mathjs/lib/function/probability/permutations.js

'use strict';

module.exports = function (math) {
  var util = require('../../util/index'),

      BigNumber = math.type.BigNumber,

      isNumber = util.number.isNumber,
      isInteger = util.number.isInteger;

  /**
   * Compute the number of ways of obtaining an ordered subset of `k` elements
   * from a set of `n` elements.
   *
   * Permutations only takes integer arguments.
   * The following condition must be enforced: k <= n.
   *
   * Syntax:
   *
   *     math.permutations(n)
   *     math.permutations(n, k)
   *
   * Examples:
   *
   *    math.permutations(5);     // 120
   *    math.permutations(5, 3);  // 60
   *
   * See also:
   *
   *    combinations, factorial
   *
   * @param {Number | BigNumber} n  The number of objects in total
   * @param {Number | BigNumber} k  The number of objects in the subset
   * @return {Number | BigNumber}   The number of permutations
   */
  math.permutations = function permutations (n, k) {
    var result, i;

    var arity = arguments.length;
    if (arity > 2) {
      throw new math.error.ArgumentsError('permutations', arguments.length, 2);
    }

    if (isNumber(n)) {
      if (!isInteger(n) || n < 0) {
        throw new TypeError('Positive integer value expected in function permutations');
      }
      
      // Permute n objects
      if (arity == 1) {
        return math.factorial(n);
      }
      
      // Permute n objects, k at a time
      if (arity == 2) {
        if (isNumber(k)) {
          if (!isInteger(k) || k < 0) {
            throw new TypeError('Positive integer value expected in function permutations');
          }
          if (k > n) {
            throw new TypeError('second argument k must be less than or equal to first argument n');
          }

          result = 1;
          for (i = n - k + 1; i <= n; i++) {
            result = result * i;
          }
          return result;
        }
      }
    }

    if (n instanceof BigNumber) {
      if (k === undefined && isPositiveInteger(n)) {
        return math.factorial(n);
      }

      // make sure k is a BigNumber as well
      // not all numbers can be converted to BigNumber
      k = BigNumber.convert(k);

      if (!(k instanceof BigNumber) || !isPositiveInteger(n) || !isPositiveInteger(k)) {
        throw new TypeError('Positive integer value expected in function permutations');
      }
      if (k.gt(n)) {
        throw new TypeError('second argument k must be less than or equal to first argument n');
      }

      result = new BigNumber(1);
      for (i = n.minus(k).plus(1); i.lte(n); i = i.plus(1)) {
        result = result.times(i);
      }
      return result;
    }

    throw new math.error.UnsupportedTypeError('permutations', math['typeof'](n));
  };

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