//******************************
// 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;

namespace Wintellect.PowerCollections
{
    /// <summary>
    /// OrderedSet&lt;T&gt; is a collection that contains items of type T. 
    /// The item are maintained in a sorted order, and duplicate items are not allowed. Each item has
    /// an index in the set: the smallest item has index 0, the next smallest item has index 1,
    /// and so forth.
    /// </summary>
    /// <remarks>
    /// <p>The items are compared in one of three ways. If T implements IComparable&lt;TKey&gt; or IComparable,
    /// then the CompareTo method of that interface will be used to compare items. Alternatively, a comparison
    /// function can be passed in either as a delegate, or as an instance of IComparer&lt;TKey&gt;.</p>
    /// <p>OrderedSet is implemented as a balanced binary tree. Inserting, deleting, and looking up an
    /// an element all are done in log(N) type, where N is the number of keys in the tree.</p>
    /// <p><see cref="Set&lt;T&gt;"/> is similar, but uses hashing instead of comparison, and does not maintain
    /// the items in sorted order.</p>
    ///</remarks>
    ///<seealso cref="Set&lt;T&gt;"/>
    [Serializable]
    public class OrderedSet<T> : CollectionBase<T>, ICollection<T>, ICloneable
    {
        // The comparer used to compare items. 
        private IComparer<T> comparer;

        // The red-black tree that actually does the work of storing the items.
        private RedBlackTree<T> tree;

        #region Constructors

        /// <summary>
        /// Creates a new OrderedSet. The T must implement IComparable&lt;T&gt;
        /// or IComparable. 
        /// The CompareTo method of this interface will be used to compare items in this set.
        /// </summary>
        ///<remarks>
        /// Items that are null are permitted, and will be sorted before all other items.
        ///</remarks>
        /// <exception cref="InvalidOperationException">T does not implement IComparable&lt;TKey&gt;.</exception>
        public OrderedSet(): 
            this(Comparers.DefaultComparer<T>())
        {
        }

        /// <summary>
        /// Creates a new OrderedSet. The passed delegate will be used to compare items in this set.
        /// </summary>
        /// <param name="comparison">A delegate to a method that will be used to compare items.</param>
        public OrderedSet(Comparison<T> comparison) :
            this(Comparers.ComparerFromComparison<T>(comparison))
        {
        }

        /// <summary>
        /// Creates a new OrderedSet. The Compare method of the passed comparison object
        /// will be used to compare items in this set.
        /// </summary>
        /// <remarks>
        /// The GetHashCode and Equals methods of the provided IComparer&lt;T&gt; will never
        /// be called, and need not be implemented.
        /// </remarks>
        /// <param name="comparer">An instance of IComparer&lt;T&gt; that will be used to compare items.</param>
        public OrderedSet(IComparer<T> comparer)
        {
            if (comparer == null)
                throw new ArgumentNullException("comparer");

            this.comparer = comparer;
            tree = new RedBlackTree<T>(comparer);
        }

        /// <summary>
        /// Creates a new OrderedSet. The T must implement IComparable&lt;T&gt;
        /// or IComparable. 
        /// The CompareTo method of this interface will be used to compare items in this set. The set is
        /// initialized with all the items in the given collection.
        /// </summary>
        ///<remarks>
        /// Items that are null are permitted, and will be sorted before all other items.
        ///</remarks>
        /// <param name="collection">A collection with items to be placed into the OrderedSet.</param>
        /// <exception cref="InvalidOperationException">T does not implement IComparable&lt;TKey&gt;.</exception>
        public OrderedSet(IEnumerable<T> collection): 
            this(collection, Comparers.DefaultComparer<T>())
        {
        }

        /// <summary>
        /// Creates a new OrderedSet. The passed delegate 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 OrderedSet.</param>
        /// <param name="comparison">A delegate to a method that will be used to compare items.</param>
        public OrderedSet(IEnumerable<T> collection, Comparison<T> comparison):
            this(collection, Comparers.ComparerFromComparison<T>(comparison))
        {
        }

        /// <summary>
        /// Creates a new OrderedSet. The Compare method of the passed comparison object
        /// will be used to compare items in this set. The set is
        /// initialized with all the items in the given collection.
        /// </summary>
        /// <remarks>
        /// The GetHashCode and Equals methods of the provided IComparer&lt;T&gt; will never
        /// be called, and need not be implemented.
        /// </remarks>
        /// <param name="collection">A collection with items to be placed into the OrderedSet.</param>
        /// <param name="comparer">An instance of IComparer&lt;T&gt; that will be used to compare items.</param>
        public OrderedSet(IEnumerable<T> collection, IComparer<T> comparer):
            this(comparer)
        {
            AddMany(collection);
        }

        /// <summary>
        /// Creates a new OrderedSet given a comparer and a tree that contains the data. Used
        /// internally for Clone.
        /// </summary>
        /// <param name="comparer">Comparer for the set.</param>
        /// <param name="tree">Data for the set.</param>
        private OrderedSet(IComparer<T> comparer, RedBlackTree<T> tree)
        {
            this.comparer = comparer;
            this.tree = tree;
        }

        #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 OrderedSet<T> Clone()
        {
            OrderedSet<T> newSet = new OrderedSet<T>(comparer, tree.Clone());
            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 log 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 OrderedSet<T> CloneContents()
        {
            bool itemIsValueType;
            if (!Util.IsCloneableType(typeof(T), out itemIsValueType))
                throw new InvalidOperationException(string.Format(Strings.TypeNotCloneable, typeof(T).FullName));

            OrderedSet<T> clone = new OrderedSet<T>(comparer);

