//******************************
// Written by Peter Golde
// Copyright (c) 2004-2005, Wintellect
//
// Use and restribution of this code is subject to the license agreement 
// contained in the file "License.txt" accompanying this file.
//******************************

using System;
using System.Collections.Generic;
using System.Collections;
using System.Diagnostics;

namespace Wintellect.PowerCollections
{
    /// <summary>
    /// Set&lt;T&gt; is a collection that contains items of type T. 
    /// The item are maintained in a haphazard, unpredictable order, and duplicate items are not allowed.
    /// </summary>
    /// <remarks>
    /// <p>The items are compared in one of two ways. If T implements IComparable&lt;T&gt; 
    /// then the Equals method of that interface will be used to compare items, otherwise the Equals
    /// method from Object will be used. Alternatively, an instance of IComparer&lt;T&gt; can be passed
    /// to the constructor to use to compare items.</p>
    /// <p>Set is implemented as a hash table. Inserting, deleting, and looking up an
    /// an element all are done in approximately constant time, regardless of the number of items in the Set.</p>
    /// <p><see cref="OrderedSet&lt;T&gt;"/> is similar, but uses comparison instead of hashing, and does maintains
    /// the items in sorted order.</p>
    ///</remarks>
    ///<seealso cref="OrderedSet&lt;T&gt;"/>
    [Serializable]
    public class Set<T> : CollectionBase<T>, ICollection<T>, ICloneable
    {
        // The comparer used to hash/compare items. 
        private IEqualityComparer<T> equalityComparer;

        // The hash table that actually does the work of storing the items.
        private Hash<T> hash;

        #region Constructors

        /// <summary>
        /// Creates a new Set. The Equals method and GetHashCode method on T
        /// will be used to compare items for equality.
        /// </summary>
        ///<remarks>
        /// Items that are null are permitted, and will be sorted before all other items.
        ///</remarks>
        public Set(): 
            this(EqualityComparer<T>.Default)
        {
        }

        /// <summary>
        /// Creates a new Set. The Equals and GetHashCode method of the passed comparer object
        /// will be used to compare items in this set.
        /// </summary>
        /// <param name="equalityComparer">An instance of IEqualityComparer&lt;T&gt; that will be used to compare items.</param>
        public Set(IEqualityComparer<T> equalityComparer)
        {
            if (equalityComparer == null)
                throw new ArgumentNullException("equalityComparer");

            this.equalityComparer = equalityComparer;
            hash = new Hash<T>(equalityComparer);
        }

        /// <summary>
        /// Creates a new Set. The Equals method and GetHashCode method on T
        /// will be used to compare items for equality.
        /// </summary>
        ///<remarks>
        /// Items that are null are permitted.
        ///</remarks>
        /// <param name="collection">A collection with items to be placed into the Set.</param>
        public Set(IEnumerable<T> collection): 
            this(collection, EqualityComparer<T>.Default)
        {
        }

        /// <summary>
        /// Creates a new Set. The Equals and GetHashCode method of the passed comparer object
        /// will be used to compare items in this set. The set is
        /// initialized with all the items in the given collection.
        /// </summary>
        /// <param name="collection">A collection with items to be placed into the Set.</param>
        /// <param name="equalityComparer">An instance of IEqualityComparer&lt;T&gt; that will be used to compare items.</param>
        public Set(IEnumerable<T> collection, IEqualityComparer<T> equalityComparer)
           : this(equalityComparer)
        {
            AddMany(collection);
        }

        /// <summary>
        /// Creates a new Set given a comparer and a tree that contains the data. Used
        /// internally for Clone.
        /// </summary>
        /// <param name="equalityComparer">EqualityComparer for the set.</param>
        /// <param name="hash">Data for the set.</param>
        private Set(IEqualityComparer<T> equalityComparer, Hash<T> hash)
        {
            this.equalityComparer = equalityComparer;
            this.hash = hash;
        }

        #endregion Constructors

        #region Cloning

        /// <summary>
        /// Makes a shallow clone of this set; i.e., if items of the
        /// set are reference types, then they are not cloned. If T is a value type,
        /// then each element is copied as if by simple assignment.
        /// </summary>
        /// <remarks>Cloning the set takes time O(N), where N is the number of items in the set.</remarks>
        /// <returns>The cloned set.</returns>
        object ICloneable.Clone()
        {
            return this.Clone();
        }

