mathjs/src/function/probability/combinations.js

import { factory } from '../../utils/factory'
import { combinationsNumber } from '../../plain/number/combinations'

const name = 'combinations'
const dependencies = ['typed']

export const createCombinations = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {
  /**
   * Compute the number of ways of picking `k` unordered outcomes from `n`
   * possibilities.
   *
   * Combinations only takes integer arguments.
   * The following condition must be enforced: k <= n.
   *
   * Syntax:
   *
   *     math.combinations(n, k)
   *
   * Examples:
   *
   *    math.combinations(7, 5) // returns 21
   *
   * See also:
   *
   *    combinationsWithRep, permutations, factorial
   *
   * @param {number | BigNumber} n    Total number of objects in the set
   * @param {number | BigNumber} k    Number of objects in the subset
   * @return {number | BigNumber}     Number of possible combinations.
   */
  return typed(name, {
    'number, number': combinationsNumber,

    'BigNumber, BigNumber': function (n, k) {
      const BigNumber = n.constructor
      let result, i
      const nMinusk = n.minus(k)
      const one = new BigNumber(1)

      if (!isPositiveInteger(n) || !isPositiveInteger(k)) {
        throw new TypeError('Positive integer value expected in function combinations')
      }
      if (k.gt(n)) {
        throw new TypeError('k must be less than n in function combinations')
      }

      result = one
      if (k.lt(nMinusk)) {
        for (i = one; i.lte(nMinusk); i = i.plus(one)) {
          result = result.times(k.plus(i)).dividedBy(i)
        }
      } else {
        for (i = one; i.lte(k); i = i.plus(one)) {
          result = result.times(nMinusk.plus(i)).dividedBy(i)
        }
      }

      return result
    }

    // TODO: implement support for collection in combinations
  })
})

/**
 * Test whether BigNumber n is a positive integer
 * @param {BigNumber} n
 * @returns {boolean} isPositiveInteger
 */
function isPositiveInteger (n) {
  return n.isInteger() && n.gte(0)
}