是否有内置 function 来计算 C++ 中的 nCr？

Question

In python 3.8, there is a built-in function for calculating the number of combinations ( nCr(n, k) ):

>>>from math import comb
>>>comb(10,3)
120

Is there any such function in C++?

Answer 1

The beta function from the mathematical library can be used to express binomial coefficients (aka nCr).

double binom(int n, int k) {
    return 1/((n+1)*std::beta(n-k+1,k+1));
}

Source.

This function is available either with C++17 or as part of an implementation of the mathematical special functions extensions for C++ (ISO/IEC 29124:2010).In the latter case, your implementation may require you to #define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1 before including the <cmath> header for the function to be available.

Note that, unlike Python, C++ does not have built-in support for big integer numbers, so using floating point arithmetic is probably a good choice here in the first place.

Answer 2

Disclaimer: If using C++17, use the beta function as described by @ComicSansMS Otherwise you can use the tgamma or even lgamma functions if using C++11

Using lgamma :

double comb_l(double n, double k) {
    return std::exp(std::lgamma(n + 1)- std::lgamma(k + 1) - std::lgamma(n - k + 1));
}

Using tgamma :

double comb_t(double n, double k) {
        return std::tgamma(n + 1) / std::tgamma(k + 1) / std::tgamma(n - k + 1));
}

Answer 3

In python 3.8, there is a built-in function for calculating the number of combinations ( nCr(n, k) ):

>>>from math import comb
>>>comb(10,3)
120

Is there any such function in C++?