        /// <summary>
        /// Makes a shallow clone of this set; i.e., if items of the
        /// set are reference types, then they are not cloned. If T is a value type,
        /// then each element is copied as if by simple assignment.
        /// </summary>
        /// <remarks>Cloning the set takes time O(N), where N is the number of items in the set.</remarks>
        /// <returns>The cloned set.</returns>
        public Set<T> Clone()
        {
            Set<T> newSet = new Set<T>(equalityComparer, hash.Clone(null));
            return newSet; 
        }

        /// <summary>
        /// Makes a deep clone of this set. A new set is created with a clone of
        /// each element of this set, by calling ICloneable.Clone on each element. If T is
        /// a value type, then each element is copied as if by simple assignment.
        /// </summary>
        /// <remarks><para>If T is a reference type, it must implement
        /// ICloneable. Otherwise, an InvalidOperationException is thrown.</para>
        /// <para>Cloning the set takes time O(N), where N is the number of items in the set.</para></remarks>
        /// <returns>The cloned set.</returns>
        /// <exception cref="InvalidOperationException">T is a reference type that does not implement ICloneable.</exception>
        public Set<T> CloneContents()
        {
            bool itemIsValueType;
            if (!Util.IsCloneableType(typeof(T), out itemIsValueType))
                throw new InvalidOperationException(string.Format(Strings.TypeNotCloneable, typeof(T).FullName));

            Set<T> clone = new Set<T>(equalityComparer);

            // Clone each item, and add it to the new ordered set.
            foreach (T item in this) {
                T itemClone;

                if (itemIsValueType)
                    itemClone = item;
                else {
                    if (item == null)
                        itemClone = default(T);    // Really null, because we know T is a reference type
                    else
                        itemClone = (T)(((ICloneable)item).Clone());
                }

                clone.Add(itemClone);
            }

            return clone;
        }

        #endregion Cloning

        #region Basic collection containment

        /// <summary>
        /// Returns the IEqualityComparer&lt;T&gt; used to compare items in this set. 
        /// </summary>
        /// <value>If the set was created using a comparer, that comparer is returned. Otherwise
        /// the default comparer for T (EqualityComparer&lt;T&gt;.Default) is returned.</value>
        public IEqualityComparer<T> Comparer
        {
            get
            {
                return this.equalityComparer;
            }
        }

        /// <summary>
        /// Returns the number of items in the set.
        /// </summary>
        /// <remarks>The size of the set is returned in constant time.</remarks>
        /// <value>The number of items in the set.</value>
        public sealed override int Count
        {
            get
            {
                return hash.ElementCount;
            }
        }

        /// <summary>
        /// Returns an enumerator that enumerates all the items in the set. 
        /// The items are enumerated in sorted order.
        /// </summary>
        /// <remarks>
        /// <p>Typically, this method is not called directly. Instead the "foreach" statement is used
        /// to enumerate the items, which uses this method implicitly.</p>
        /// <p>If an item is added to or deleted from the set while it is being enumerated, then 
        /// the enumeration will end with an InvalidOperationException.</p>
        /// <p>Enumerating all the items in the set takes time O(N), where N is the number
        /// of items in the set.</p>
        /// </remarks>
        /// <returns>An enumerator for enumerating all the items in the Set.</returns>		
        public sealed override IEnumerator<T> GetEnumerator()
        {
            return hash.GetEnumerator();
        }

        /// <summary>
        /// Determines if this set contains an item equal to <paramref name="item"/>. The set
        /// is not changed.
        /// </summary>
        /// <remarks>Searching the set for an item takes approximately constant time, regardless of the number of items in the set.</remarks>
        /// <param name="item">The item to search for.</param>
        /// <returns>True if the set contains <paramref name="item"/>. False if the set does not contain <paramref name="item"/>.</returns>
        public sealed override bool Contains(T item)
        {
            T dummy;
            return hash.Find(item, false, out dummy);
        }

