new empty `ImmutableSet` object. If the optional iterable parameter is supplied, updates the set with elements obtained from iteration. All of the elements in iterable should be immutable or be transformable to an immutable using the protocol described in section Protocol for automatic conversion to immutable.

  Because `ImmutableSet` objects provide a `__hash__()` method, they can be used as set elements or as dictionary keys. `ImmutableSet` objects do not have methods for adding or removing elements, so all of the elements must be known when the constructor is called.

## 8.7.1. Set Objects

Instances of `Set` and `ImmutableSet` both provide the following operations:

Operation | Equivalent | Result
--- | --- | ---
`len(s)` |  | number of elements in set s (cardinality)
`x in s` |  | test x for membership in s
`x not in s` |  | test x for non-membership in s
`s.issubset(t)` | `s <= t` | test whether every element in s is in t
`s.issuperset(t)` | `s >= t` | test whether every element in t is in s
`s.union(t)` | `s | t` | new set with elements from both s and t
`s.intersection(t)` | `s & t` | new set with elements common to s and t
`s.difference(t)` | `s - t` | new set with elements in s but not in t
`s.symmetric_difference(t)` | `s ^ t` | new set with elements in either s or t but not both
`s.copy()` |  | new set with a shallow copy of s

Note, the non-operator versions of `union()`, `intersection()`, `difference()`, and `symmetric_difference()` will accept any iterable as an argument. In contrast, their operator based counterparts require their arguments to be sets. This precludes error-prone constructions like `Set('abc') & 'cbs'` in favor of the more readable `Set('abc').intersection('cbs')`.

Changed in version 2.3.1: Formerly all arguments were required to be sets.

In addition, both `Set` and `ImmutableSet` support set to set comparisons. Two sets are equal if and only if every element of each set is contained in the other (each is a subset of the other). A set is less than another set if and only if the first set is a proper subset of the second set (is a subset, but is not equal). A set is greater than another set if and only if the first set is a proper superset of the second set (is a superset, but is not equal).

The subset and equality comparisons do not generalize to a complete ordering function. For example, any two disjoint sets are not equal and are not subsets of each other, so all of the following return `False`: `a<b`, `a==b`, or `a>b`. Accordingly, sets do not implement the `__cmp__()` method.

Since sets only define partial ordering (subset relationships), the output of the `list.sort()` method is undefined for lists of sets.

The following table lists operations available in `ImmutableSet` but not found in `Set`:

Operation | Result
--- | ---
`hash(s)` | returns a hash value for s

The following table lists operations available in `Set` but not found in `ImmutableSet`:

Operation | Equivalent | Result
--- | --- | ---
`s.update(t)` | s |= t | return set s with elements added from t
`s.intersection_update(t)` | s &= t | return set s keeping only elements also found in t
`s.difference_update(t)` | s -= t | return set s after removing elements found in t
`s.symmetric_difference_update(t)` | s ^= t | return set s with elements from s or t but not both
`s.add(x)` |  | add element x to set s
`s.remove(x)` |  | remove x from set s; raises `KeyError` if not present
`s.discard(x)` |  | removes x from set s if present
`s.pop()` |  | remove and return an arbitrary element from s; raises `KeyError` if empty
`s.clear()` |  | remove all elements from set s

Note, the non-operator versions of `update()`, `intersection_update()`, `difference_update()`, and `symmetric_difference_update()` will accept any iterable as an argument.

Changed in version 2.3.1: Formerly all arguments were required to be sets.

Also note, the module also includes a `union_update()` method which is an alias for `update()`. The method is included for backwards compatibility. Programmers should prefer the `update()` method because it is supported by the built-in `set()` and `frozenset()` types.

## 8.7.2. Example

    >>> from sets import Set
    >>> engineers = Set(['John', 'Jane', 'Jack', 'Janice'])
    >>> programmers = Set(['Jack', 'Sam', 'Susan', 'Janice'])
    >>> managers = Set(['Jane', 'Jack', 'Susan', 'Zack'])
    >>> employees = engineers | programmers | managers           # union
    >>> engineering_management = engineers & managers            # intersection
    >>> fulltime_management = managers - engineers - programmers # difference
    >>> engineers.add('Marvin')                                  # add element
    >>> print engineers # doctest: +SKIP
    Set(['Jane', 'Marvin', 'Janice', 'John', 'Jack'])
    >>> employees.issuperset(engineers)     # superset test
    False
    >>> employees.update(engineers)         # update from another set
    >>> employees.issuperset(engineers)
    True
    >>> for group in [engineers, programmers, managers, employees]: # doctest: +SKIP
    ...     group.discard('Susan')          # unconditionally remove element
    ...     print group
    ...
    Set(['Jane', 'Marvin', 'Janice', 'John', 'Jack'])
    Set(['Janice', 'Jack', 'Sam'])
    Set(['Jane', 'Zack', 'Jack'])
    Set(['Jack', 'Sam', 'Jane', 'Marvin', 'Janice', 'John', 'Zack'])

## 8.7.3. Protocol for automatic conversion to immutable

Sets can only contain immutable elements. For convenience, mutable `Set` objects are automatically copied to an `ImmutableSet` before being added as a set element.

The mechanism is to always add a hashable element, or if it is not hashable, the element is checked to see if it has an `__as_immutable__()` method which returns an immutable equivalent.

Since `Set` objects have a `__as_immutable__()` method returning an instance of `ImmutableSet`, it is possible to construct sets of sets.

A similar mechanism is needed by the `__contains__()` and `remove()` methods which need to hash an element to check for membership in a set. Those methods check an element for hashability and, if not, check for a `__as_temporarily_immutable__()` method which returns the element wrapped by a class that provides temporary methods for `__hash__()`, `__eq__()`, and `__ne__()`.

The alternate mechanism spares the need to build a separate copy of the original mutable object.

`Set` objects implement the `__as_temporarily_immutable__()` method which returns the `Set` object wrapped by a new class `_TemporarilyImmutableSet`.

The two mechanisms for adding hashability are normally invisible to the user; however, a conflict can arise in a multi-threaded environment where one thread is updating a set while another has temporarily wrapped it in `_TemporarilyImmutableSet`. In other words, sets of mutable sets are not thread-safe.

## 8.7.4. Comparison to the built-in `set` types

The built-in `set` and `frozenset` types were designed based on lessons learned from the `sets` module. The key differences are:

- `Set` and `ImmutableSet` were renamed to `set` and `frozenset`.
- There is no equivalent to `BaseSet`. Instead, use `isinstance(x, (set, frozenset))`.
- The hash algorithm for the built-ins performs significantly better (fewer collisions) for most datasets.
- The built-in versions have more space efficient pickles.
- The built-in versions do not have a `union_update()` method. Instead, use the `update()` method which is equivalent.
- The built-in versions do not have a `_repr(sorted=True)` method. Instead, use the built-in `repr()` and `sorted()` functions: `repr(sorted(s))`.
- The built-in version does not have a protocol for automatic conversion to immutable. Many found this feature to be confusing and no one in the community reported having found real uses for it.