In Python, how to write a set containing a set?

Question

We know in Python, a set can be defined by writing out all its elements like this:

a_set={1,"xyz"}

And books of Python all say elements of a set can be any datatype. So we should be able to write out a set containing a set. I tried to write it as:

a_set={1,{"xyz"}}

But IDLE reported an error:

Traceback (most recent call last):
  File "<pyshell#58>", line 1, in <module>
    a_set={1,{"xyz"}}
TypeError: unhashable type: 'set'

I think this may be because Python is trying to understand it as a dictionary. Then, how to write out a set containing a set in Python?

While it doesn't directly answer the question, [Why must dictionary keys be immutable?](http://docs.python.org/3.3/faq/design.html#why-must-dictionary-keys-be-immutable) in the Python FAQ is relevant here. A set's values are basically the same as a dictionary's keys (they're both stored in hash tables), so you can't put a set in a set for the same reason you can't use a dict as a dict key. — abarnert, May 18 '13 at 01:07

score 16 · Accepted Answer · edited Jun 20 '20 at 09:12

16

The inner most sets need to be of type frozenset which is an immutable version of a set.

>>> a_set = {1, frozenset(['xyz'])}
>>> a_set
set([1, frozenset(['xyz'])])

From the docs:

class frozenset([iterable])

Return a new set or frozenset object whose elements are taken from iterable. The elements of a set must be hashable. To represent sets of sets, the inner sets must be frozenset objects. If iterable is not specified, a new empty set is returned.

edited Jun 20 '20 at 09:12

Community

1
1

answered May 17 '13 at 23:14

Jon Clements

138,671
33
247
280

2

+1. But it might be more clearer to write `{1, frozenset({'xyz'})}`. – abarnert May 17 '13 at 23:17
2

Phfff, 6 up-votes for the question and 12 for the RTFM answer? Standards are pretty low here on SO. – martineau May 18 '13 at 00:48

score 6 · Answer 2 · answered May 17 '13 at 23:14

6

Sets can only store immutable objects, while sets are mutable themselves. So a set can't contain another set.

Use a frozenset:

To represent sets of sets , the inner sets must be frozenset objects.

answered May 17 '13 at 23:14

Ashwini Chaudhary

244,495
58
464
504

1

It's worth noting that the limitation is that sets can only contain "hashable" objects, which are usually, but not necessarily "immutable". For example, instances of a custom classes that doesn't define `__hash__` or `__eq__` are hashable but can be mutated by assigning to attributes. This is allowed because such an object's hash is not influenced by its contents, only its identity, so it won't change if the the object is mutated. You can create objects that are partially mutable and partially immutable, and use the immutable parts to define the hash. – Blckknght May 18 '13 at 04:24

score 1 · Answer 3 · answered May 17 '13 at 23:21

1

This example illustrates the use of frozenset:

a_set = frozenset([1,2,3])
b_set = frozenset([1,3])
a_set_copy = frozenset([2,3,1])

set_of_sets = set([a_set, b_set, a_set_copy])

print set_of_sets
# set([frozenset([1, 3]), frozenset([1, 2, 3])])

answered May 17 '13 at 23:21

tzelleke

15,023
5
33
49

In Python, how to write a set containing a set?

3 Answers3