my_python_library

A Python library of common algorithms and data structures for competitive programming.

Features

This library provides modular, tested implementations of frequently used components.

Tier	File Name	Description	Key Complexity
🥇 Tier 1	union_find.py	Disjoint Set Union (DSU)	$O(\alpha(N))$
	mod_pow.py	Modular Exponentiation (a^b % m)	$O(\log b)$
	mod_inverse.py	Modular Multiplicative Inverse (a^-1 % m)	$O(\log m)$
	prime_factorization.py	Prime factorization of an integer	$O(\sqrt{N})$
🥈 Tier 2	dijkstra.py	Single-Source Shortest Path (SSSP)	$O((E+V)\log V)$
	sieve_of_eratosthenes.py	Sieve for primes and minimum prime factor table	$O(N \log \log N)$
	combination.py	nCk % M using precomputed factorials	$O(1)$ per query
🥉 Tier 3	binary_indexed_tree.py	Point updates, range sum queries (BIT/Fenwick)	$O(\log N)$
	segment_tree.py	Point updates, range queries (e.g., min, max, sum)	$O(\log N)$

How to Use

This library is structured as a Python package. To use it in your own scripts, make sure your script is in a directory that can see the my_python_library package.

For example, if your script is in the project root (/Users/mei/my_python_library/), you can import modules like this:

import sys
# It may be necessary to increase Python's recursion limit for graph problems
sys.setrecursionlimit(2000000) 

from my_python_library.union_find import UnionFind
from my_python_library.dijkstra import dijkstra

def solve():
    # ... your solution code using the imported modules ...
    uf = UnionFind(10)
    uf.unite(0, 1)
    # ...

Testing

The library includes a suite of unit tests to ensure correctness. To run the tests, execute the following command from the project root directory:

python3 -m unittest discover tests