mathjs/lib/esm/function/probability/combinationsWithRep.js

import { factory } from '../../utils/factory.js';
import { isInteger } from '../../utils/number.js';
import { product } from '../../utils/product.js';
var name = 'combinationsWithRep';
var dependencies = ['typed'];
export var createCombinationsWithRep = /* #__PURE__ */factory(name, dependencies, (_ref) => {
  var {
    typed
  } = _ref;

  /**
   * Compute the number of ways of picking `k` unordered outcomes from `n`
   * possibilities, allowing individual outcomes to be repeated more than once.
   *
   * CombinationsWithRep only takes integer arguments.
   * The following condition must be enforced: k <= n + k -1.
   *
   * Syntax:
   *
   *     math.combinationsWithRep(n, k)
   *
   * Examples:
   *
   *    math.combinationsWithRep(7, 5) // returns 462
   *
   * See also:
   *
   *    combinations, 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 with replacement.
   */
  return typed(name, {
    'number, number': function numberNumber(n, k) {
      if (!isInteger(n) || n < 0) {
        throw new TypeError('Positive integer value expected in function combinationsWithRep');
      }

      if (!isInteger(k) || k < 0) {
        throw new TypeError('Positive integer value expected in function combinationsWithRep');
      }

      if (n < 1) {
        throw new TypeError('k must be less than or equal to n + k - 1');
      }

      if (k < n - 1) {
        var _prodrange = product(n, n + k - 1);

        return _prodrange / product(1, k);
      }

      var prodrange = product(k + 1, n + k - 1);
      return prodrange / product(1, n - 1);
    },
    'BigNumber, BigNumber': function BigNumberBigNumber(n, k) {
      var BigNumber = n.constructor;
      var result, i;
      var one = new BigNumber(1);
      var nMinusOne = n.minus(one);

      if (!isPositiveInteger(n) || !isPositiveInteger(k)) {
        throw new TypeError('Positive integer value expected in function combinationsWithRep');
      }

      if (n.lt(one)) {
        throw new TypeError('k must be less than or equal to n + k - 1 in function combinationsWithRep');
      }

      result = one;

      if (k.lt(nMinusOne)) {
        for (i = one; i.lte(nMinusOne); 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(nMinusOne.plus(i)).dividedBy(i);
        }
      }

      return result;
    }
  });
});
/**
 * Test whether BigNumber n is a positive integer
 * @param {BigNumber} n
 * @returns {boolean} isPositiveInteger
 */

function isPositiveInteger(n) {
  return n.isInteger() && n.gte(0);
}