# Python Big-O: Time & Space Complexity > Comprehensive documentation of time and space complexity for Python built-in operations and standard library modules. This site documents the Big-O time and space complexity of Python operations across built-in types, built-in functions, and standard library modules. It covers CPython 3.10–3.14, with notes on PyPy, Jython, and IronPython. ## Built-in Types - [Lists](https://pythoncomplexity.com/builtins/list/): Time and space complexity for list operations (append, insert, pop, sort, slicing, etc.) - [Dictionaries](https://pythoncomplexity.com/builtins/dict/): Complexity for dict operations (lookup, insert, delete, iteration) - [Sets](https://pythoncomplexity.com/builtins/set/): Complexity for set operations (membership, union, intersection, difference) - [Tuples](https://pythoncomplexity.com/builtins/tuple/): Complexity for tuple operations (indexing, slicing, membership) - [Strings](https://pythoncomplexity.com/builtins/str/): Complexity for string operations (find, replace, split, join, slicing) - [Bytes & Bytearray](https://pythoncomplexity.com/builtins/bytes/): Complexity for bytes and bytearray operations - [Frozenset](https://pythoncomplexity.com/builtins/frozenset/): Complexity for frozenset operations - [Range](https://pythoncomplexity.com/builtins/range/): Complexity for range operations (O(1) membership testing) - [Integer](https://pythoncomplexity.com/builtins/int/): Complexity for arbitrary-precision integer arithmetic - [Float](https://pythoncomplexity.com/builtins/float/): Complexity for floating-point operations - [Boolean](https://pythoncomplexity.com/builtins/bool/): Complexity for boolean operations ## Built-in Functions - [len()](https://pythoncomplexity.com/builtins/len/): O(1) for built-in types - [sorted()](https://pythoncomplexity.com/builtins/sorted/): O(n log n) Timsort - [max()](https://pythoncomplexity.com/builtins/max/): O(n) linear scan - [min()](https://pythoncomplexity.com/builtins/min/): O(n) linear scan - [sum()](https://pythoncomplexity.com/builtins/sum/): O(n) accumulation - [map()](https://pythoncomplexity.com/builtins/map/): Lazy O(1) per element - [filter()](https://pythoncomplexity.com/builtins/filter/): Lazy O(1) per element - [zip()](https://pythoncomplexity.com/builtins/zip/): Lazy O(1) per element - [enumerate()](https://pythoncomplexity.com/builtins/enumerate/): Lazy O(1) per element - [reversed()](https://pythoncomplexity.com/builtins/reversed/): O(1) iterator creation - [all()](https://pythoncomplexity.com/builtins/all/): O(n) short-circuit - [any()](https://pythoncomplexity.com/builtins/any/): O(n) short-circuit - [hash()](https://pythoncomplexity.com/builtins/hash/): Varies by type - [isinstance()](https://pythoncomplexity.com/builtins/isinstance/): O(n) MRO lookup ## Standard Library (Key Modules) - [collections](https://pythoncomplexity.com/stdlib/collections/): Container datatypes (deque, Counter, OrderedDict, defaultdict, namedtuple, ChainMap) - [collections.deque](https://pythoncomplexity.com/stdlib/deque/): O(1) append/pop from both ends - [collections.Counter](https://pythoncomplexity.com/stdlib/counter/): Counting and multiset operations - [collections.defaultdict](https://pythoncomplexity.com/stdlib/defaultdict/): Dict with default factory - [collections.OrderedDict](https://pythoncomplexity.com/stdlib/ordereddict/): Insertion-ordered dict with O(1) move_to_end - [collections.namedtuple](https://pythoncomplexity.com/stdlib/namedtuple/): Lightweight named tuples - [heapq](https://pythoncomplexity.com/stdlib/heapq/): O(log n) push/pop, O(n) heapify - [bisect](https://pythoncomplexity.com/stdlib/bisect/): O(log n) binary search, O(n) insertion - [itertools](https://pythoncomplexity.com/stdlib/itertools/): Lazy iterator combinatorics - [functools](https://pythoncomplexity.com/stdlib/functools/): Higher-order functions (lru_cache, reduce, partial) - [re](https://pythoncomplexity.com/stdlib/re/): Regular expression complexity - [json](https://pythoncomplexity.com/stdlib/json/): JSON encoding/decoding complexity - [datetime](https://pythoncomplexity.com/stdlib/datetime/): Date/time operations - [math](https://pythoncomplexity.com/stdlib/math/): Mathematical functions - [hashlib](https://pythoncomplexity.com/stdlib/hashlib/): Cryptographic hash functions - [pathlib](https://pythoncomplexity.com/stdlib/pathlib/): Filesystem path operations - [sqlite3](https://pythoncomplexity.com/stdlib/sqlite3/): SQLite database operations - [difflib](https://pythoncomplexity.com/stdlib/difflib/): Sequence comparison (SequenceMatcher, unified_diff) - [copy](https://pythoncomplexity.com/stdlib/copy/): Shallow and deep copy complexity - [array](https://pythoncomplexity.com/stdlib/array/): Typed array operations - [queue](https://pythoncomplexity.com/stdlib/queue/): Thread-safe queue implementations - [decimal](https://pythoncomplexity.com/stdlib/decimal/): Arbitrary-precision decimal arithmetic - [graphlib](https://pythoncomplexity.com/stdlib/graphlib/): Topological sorting - [operator](https://pythoncomplexity.com/stdlib/operator/): Function versions of operators - [random](https://pythoncomplexity.com/stdlib/random/): Random number generation - [statistics](https://pythoncomplexity.com/stdlib/statistics/): Statistical functions - [string](https://pythoncomplexity.com/stdlib/string/): String constants and templates - [struct](https://pythoncomplexity.com/stdlib/struct/): Binary data packing/unpacking - [typing](https://pythoncomplexity.com/stdlib/typing/): Type hint support ## Python Implementations - [CPython](https://pythoncomplexity.com/implementations/cpython/): Reference implementation details - [PyPy](https://pythoncomplexity.com/implementations/pypy/): JIT-compiled implementation differences - [Jython](https://pythoncomplexity.com/implementations/jython/): JVM-based implementation differences - [IronPython](https://pythoncomplexity.com/implementations/ironpython/): .NET-based implementation differences ## Python Versions - [Python 3.14](https://pythoncomplexity.com/versions/py314/): Complexity changes in 3.14 - [Python 3.13](https://pythoncomplexity.com/versions/py313/): Complexity changes in 3.13 - [Python 3.12](https://pythoncomplexity.com/versions/py312/): Complexity changes in 3.12 - [Python 3.11](https://pythoncomplexity.com/versions/py311/): Complexity changes in 3.11 - [Python 3.10](https://pythoncomplexity.com/versions/py310/): Complexity changes in 3.10