Sets & Frozensets

Sets store unique hashable elements with fast membership tests. Frozensets are immutable sets you can use as dict keys or elements of other sets.

Recipe

seen: set[int] = set()
for value in [1, 2, 2, 3]:
    if value not in seen:
        seen.add(value)
 
a, b = {1, 2, 3}, {3, 4}
union = a | b
only_a = a - b

When to reach for this:

Deduplicating sequences before processing
Permission/tag intersections
Graph neighbor collections
Finding symmetric differences between snapshots

Working Example

def unique_preserve_order(items: list[str]) -> list[str]:
    seen: set[str] = set()
    result: list[str] = []
    for item in items:
        if item not in seen:
            seen.add(item)
            result.append(item)
    return result
 
def jaccard(tags_a: set[str], tags_b: set[str]) -> float:
    if not tags_a and not tags_b:
        return 1.0
    return len(tags_a & tags_b) / len(tags_a | tags_b)
 
def frozen_key(groups: list[frozenset[str]]) -> dict[frozenset[str], int]:
    return {group: len(group) for group in groups}
 
if __name__ == "__main__":
    print(unique_preserve_order(["a", "b", "a", "c"]))
    print(jaccard({"py", "ml"}, {"py", "web"}))
    print(frozen_key([frozenset({"a", "b"}), frozenset({"c"})]))

What this demonstrates:

Manual order-preserving dedupe when dict.fromkeys is not enough ordering control
& and | for intersection and union
frozenset as dict key for groupings

Deep Dive

How It Works

Hash set - Same average O(1) as dict keys without values.
Unordered - Iteration order is implementation-dependent - do not rely for semantics.
frozenset - Immutable; hashable if elements hashable.
Subset tests - a <= b, a < b, a >= b for containment.
Comprehensions - {x for x in items if cond} builds sets directly.

Operations

Operator	Meaning
`\|`	union
`&`	intersection
`-`	difference
`^`	symmetric difference

Python Notes

# empty set - not {}
empty = set()
 
# bulk add
tags.update(["a", "b", "c"])
 
# discard vs remove - discard ignores missing
tags.discard("missing")

Gotchas

{} is empty dict - Use set() for empty set. Fix: set() or {0} placeholder only if intentional.
Unhashable elements - Lists in sets fail. Fix: Convert to tuple or frozenset.
Order assumptions - Sets do not preserve insert order for logic. Fix: dict.fromkeys trick or ordered dedupe loop.
Tiny sets slower than list scan - Constant overhead matters for n < ~10. Fix: Profile before optimizing.
Mutating set during iteration - Size change error. Fix: Copy set(s) before removing in loop.

Alternatives

Alternative	Use When	Don't Use When
`dict.fromkeys`	Order-preserving unique keys	Need set algebra
`list` + `in`	Very small n	Large membership checks
`bloom filter`	Probabilistic huge scale	Need exact membership
`pandas.unique`	Column dedupe in dataframes	Plain Python script

FAQs

set or list for uniqueness?

set when order does not matter and membership is frequent. Order-preserving dedupe uses dict or manual loop.

What is frozenset for?

Hashable set - dict keys, set elements, cache keys from frozenset of tags.

How do I intersect many sets?

from functools import reduce; reduce(set.__and__, sets) or loop with acc &= s.

issubset vs <=?

Same for sets - pick readable operator or method consistently in codebase.

Can sets hold mixed types?

Yes if all elements hashable and comparable for equality - but harms clarity; prefer homogeneous sets.

How dedupe preserve order Python 3.7+?

list(dict.fromkeys(items)) - fast idiomatic pattern.

symmetric_difference use case?

Elements in either set but not both - diffing permission grants between environments.

set comprehension vs filter?

{x for x in items if pred(x)} builds set directly without intermediate list.

Are sets thread-safe?

Individual operations atomic in CPython but compound read-modify-write needs locks.

pop from set?

set.pop() removes arbitrary element - useful only when any element acceptable.

Dictionaries - maps vs sets
Immutability & Hashability - hash rules
collections Module - Counter uses dict not set
Choosing the Right Data Structure - membership patterns

Stack versions: This page was written for Python 3.14.0 (stable 3.14, maintenance 3.13), FastAPI 0.115+, Django 5.2, Flask 3.1, Pydantic 2, PyTorch 2.6+, pandas 2.2+, Polars 1.x, ruff 0.9+, and uv 0.6+.

