mathjs/lib/function/probability/permutations.js

'use strict';

var isInteger = require('../../utils/number').isInteger;

function factory (type, config, load, typed) {
  var factorial = load(require('./factorial'));

  /**
   * 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
   */
  var permutations = typed('permutations', {
    'number | BigNumber': factorial,

    'number, number': function (n, k) {
      var result, i;

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

      // Permute n objects, k at a time
      result = 1;
      for (i = n - k + 1; i <= n; i++) {
        result = result * i;
      }

      return result;
    },

    'BigNumber, BigNumber': function (n, k) {
      var result, i;

      if (!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 type.BigNumber(1);
      for (i = n.minus(k).plus(1); i.lte(n); i = i.plus(1)) {
        result = result.times(i);
      }

      return result;
    }

    // TODO: implement support for collection in permutations
  });

  permutations.toTex = '\\mathrm{${name}}\\left(${args}\\right)';

  return permutations;
}

/**
 * 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 = 'permutations';
exports.factory = factory;