maia-util/es6/binomial_coefficient.js

Utility math and music functions supporting various applications by Music Artificial Intelligence Algorithms, Inc.

import factorial from './factorial'

/**
 * This function calculates the factorial of an input number, e.g.,
 * x * (x - 1) * (x - 2) * ... * 2 * 1.
 *
 * @author Tom Collins
 * @comment 30th March 2023
 * @param {number} x - An integer.
 * @return {number} The calculated factorial.
 *
 * @example
 *     factorial(4)
 * →
 * 24
 */
 export default function binomial_coefficient(n, k){
   if (n - k < 0){
     return NaN
   }
   let ans = 1
   for (let i = 1; i <= Math.min(k, n - k); i++){
     ans *= (n + 1 - i)/i
   }
   return ans
 }

// This version clearly more closely related to the formula, but inefficient/
// impossible to calculate factorial(n) for large n.
// export default function binomial_coefficient(n, k){
//   return factorial(n)/factorial(k)/factorial(n - k >= 0 ? n - k : NaN)
// }