Sets & Frozensets

Sets store unique hashable elements with fast membership tests. Frozensets are immutable sets you can use as dict keys or elements of other sets.

Recipe

seen: set[int] = set()
for value in [1, 2, 2, 3]:
    if value not in seen:
        seen.add(value)
 
a, b = {1, 2, 3}, {3, 4}
union = a | b
only_a = a - b

When to reach for this:

Deduplicating sequences before processing
Permission/tag intersections
Graph neighbor collections
Finding symmetric differences between snapshots

Working Example

def unique_preserve_order(items: list[str]) -> list[str]:
    seen: set[str] = set()
    result: list[str] = []
    for item in items:
        if item not in seen:
            seen.add(item)
            result.append(item)
    return result
 
def jaccard(tags_a: set[str], tags_b: set[str]) -> float:
    if not tags_a and not tags_b:
        return 1.0
    return len(tags_a & tags_b) / len(tags_a | tags_b)
 
def frozen_key(groups: list[frozenset[str]]) -> dict[frozenset[str], int]:
    return {group: len(group) for group in groups}
 
if __name__ == "__main__":
    print(unique_preserve_order(["a", "b", "a", "c"]))
    print(jaccard({"py", "ml"}, {"py", "web"}))
    print(frozen_key([frozenset({"a", "b"}), frozenset({"c"})]))

What this demonstrates:

Manual order-preserving dedupe when dict.fromkeys is not enough ordering control
& and | for intersection and union
frozenset as dict key for groupings

Deep Dive

How It Works

Hash set - Same average O(1) as dict keys without values.
Unordered - Iteration order is implementation-dependent - do not rely for semantics.
frozenset - Immutable; hashable if elements hashable.
Subset tests - a <= b, a < b, a >= b for containment.
Comprehensions - {x for x in items if cond} builds sets directly.

Operations

Operator	Meaning
`\|`	union
`&`	intersection
`-`	difference
`^`	symmetric difference

Python Notes

# empty set - not {}
empty = set()
 
# bulk add
tags.update(["a", "b", "c"])
 
# discard vs remove - discard ignores missing
tags.discard("missing")

Gotchas

{} is empty dict - Use set() for empty set. Fix: set() or {0} placeholder only if intentional.
Unhashable elements - Lists in sets fail. Fix: Convert to tuple or frozenset.
Order assumptions - Sets do not preserve insert order for logic. Fix: dict.fromkeys trick or ordered dedupe loop.
Tiny sets slower than list scan - Constant overhead matters for n < ~10. Fix: Profile before optimizing.
Mutating set during iteration - Size change error. Fix: Copy set(s) before removing in loop.

Alternatives

Alternative	Use When	Don't Use When
`dict.fromkeys`	Order-preserving unique keys	Need set algebra
`list` + `in`	Very small n	Large membership checks
`bloom filter`	Probabilistic huge scale	Need exact membership
`pandas.unique`	Column dedupe in dataframes	Plain Python script

FAQs

set or list for uniqueness?

set when order does not matter and membership is frequent. Order-preserving dedupe uses dict or manual loop.

What is frozenset for?

Hashable set - dict keys, set elements, cache keys from frozenset of tags.

How do I intersect many sets?

from functools import reduce; reduce(set.__and__, sets) or loop with acc &= s.

issubset vs <=?

Same for sets - pick readable operator or method consistently in codebase.

Can sets hold mixed types?

Yes if all elements hashable and comparable for equality - but harms clarity; prefer homogeneous sets.

How dedupe preserve order Python 3.7+?

list(dict.fromkeys(items)) - fast idiomatic pattern.

symmetric_difference use case?

Elements in either set but not both - diffing permission grants between environments.

set comprehension vs filter?

{x for x in items if pred(x)} builds set directly without intermediate list.

Are sets thread-safe?

Individual operations atomic in CPython but compound read-modify-write needs locks.

pop from set?

set.pop() removes arbitrary element - useful only when any element acceptable.

Dictionaries - maps vs sets
Immutability & Hashability - hash rules
collections Module - Counter uses dict not set
Choosing the Right Data Structure - membership patterns

Stack versions: This page was written for Python 3.14.0 (stable 3.14, maintenance 3.13), FastAPI 0.115+, Django 5.2, Flask 3.1, Pydantic 2, PyTorch 2.6+, pandas 2.2+, Polars 1.x, ruff 0.9+, and uv 0.6+.

Sets & Frozensets

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Sets & Frozensets