/**
 * Keeps track of a set of elements partitioned into a
 * number of disjoint (nonoverlapping) subsets.
 * Allows to check whether the path between two nodes exists.
 * <br>
 * The algorithm is inspired by Robert Sedgewick's Java implementation.
 * {@link http://algs4.cs.princeton.edu/home/}
 *
 * @example
 *
 * var QuickUnion = require('path-to-algorithms/' +
 * 'src/sets/quickunion').QuickUnion;
 *
 * var qunion = new QuickUnion(10);
 * qunion.union(0, 1);
 * qunion.union(2, 1);
 * qunion.union(3, 4);
 * qunion.union(8, 9);
 * qunion.union(4, 8);
 *
 * console.log(qunion.connected(0, 9)); // false
 * console.log(qunion.connected(3, 9)); // true
 *
 * @public
 * @module sets/quickunion
 */

(function (exports) {
  'use strict';

  /**
   * Initialization.<br><br>
   * Time complexity: O(N).
   *
   * @public
   * @constructor
   * @param {Numner} size Count of the nodes.
   */
  exports.QuickUnion = function (n) {
    this._ids = [];
    for (var i = 0; i < n; i += 1) {
      this._ids[i] = i;
    }
  };

  /**
   * Finds the root of given node.<br><br>
   * Time complexity: O(N).
   * @private
   * @param {Number} i The given node.
   * @return {Number} Root of the given node.
   */
  exports.QuickUnion.prototype._root = function (i) {
    while (i !== this._ids[i]) {
      i = this._ids[i];
    }
    return i;
  };

  /**
   * Connects two nodes - p and q.<br><br>
   * Time complexity: O(N).
   *
   * @public
   * @method
   * @param {Number} p The first node.
   * @param {Number} q The second node.
   */
  exports.QuickUnion.prototype.union = function (p, q) {
    var pRoot = this._root(p);
    var qRoot = this._root(q);
    this._ids[pRoot] = qRoot;
  };

  /**
   * Checks whether two nodes are connected.<br><br>
   * Time complexity: O(N).
   *
   * @param {Number} p The first node.
   * @param {Number} q The second node.
   * @return {Boolean} True/false depending on whether the nodes are connected.
   */
  exports.QuickUnion.prototype.connected = function (p, q) {
    return this._root(p) === this._root(q);
  };
})(typeof window === 'undefined' ? module.exports : window);