CodeCogs

Calculates the logarithm of the binomial coefficient with given arguments.

Interface

#include <codecogs/maths/combinatorics/arithmetic/log_binomial.h>

using namespace Maths::Combinatorics::Arithmetic;

inline double log_binomial(int n, int k)

This function calculates the following expression

$\mathrm{log binomial}(n) = \mathrm{ln} \left(\begin{array}{c}n\\k \end{array} \right) = \mathrm{ln}\,\left( \frac{n!}{k!(n-k)!} \right)$

(1)

In the given example, values of this function are returned for various arguments. The algorithm is designed in such a way to permit large values of the arguments, without creating overflow errors during the calculations. The example also demonstrates this feature, with n equal to 100 and k taking values from 70 up to 80.

Example 1

#include <codecogs/maths/combinatorics/arithmetic/log_binomial.h>
#include <iostream>
#include <iomanip>

int main()
{
  std::cout << std::setprecision(10);
  for (int i = 70; i <= 80; i++)
  {
    std::cout << "log_binomial(100, " << i << ") = ";
    std::cout << Maths::Combinatorics::Arithmetic::log_binomial(100, i);
    std::cout << std::endl;
  }
  return 0;
}

Output

log_binomial(100, 70) = 58.64209564
log_binomial(100, 71) = 57.78061315
log_binomial(100, 72) = 56.87124286
log_binomial(100, 73) = 55.91298793
log_binomial(100, 74) = 54.9047597
log_binomial(100, 75) = 53.84536812
log_binomial(100, 76) = 52.73351061
log_binomial(100, 77) = 51.56775902
log_binomial(100, 78) = 50.34654441
log_binomial(100, 79) = 49.06813901
log_binomial(100, 80) = 47.73063481

Parameters

the first argument of the binomial coefficient (the number of objects)

the second argument of the binomial coefficient (the number of choices)

Returns

the logarithm of the binomial coefficient with given arguments n and k

Interactive Calculator

Result –