mathjs/src/function/probability/combinations.js

'use strict'

const isInteger = require('../../utils/number').isInteger
const product = require('./product')
function factory (type, config, load, 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:
   *
   *    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.
   */

  const combinations = typed('combinations', {
    'number, number': function (n, k) {
      let prodrange, nMinusk

      if (!isInteger(n) || n < 0) {
        throw new TypeError('Positive integer value expected in function combinations')
      }
      if (!isInteger(k) || k < 0) {
        throw new TypeError('Positive integer value expected in function combinations')
      }
      if (k > n) {
        throw new TypeError('k must be less than or equal to n')
      }

      nMinusk = n - k

      if (k < nMinusk) {
        prodrange = product(nMinusk + 1, n)
        return prodrange / product(1, k)
      }
      prodrange = product(k + 1, n)
      return prodrange / product(1, nMinusk)
    },

    'BigNumber, BigNumber': function (n, k) {
      let max, result, i, ii
      const one = new type.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')
      }

      max = n.minus(k)
      if (k.lt(max)) max = k
      result = one
      for (i = one, ii = n.minus(max); i.lte(ii); i = i.plus(1)) {
        result = result.times(max.plus(i)).dividedBy(i)
      }

      return result
    }

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

  combinations.toTex = { 2: `\\binom{\${args[0]}}{\${args[1]}}` }

  return combinations
}

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

exports.name = 'combinations'
exports.factory = factory