        /// <summary>
        /// <para>Determines if this set contains an item equal to <paramref name="item"/>, according to the 
        /// comparison mechanism that was used when the set was created. The set
        /// is not changed.</para>
        /// <para>If the set does contain an item equal to <paramref name="item"/>, then the item from the set is returned.</para>
        /// </summary>
        /// <remarks>Searching the set for an item takes approximately constant time, regardless of the number of items in the set.</remarks>
        /// <example>
        /// In the following example, the set contains strings which are compared in a case-insensitive manner. 
        /// <code>
        /// Set&lt;string&gt; set = new Set&lt;string&gt;(StringComparer.CurrentCultureIgnoreCase);
        /// set.Add("HELLO");
        /// string s;
        /// bool b = set.TryGetItem("Hello", out s);   // b receives true, s receives "HELLO".
        /// </code>
        /// </example>
        /// <param name="item">The item to search for.</param>
        /// <param name="foundItem">Returns the item from the set that was equal to <paramref name="item"/>.</param>
        /// <returns>True if the set contains <paramref name="item"/>. False if the set does not contain <paramref name="item"/>.</returns>
        public bool TryGetItem(T item, out T foundItem)
        {
            return hash.Find(item, false, out foundItem);
        }

        #endregion

        #region Adding elements

        /// <summary>
        /// Adds a new item to the set. If the set already contains an item equal to
        /// <paramref name="item"/>, that item is replaced with <paramref name="item"/>.
        /// </summary>
        /// <remarks>
        /// <para>Equality between items is determined by the comparison instance or delegate used
        /// to create the set.</para>
        /// <para>Adding an item takes approximately constant time, regardless of the number of items in the set.</para></remarks>
        /// <param name="item">The item to add to the set.</param>
        /// <returns>True if the set already contained an item equal to <paramref name="item"/> (which was replaced), false 
        /// otherwise.</returns>
        public new bool Add(T item)
        {
            T dummy;
            return !hash.Insert(item, true, out dummy);
        }

        /// <summary>
        /// Adds a new item to the set. If the set already contains an item equal to
        /// <paramref name="item"/>, that item is replaced with <paramref name="item"/>.
        /// </summary>
        /// <remarks>
        /// <para>Equality between items is determined by the comparison instance or delegate used
        /// to create the set.</para>
        /// <para>Adding an item takes approximately constant time, regardless of the number of items in the set.</para></remarks>
        /// <param name="item">The item to add to the set.</param>
        /// <returns>True if the set already contained an item equal to <paramref name="item"/> (which was replaced), false 
        /// otherwise.</returns>
        void ICollection<T>.Add(T item)
        {
            Add(item);
        }

        /// <summary>
        /// Adds all the items in <paramref name="collection"/> to the set. If the set already contains an item equal to
        /// one of the items in <paramref name="collection"/>, that item will be replaced.
        /// </summary>
        /// <remarks>
        /// <para>Equality between items is determined by the comparison instance or delegate used
        /// to create the set.</para>
        /// <para>Adding the collection takes time O(M), where M is the 
        /// number of items in <paramref name="collection"/>.</para></remarks>
        /// <param name="collection">A collection of items to add to the set.</param>
        public void AddMany(IEnumerable<T> collection)
        {
            if (collection == null)
                throw new ArgumentNullException("collection");

            // If we're adding ourselves, then there is nothing to do.
            if (object.ReferenceEquals(collection, this))
                return;

            foreach (T item in collection)
                Add(item);
        }

        #endregion Adding elements

        #region Removing elements

        /// <summary>
        /// Searches the set for an item equal to <paramref name="item"/>, and if found,
        /// removes it from the set. If not found, the set is unchanged.
        /// </summary>
        /// <remarks>
        /// <para>Equality between items is determined by the comparison instance or delegate used
        /// to create the set.</para>
        /// <para>Removing an item from the set takes approximately constant time, regardless of the size of the set.</para></remarks>
        /// <param name="item">The item to remove.</param>
        /// <returns>True if <paramref name="item"/> was found and removed. False if <paramref name="item"/> was not in the set.</returns>
        public sealed override bool Remove(T item)
        {
            T dummy;
            return hash.Delete(item, out dummy);
        }

