Standard Library Modules

The standard library modules most relevant to competitive programming: math, itertools, functools, and sys.

math

The math module provides mathematical functions and constants.

Constants

math.inf is useful as an initial value when searching for a minimum:

Integer Functions

math.isqrt is preferred over int(math.sqrt(n)) in CP because sqrt can return slightly off results due to floating point — for example int(math.sqrt(25)) could theoretically return 4 on some systems.

GCD and LCM

Logarithms and Powers

Checking Special Values

math.comb and math.perm

Binomial coefficients and permutations — useful in combinatorics problems:

itertools

The itertools module provides building blocks for working with iterators. Most useful for brute-force enumeration problems.

combinations and permutations

Counting without generating:

combinations_with_replacement

Like combinations but allows picking the same element more than once:

product

Generates the Cartesian product — equivalent to nested loops:

This is cleaner than writing deeply nested for loops when the depth is variable.

accumulate

Computes running totals (or any running operation):

chain

Connects multiple iterables into one sequence without copying any data — useful when you want to iterate over several collections as if they were one:

Iterating over multiple arrays in one loop:

Flatten a 2D list — scan all cells in one loop:

Prepend or append extra values to an iterator:

Merge adjacency lists in a graph:

groupby

Groups consecutive identical elements. Note: the input must be sorted first if you want to group all equal elements together:

functools

The functools module provides tools for working with functions.

lru_cache — Memoization

lru_cache is a decorator that automatically caches the results of a function. It is the fastest way to add memoization to a recursive function — one line transforms naive recursion into dynamic programming: