In mathematics, there are sets and ordered sets (osets).
- set: an unordered container of unique elements (Implemented)
- oset: an ordered container of unique elements (NotImplemented)
In Python, only sets are directly implemented. We can emulate osets with regular dict keys (3.7+).
Given
a = [1, 2, 20, 6, 210, 2, 1]
b = {2, 6}
Code
oset = dict.fromkeys(a).keys()
# dict_keys([1, 2, 20, 6, 210])
Demo
Replicates are removed, insertion-order is preserved.
list(oset)
# [1, 2, 20, 6, 210]
Set-like operations on dict keys.
oset - b
# {1, 20, 210}
oset | b
# {1, 2, 5, 6, 20, 210}
oset & b
# {2, 6}
oset ^ b
# {1, 5, 20, 210}
Details
Note: an unordered structure does not preclude ordered elements. Rather, maintained order is not guaranteed. Example:
assert {1, 2, 3} == {2, 3, 1} # sets (order is ignored)
assert [1, 2, 3] != [2, 3, 1] # lists (order is guaranteed)
One may be pleased to discover that a list and multiset (mset) are two more fascinating, mathematical data structures:
- list: an ordered container of elements that permits replicates (Implemented)
- mset: an unordered container of elements that permits replicates (NotImplemented)*
Summary
Container | Ordered | Unique | Implemented
----------|---------|--------|------------
set | n | y | y
oset | y | y | n
list | y | n | y
mset | n | n | n*
*A multiset can be indirectly emulated with collections.Counter()
, a dict-like mapping of multiplicities (counts).
unique = list(dict.fromkeys([1, 2, 1]).keys())
. This works becausedict
s preserve insertion order now. – Cramoisy