        /// <summary>
        /// Removes all the items in <paramref name="collection"/> from the set. 
        /// </summary>
        /// <remarks>
        /// <para>Equality between items is determined by the comparison instance or delegate used
        /// to create the set.</para>
        /// <para>Removing the collection takes time O(M), where M is the 
        /// number of items in <paramref name="collection"/>.</para></remarks>
        /// <param name="collection">A collection of items to remove from the set.</param>
        /// <returns>The number of items removed from the set.</returns>
        /// <exception cref="ArgumentNullException"><paramref name="collection"/> is null.</exception>
        public int RemoveMany(IEnumerable<T> collection)
        {
            if (collection == null)
                throw new ArgumentNullException("collection");

            int count = 0;

            if (collection == this) {
                count = Count;
                Clear();            // special case, otherwise we will throw.
            }
            else {
                foreach (T item in collection) {
                    if (Remove(item))
                        ++count;
                }
            }

            return count;
        }

        /// <summary>
        /// Removes all items from the set.
        /// </summary>
        /// <remarks>Clearing the set takes a constant amount of time, regardless of the number of items in it.</remarks>
        public sealed override void Clear()
        {
            hash.StopEnumerations();  // Invalidate any enumerations.

            // The simplest and fastest way is simply to throw away the old tree and create a new one.
            hash = new Hash<T>(equalityComparer);
        }

        #endregion Removing elements

        #region Set operations

        /// <summary>
        /// Check that this set and another set were created with the same comparison
        /// mechanism. Throws exception if not compatible.
        /// </summary>
        /// <param name="otherSet">Other set to check comparision mechanism.</param>
        /// <exception cref="InvalidOperationException">If otherSet and this set don't use the same method for comparing items.</exception>
        private void CheckConsistentComparison(Set<T> otherSet)
        {
            if (otherSet == null)
                throw new ArgumentNullException("otherSet");

            if (!object.Equals(equalityComparer, otherSet.equalityComparer))
                throw new InvalidOperationException(Strings.InconsistentComparisons);
        }

        /// <summary>
        /// Determines if this set is a superset of another set. Neither set is modified.
        /// This set is a superset of <paramref name="otherSet"/> if every element in
        /// <paramref name="otherSet"/> is also in this set.
        /// <remarks>IsSupersetOf is computed in time O(M), where M is the size of the 
        /// <paramref name="otherSet"/>.</remarks>
        /// </summary>
        /// <param name="otherSet">Set to compare to.</param>
        /// <returns>True if this is a superset of <paramref name="otherSet"/>.</returns>
        /// <exception cref="InvalidOperationException">This set and <paramref name="otherSet"/> don't use the same method for comparing items.</exception>
        public bool IsSupersetOf(Set<T> otherSet)
        {
            CheckConsistentComparison(otherSet);

            if (otherSet.Count > this.Count)
                return false;     // Can't be a superset of a bigger set

            // Check each item in the other set to make sure it is in this set.
            foreach (T item in otherSet) {
                if (!this.Contains(item))
                    return false;
            }

            return true; 
        }

        /// <summary>
        /// Determines if this set is a proper superset of another set. Neither set is modified.
        /// This set is a proper superset of <paramref name="otherSet"/> if every element in
        /// <paramref name="otherSet"/> is also in this set.
        /// Additionally, this set must have strictly more items than <paramref name="otherSet"/>.
        /// </summary>
        /// <remarks>IsProperSubsetOf is computed in time O(M), where M is the size of
        /// <paramref name="otherSet"/>.</remarks>
        /// <param name="otherSet">Set to compare to.</param>
        /// <returns>True if this is a proper superset of <paramref name="otherSet"/>.</returns>
        /// <exception cref="InvalidOperationException">This set and <paramref name="otherSet"/> don't use the same method for comparing items.</exception>
        public bool IsProperSupersetOf(Set<T> otherSet)
        {
            CheckConsistentComparison(otherSet);

            if (otherSet.Count >= this.Count)
                return false;     // Can't be a proper superset of a bigger or equal set

