Multinomial

Calculates the multinomial coefficient with the given arguments.

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Multinomial
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Interface

C++

Multinomial

intmultinomial(	int	`n`
	int*	`factors`	)

This function calculates the multinomial coefficient with the given arguments $\inline k_1, k_2, \ldots k_n$ ,

$(k_1, k_2, \ldots k_n)! = \frac{(k_1 + k_2 + \ldots + k_n)!}{k_1! k_2! \ldots k_n!}$

(2)

It uses a direct algorithm and so computer overflow may occur during the intermediate calculations, as opposed to the other multinomial component.

References:

SUBSET, a C++ library of combinatorial routines, http://www.csit.fsu.edu/~burkardt/cpp_src/subset/subset.html

Example 1

#include <codecogs/maths/combinatorics/arithmetic/multinomial.h>
#include <iostream>
int main()
{
  int factors[4] = {1, 2, 3, 4};
  std::cout << "In the case of the following factors" << std::endl;
  for (int i = 0; i < 4; i++)
    std::cout << factors[i] << "  ";
  std::cout << std::endl << "the multinomial coefficient is" << std::endl;
  std::cout << Maths::Combinatorics::Arithmetic::multinomial(4, factors) << std::endl;
  return 0;
}

Output: In the case of the following factors 1 2 3 4 the multinomial coefficient is 12600

Parameters

n	the number of arguments
factors	the factors of the multinomial, given as an array

Returns

the multinomial coefficient based on the values of the factors

Authors

Lucian Bentea (August 2005)

Source Code

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