Complexity Cheat Sheet for Python Operations

Python built-in data structures like lists, sets, and dictionaries provide a large number of operations making it easier to write concise code However, not understanding the complexity of these operations can sometimes cause your programs to run slower than expected.

This cheat sheet is designed to help developers understand the average and worst-case complexities of common operations for these data structures that help them write optimized and efficient code in Python.

List Time Complexity

Python's list is an ordered, mutable sequence, often implemented as a dynamic array. Below are the time complexities for common list operations:

Note: Tuples have the same operations (non-mutable) and complexities. 

Dictionary Time Complexity

Dictionaries in Python are implemented as hash tables, making them highly efficient for key-based operations. Here are the complexities:

Note: Defaultdict has operations same as dict with same time complexity as it inherits from dict.  

Set Time Complexity

Python’s set is another hash-based collection, optimized for membership checks and set operations:

Tuples Time Complexity

Tuples are immutable sequences, making them lighter but with limited operations compared to lists:

Strings Time Complexity

Strings are immutable and behave similarly to tuples in terms of time complexities:

Key Notes -

Lists:

• Amortized complexity applies to append() because resizing happens occasionally.
• Insertions and deletions at arbitrary positions require shifting elements.

Dictionaries and Sets:

• Hash collisions in dictionaries and sets can degrade O(1)operations to O(n).
• Worst-case complexity arises when all elements are in a single hash bucket.

Tuples and Strings:

• Both are immutable, making operations like insertion or deletion invalid.
• Access and iteration are linear due to sequential traversal requirements.

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Article Tags :

• Python
• python-utility

Practice Tags :

• python