            return IsSupersetOf(otherSet);
        }

        /// <summary>
        /// Determines if this set is a subset of another set. Neither set is modified.
        /// This set is a subset of <paramref name="otherSet"/> if every element in this set
        /// is also in <paramref name="otherSet"/>.
        /// </summary>
        /// <remarks>IsSubsetOf is computed in time O(N), where N is the size of the this set.</remarks>
        /// <param name="otherSet">Set to compare to.</param>
        /// <returns>True if this is a subset of <paramref name="otherSet"/>.</returns>
        /// <exception cref="InvalidOperationException">This set and <paramref name="otherSet"/> don't use the same method for comparing items.</exception>
        public bool IsSubsetOf(Set<T> otherSet)
        {
            return otherSet.IsSupersetOf(this);
        }

        /// <summary>
        /// Determines if this set is a proper subset of another set. Neither set is modified.
        /// This set is a subset of <paramref name="otherSet"/> if every element in this set
        /// is also in <paramref name="otherSet"/>. Additionally, this set must have strictly 
        /// fewer items than <paramref name="otherSet"/>.
        /// </summary>
        /// <remarks>IsProperSubsetOf is computed in time O(N), where N is the size of the this set.</remarks>
        /// <param name="otherSet">Set to compare to.</param>
        /// <returns>True if this is a proper subset of <paramref name="otherSet"/>.</returns>
        /// <exception cref="InvalidOperationException">This set and <paramref name="otherSet"/> don't use the same method for comparing items.</exception>
        public bool IsProperSubsetOf(Set<T> otherSet)
        {
            return otherSet.IsProperSupersetOf(this);
        }

        /// <summary>
        /// Determines if this set is equal to another set. This set is equal to
        /// <paramref name="otherSet"/> if they contain the same items.
        /// </summary>
        /// <remarks>IsEqualTo is computed in time O(N), where N is the number of items in 
        /// this set.</remarks>
        /// <param name="otherSet">Set to compare to</param>
        /// <returns>True if this set is equal to <paramref name="otherSet"/>, false otherwise.</returns>
        /// <exception cref="InvalidOperationException">This set and <paramref name="otherSet"/> don't use the same method for comparing items.</exception>
        public bool IsEqualTo(Set<T> otherSet)
        {
            CheckConsistentComparison(otherSet);

            // Must be the same size.
            if (otherSet.Count != this.Count)
                return false;

            // Check each item in the other set to make sure it is in this set.
            foreach (T item in otherSet) {
                if (!this.Contains(item))
                    return false;
            }

            return true;
        }

        /// <summary>
        /// Determines if this set is disjoint from another set. Two sets are disjoint
        /// if no item from one set is equal to any item in the other set.
        /// </summary>
        /// <remarks>
        /// <para>The answer is computed in time O(N), where N is the size of the smaller set.</para>
        /// </remarks>
        /// <param name="otherSet">Set to check disjointness with.</param>
        /// <returns>True if the two sets are disjoint, false otherwise.</returns>
        /// <exception cref="InvalidOperationException">This set and <paramref name="otherSet"/> don't use the same method for comparing items.</exception>
        public bool IsDisjointFrom(Set<T> otherSet)
        {
            CheckConsistentComparison(otherSet);
            Set<T> smaller, larger;
            if (otherSet.Count > this.Count) {
                smaller = this; larger = otherSet;
            }
            else {
                smaller = otherSet; larger = this;
            }

            foreach (T item in smaller) {
                if (larger.Contains(item))
                    return false;
            }

            return true;
        }

        /// <summary>
        /// Computes the union of this set with another set. The union of two sets
        /// is all items that appear in either or both of the sets. This set receives
        /// the union of the two sets, the other set is unchanged.
        /// </summary>
        /// <remarks>
        /// <para>If equal items appear in both sets, the union will include an arbitrary choice of one of the
        /// two equal items.</para>
        /// <para>The union of two sets is computed in time O(M + N), where M is the size of the 
        /// larger set, and N is the size of the smaller set.</para>
        /// </remarks>
        /// <param name="otherSet">Set to union with.</param>
        /// <exception cref="InvalidOperationException">This set and <paramref name="otherSet"/> don't use the same method for comparing items.</exception>
        public void UnionWith(Set<T> otherSet)
        {
            CheckConsistentComparison(otherSet);

