binomial_coefficient Module Reference

Compute binomial coefficients. More...

Functions
template<Integer T>
constexpr T	ntlib::binom (T n, T k) noexcept
	Computes a single binomial coefficient.
template<Integer T>
constexpr T	ntlib::mod_p_binom (T n, T k, T p) noexcept
	Compute a single binomial coefficient module a sufficiently large prime.
template<Integer T>
constexpr T	ntlib::mod_pp_binom (T n, T k, T p, T e)
	Computes a single binomial coefficient modulo a prime power.
template<Integer T>
constexpr T	ntlib::mod_binom (T n, T k, T m)
	Computes a single binomial coefficient modulo an arbitrary number.
template<Integer T>
constexpr std::vector< std::vector< T > >	ntlib::binom_table (T N)
	Computes the first \(N\) rows of Pascal's triangle.
template<Integer T>
constexpr std::vector< std::vector< T > >	ntlib::mod_binom_table (std::size_t N, T m)
	Computes the first \(N\) rows of Pascal's triangle module some number \(m\).

Detailed Description

Compute binomial coefficients.

Compute the binomial coefficient \({n \choose k}\) for \(0 \leq k \leq n\), possibly modulo some number \(m\). The binomial coeffient counts the number of \(k\)-element subsets of an \(n\)-element universe.

Code for one-shot computation modulo a number \(m\) is based on https://cp-algorithms.com/combinatorics/binomial-coefficients.html.

Files
file	modules/combinatorics/binomial_coefficient.cpp
	Primary module interface unit for module binomial_coefficient.

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