Set Operations
Complete reference for Python set operations and methods. Sets are mutable, unordered collections of unique elements that provide efficient membership testing and mathematical set operations.
| Operation | Syntax | Example | Result | Description |
|---|
| Empty Set | set() | my_set = set() | set() | Create empty set (not {}) |
| Set Literal | {item1, item2, ...} | {1, 2, 3} | {1, 2, 3} | Create set with items |
| Set from Iterable | set(iterable) | set([1, 2, 2, 3]) | {1, 2, 3} | Convert iterable to set (removes duplicates) |
| Set Comprehension | {expr for item in iterable} | {x*2 for x in range(3)} | {0, 2, 4} | Create set with expression |
| Length | len(set) | len({1, 2, 3}) | 3 | Get number of unique items |
| Membership | item in set | 2 in {1, 2, 3} | True | Check if item exists |
| Copy | set.copy() | new_set = my_set.copy() | New set | Create shallow copy |
| Method | Purpose | Example | Result | Description |
|---|
| add() | Add single element | s.add(4) | Modifies set | Adds element to set (no effect if already present) |
| update() | Add multiple elements | s.update([4, 5, 6]) | Modifies set | Adds all elements from iterable |
| Method | Purpose | Example | Result | Description |
|---|
| remove() | Remove element | s.remove(2) | Modifies set | Removes element (raises KeyError if not found) |
| discard() | Remove element safely | s.discard(2) | Modifies set | Removes element (no error if not found) |
| pop() | Remove arbitrary element | s.pop() | Returns removed element | Removes and returns arbitrary element |
| clear() | Remove all elements | s.clear() | set() | Empties the set |
| Operation | Syntax | Example | Result | Description |
|---|
| Union Operator | set1 | set2 | {1, 2} | {2, 3} | {1, 2, 3} | Elements in either set |
| Union Method | set1.union(set2) | {1, 2}.union({2, 3}) | {1, 2, 3} | Elements in either set |
| Multiple Union | set1.union(set2, set3) | {1}.union({2}, {3}) | {1, 2, 3} | Union of multiple sets |
| In-place Union | set1 |= set2 | s |= {4, 5} | Modifies s | Update with union |
| Operation | Syntax | Example | Result | Description |
|---|
| Intersection Operator | set1 & set2 | {1, 2, 3} & {2, 3, 4} | {2, 3} | Elements in both sets |
| Intersection Method | set1.intersection(set2) | {1, 2, 3}.intersection({2, 3, 4}) | {2, 3} | Elements in both sets |
| Multiple Intersection | set1.intersection(set2, set3) | {1, 2}.intersection({2}, {2, 3}) | {2} | Common elements in all sets |
| In-place Intersection | set1 &= set2 | s &= {2, 3} | Modifies s | Update with intersection |
| Operation | Syntax | Example | Result | Description |
|---|
| Difference Operator | set1 - set2 | {1, 2, 3} - {2, 3, 4} | {1} | Elements in set1 but not set2 |
| Difference Method | set1.difference(set2) | {1, 2, 3}.difference({2, 3, 4}) | {1} | Elements in set1 but not set2 |
| Multiple Difference | set1.difference(set2, set3) | {1, 2, 3}.difference({2}, {3}) | {1} | Elements not in any other set |
| In-place Difference | set1 -= set2 | s -= {2, 3} | Modifies s | Update with difference |
| Operation | Syntax | Example | Result | Description |
|---|
| Symmetric Difference Operator | set1 ^ set2 | {1, 2, 3} ^ {2, 3, 4} | {1, 4} | Elements in either set, but not both |
| Symmetric Difference Method | set1.symmetric_difference(set2) | {1, 2, 3}.symmetric_difference({2, 3, 4}) | {1, 4} | Elements in either set, but not both |
| In-place Symmetric Difference | set1 ^= set2 | s ^= {2, 3} | Modifies s | Update with symmetric difference |
| Method | Purpose | Example | Result | Description |
|---|
| issubset() | Check if subset | {1, 2}.issubset({1, 2, 3}) | True | True if all elements are in other set |
| issuperset() | Check if superset | {1, 2, 3}.issuperset({1, 2}) | True | True if contains all elements of other set |
| isdisjoint() | Check if disjoint | {1, 2}.isdisjoint({3, 4}) | True | True if no common elements |
| Type | Syntax | Example | Result | Description |
|---|
| Basic | {expr for item in iterable} | {x**2 for x in range(5)} | {0, 1, 4, 9, 16} | Create set from expression |
| With Condition | {expr for item in iterable if condition} | {x for x in range(10) if x % 2 == 0} | {0, 2, 4, 6, 8} | Filter with condition |
| Nested | {expr for item in iterable for subitem in item} | {char for word in ['hello', 'world'] for char in word} | {'h', 'e', 'l', 'o', 'w', 'r', 'd'} | Flatten structures |
| Operation | Average Case | Worst Case | Notes |
|---|
| Add/Remove/Search | O(1) | O(n) | Hash collision can cause O(n) |
| Union/Intersection | O(len(s) + len(t)) | O(len(s) * len(t)) | Depends on hash distribution |
| Subset/Superset | O(len(smaller_set)) | O(len(smaller_set)) | Check each element |
| Iteration | O(n) | O(n) | Must visit all elements |
# Efficient membership testing
# Bad: using list for frequent membership tests
def slow_check(item, items_list):
return item in items_list # O(n) for each check
# Good: convert to set for frequent membership tests
def fast_check(item, items_set):
return item in items_set # O(1) for each check
# Convert once, use many times
items_list = [1, 2, 3, 4, 5] * 1000 # Large list
items_set = set(items_list) # Convert once
# Multiple membership tests are now fast
for i in range(100):
if i in items_set: # Fast O(1) lookup
pass
# Set operations are generally faster than manual loops
# Bad: manual intersection
def manual_intersection(list1, list2):
result = []
for item in list1:
if item in list2:
result.append(item)
return result
# Good: use set intersection
def set_intersection(list1, list2):
return list(set(list1) & set(list2))
- Use sets for membership testing: Much faster than lists for
in operations - Remove duplicates efficiently: Convert to set and back to list
- Use set operations: More readable than manual loops for common operations
- Consider frozenset for immutable data: When you need hashable sets
- Be careful with mutable elements: Sets can only contain hashable (immutable) elements
- Use set comprehensions: More readable and often faster than loops
- Choose appropriate data structure: Sets for uniqueness, lists for order, dicts for key-value
- Leverage mathematical operations: Union, intersection, difference for data analysis