            AddMany(otherSet);
        }

        /// <summary>
        /// Computes the union of this set with another set. The union of two sets
        /// is all items that appear in either or both of the sets. A new set is 
        /// created with the union of the sets and is returned. This set and the other set 
        /// are unchanged.
        /// </summary>
        /// <remarks>
        /// <para>If equal items appear in both sets, the union will include an arbitrary choice of one of the
        /// two equal items.</para>
        /// <para>The union of two sets is computed in time O(M + N), where M is the size of the 
        /// one set, and N is the size of the other set.</para>
        /// </remarks>
        /// <param name="otherSet">Set to union with.</param>
        /// <returns>The union of the two sets.</returns>
        /// <exception cref="InvalidOperationException">This set and <paramref name="otherSet"/> don't use the same method for comparing items.</exception>
        public Set<T> Union(Set<T> otherSet)
        {
            CheckConsistentComparison(otherSet);
            Set<T> smaller, larger, result;
            if (otherSet.Count > this.Count) {
                smaller = this; larger = otherSet;
            }
            else {
                smaller = otherSet; larger = this;
            }

            result = larger.Clone();
            result.AddMany(smaller);
            return result; 
        }

        /// <summary>
        /// Computes the intersection of this set with another set. The intersection of two sets
        /// is all items that appear in both of the sets. This set receives
        /// the intersection of the two sets, the other set is unchanged.
        /// </summary>
        /// <remarks>
        /// <para>When equal items appear in both sets, the intersection will include an arbitrary choice of one of the
        /// two equal items.</para>
        /// <para>The intersection of two sets is computed in time O(N), where N is the size of the smaller set.</para>
        /// </remarks>
        /// <param name="otherSet">Set to intersection with.</param>
        /// <exception cref="InvalidOperationException">This set and <paramref name="otherSet"/> don't use the same method for comparing items.</exception>
        public void IntersectionWith(Set<T> otherSet)
        {
            CheckConsistentComparison(otherSet);
            hash.StopEnumerations();

            Set<T> smaller, larger;
            if (otherSet.Count > this.Count) {
                smaller = this; larger = otherSet;
            }
            else {
                smaller = otherSet; larger = this;
            }

            T dummy;
            Hash<T> newHash = new Hash<T>(equalityComparer);

            foreach (T item in smaller) {
                if (larger.Contains(item))
                    newHash.Insert(item, true, out dummy);
            }

            hash = newHash;
        }

        /// <summary>
        /// Computes the intersection of this set with another set. The intersection of two sets
        /// is all items that appear in both of the sets. A new set is 
        /// created with the intersection of the sets and is returned. This set and the other set 
        /// are unchanged.
        /// </summary>
        /// <remarks>
        /// <para>When equal items appear in both sets, the intersection will include an arbitrary choice of one of the
        /// two equal items.</para>
        /// <para>The intersection of two sets is computed in time O(N), where N is the size of the smaller set.</para>
        /// </remarks>
        /// <param name="otherSet">Set to intersection with.</param>
        /// <returns>The intersection of the two sets.</returns>
        /// <exception cref="InvalidOperationException">This set and <paramref name="otherSet"/> don't use the same method for comparing items.</exception>
        public Set<T> Intersection(Set<T> otherSet)
        {
            CheckConsistentComparison(otherSet);
            Set<T> smaller, larger, result;
            if (otherSet.Count > this.Count) {
                smaller = this; larger = otherSet;
            }
            else {
                smaller = otherSet; larger = this;
            }

            result = new Set<T>(equalityComparer);
            foreach (T item in smaller) {
                if (larger.Contains(item))
                    result.Add(item);
            }

            return result; 
        }

        /// <summary>
        /// Computes the difference of this set with another set. The difference of these two sets
        /// is all items that appear in this set, but not in <paramref name="otherSet"/>. This set receives
        /// the difference of the two sets; the other set is unchanged.
        /// </summary>
        /// <remarks>
        /// <para>The difference of two sets is computed in time O(N), where N is the size of the smaller set.</para>
        /// </remarks>
        /// <param name="otherSet">Set to difference with.</param>
        /// <exception cref="InvalidOperationException">This set and <paramref name="otherSet"/> don't use the same method for comparing items.</exception>
        public void DifferenceWith(Set<T> otherSet)
        {
            // Difference with myself is nothing. This check is needed because the
            // main algorithm doesn't work correctly otherwise.
            if (this == otherSet)
                Clear();

            CheckConsistentComparison(otherSet);

            if (otherSet.Count < this.Count) {
                foreach (T item in otherSet) {
                    this.Remove(item);
                }
            }
            else {
                RemoveAll(delegate(T item) { return otherSet.Contains(item); });
            }
        }

        /// <summary>
        /// Computes the difference of this set with another set. The difference of these two sets
        /// is all items that appear in this set, but not in <paramref name="otherSet"/>. A new set is 
        /// created with the difference of the sets and is returned. This set and the other set 
        /// are unchanged.
        /// </summary>
        /// <remarks>
        /// <para>The difference of two sets is computed in time O(N), where N is the size of the smaller set.</para>
        /// </remarks>
        /// <param name="otherSet">Set to difference with.</param>
        /// <returns>The difference of the two sets.</returns>
        /// <exception cref="InvalidOperationException">This set and <paramref name="otherSet"/> don't use the same method for comparing items.</exception>
        public Set<T> Difference(Set<T> otherSet)
        {
            CheckConsistentComparison(otherSet);
            Set<T> result = this.Clone();
            result.DifferenceWith(otherSet);
            return result; 
        }

        /// <summary>
        /// Computes the symmetric difference of this set with another set. The symmetric difference of two sets
        /// is all items that appear in either of the sets, but not both. This set receives
        /// the symmetric difference of the two sets; the other set is unchanged.
        /// </summary>
        /// <remarks>
        /// <para>The symmetric difference of two sets is computed in time O(N), where N is the size of the smaller set.</para>
        /// </remarks>
        /// <param name="otherSet">Set to symmetric difference with.</param>
        /// <exception cref="InvalidOperationException">This set and <paramref name="otherSet"/> don't use the same method for comparing items.</exception>
        public void SymmetricDifferenceWith(Set<T> otherSet)
        {
            // main algorithm doesn't work correctly otherwise.
            if (this == otherSet)
                Clear();

            CheckConsistentComparison(otherSet);

            if (otherSet.Count > this.Count) {
                hash.StopEnumerations();
                Hash<T> newHash = otherSet.hash.Clone(null);
                T dummy;

                foreach (T item in this) {
                    if (newHash.Find(item, false, out dummy))
                        newHash.Delete(item, out dummy);
                    else
                        newHash.Insert(item, true, out dummy);
                }
                this.hash = newHash;
            }
            else {
                foreach (T item in otherSet) {
                    if (this.Contains(item))
                        this.Remove(item);
                    else
                        this.Add(item);
                }
            }
        }

        /// <summary>
        /// Computes the symmetric difference of this set with another set. The symmetric difference of two sets
        /// is all items that appear in either of the sets, but not both. A new set is 
        /// created with the symmetric difference of the sets and is returned. This set and the other set 
        /// are unchanged.
        /// </summary>
        /// <remarks>
        /// <para>The symmetric difference of two sets is computed in time O(N), where N is the size of the smaller set.</para>
        /// </remarks>
        /// <param name="otherSet">Set to symmetric difference with.</param>
        /// <returns>The symmetric difference of the two sets.</returns>
        /// <exception cref="InvalidOperationException">This set and <paramref name="otherSet"/> don't use the same method for comparing items.</exception>
        public Set<T> SymmetricDifference(Set<T> otherSet)
        {
            CheckConsistentComparison(otherSet);
            Set<T> smaller, larger, result;
            if (otherSet.Count > this.Count) {
                smaller = this; larger = otherSet;
            }
            else {
                smaller = otherSet; larger = this;
            }

            result = larger.Clone();
            foreach (T item in smaller) {
                if (result.Contains(item))
                    result.Remove(item);
                else
                    result.Add(item);
            }

            return result;
        }

        #endregion Set operations

    }
}