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

        /// <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 tree.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>Enumeration all the items in the set takes time O(N log N), where N is the number
        /// of items in the set.</p>
        /// </remarks>
        /// <returns>An enumerator for enumerating all the items in the OrderedSet.</returns>		
        public sealed override IEnumerator<T> GetEnumerator()
        {
            return tree.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 time O(log N), where N is 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 tree.Find(item, false, 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 time O(log N), where N is 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>
        /// OrderedSet&lt;string&gt; set = new OrderedSet&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 tree.Find(item, true, false, out foundItem);
        }

        #endregion

        #region Index by sorted order

        /// <summary>
        /// Get the item by its index in the sorted order. The smallest item has index 0,
        /// the next smallest item has index 1, and the largest item has index Count-1. 
        /// </summary>
        /// <remarks>The indexer takes time O(log N), which N is the number of items in 
        /// the set.</remarks>
        /// <param name="index">The index to get the item by.</param>
        /// <returns>The item at the given index.</returns>
        /// <exception cref="ArgumentOutOfRangeException"><paramref name="index"/> is
        /// less than zero or greater than or equal to Count.</exception>
        public T this[int index]
        {
            get {
                if (index < 0 || index >= Count)
                    throw new ArgumentOutOfRangeException("index");

                return tree.GetItemByIndex(index);
            }
        }

        /// <summary>
        /// Get the index of the given item in the sorted order. The smallest item has index 0,
        /// the next smallest item has index 1, and the largest item has index Count-1. 
        /// </summary>
        /// <remarks>Finding the index takes time O(log N), which N is the number of items in 
        /// the set.</remarks>
        /// <param name="item">The item to get the index of.</param>
        /// <returns>The index of the item in the sorted set, or -1 if the item is not present
        /// in the set.</returns>
        public int IndexOf(T item)
        {
            return tree.FindIndex(item, true);
        }

        #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 time O(log N), where N is 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 ! tree.Insert(item, DuplicatePolicy.ReplaceFirst, 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 replaces 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 time O(log N), where N is the number of items in the set.</para></remarks>
        /// <param name="item">The item to add to the set.</param>
        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 log N), where N is the number of items in the set, and 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 time O(log N), where N is the number of items in 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 tree.Delete(item, true, out dummy);
        }

        /// <summary>
        /// Removes all the items in <paramref name="collection"/> from the set. Items
        /// not present in the set are ignored.
        /// </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 log N), where N is the number of items in the set, and 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 sets takes a constant amount of time, regardless of the number of items in it.</remarks>
        public sealed override void Clear()
        {
            tree.StopEnumerations();  // Invalidate any enumerations.

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

        #endregion Removing elements

        #region First/last items

        /// <summary>
        /// If the collection is empty, throw an invalid operation exception.
        /// </summary>
        /// <exception cref="InvalidOperationException">The set is empty.</exception>
        private void CheckEmpty()
        {
            if (Count == 0)
                throw new InvalidOperationException(Strings.CollectionIsEmpty);
        }

        /// <summary>
        /// Returns the first item in the set: the item
        /// that would appear first if the set was enumerated. This is also
        /// the smallest item in the set.
        /// </summary>
        /// <remarks>GetFirst() takes time O(log N), where N is the number of items in the set.</remarks>
        /// <returns>The first item in the set. </returns>
        /// <exception cref="InvalidOperationException">The set is empty.</exception>
        public T GetFirst()
        {
            T item;
            CheckEmpty();
            tree.FirstItemInRange(tree.EntireRangeTester, out item);
            return item;
        }

        /// <summary>
        /// Returns the lastl item in the set: the item
        /// that would appear last if the set was enumerated. This is also the
        /// largest item in the set.
        /// </summary>
        /// <remarks>GetLast() takes time O(log N), where N is the number of items in the set.</remarks>
        /// <returns>The lastl item in the set. </returns>
        /// <exception cref="InvalidOperationException">The set is empty.</exception>
        public T GetLast()
        {
            T item;
            CheckEmpty();
            tree.LastItemInRange(tree.EntireRangeTester, out item);
            return item;
        }

        /// <summary>
        /// Removes the first item in the set. This is also the smallest item in the set.
        /// </summary>
        /// <remarks>RemoveFirst() takes time O(log N), where N is the number of items in the set.</remarks>
        /// <returns>The item that was removed, which was the smallest item in the set. </returns>
        /// <exception cref="InvalidOperationException">The set is empty.</exception>
        public T RemoveFirst()
        {
            CheckEmpty();
            T item;
            tree.DeleteItemFromRange(tree.EntireRangeTester, true, out item);
            return item;
        }

        /// <summary>
        /// Removes the last item in the set. This is also the largest item in the set.
        /// </summary>
        /// <remarks>RemoveLast() takes time O(log N), where N is the number of items in the set.</remarks>
        /// <returns>The item that was removed, which was the largest item in the set. </returns>
        /// <exception cref="InvalidOperationException">The set is empty.</exception>
        public T RemoveLast()
        {
            CheckEmpty();
            T item;
            tree.DeleteItemFromRange(tree.EntireRangeTester, false, out item);
            return item;
        }

        #endregion

        #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(OrderedSet<T> otherSet) 
        {
            if (otherSet == null)
                throw new ArgumentNullException("otherSet");

            if (!object.Equals(comparer, otherSet.comparer))
                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 log N), where M is the size of the 
        /// <paramref name="otherSet"/>, and N is the size of the this set.</remarks>
        /// </summary>
        /// <param name="otherSet">OrderedSet 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(OrderedSet<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>IsProperSupersetOf is computed in time O(M log N), where M is the number of unique items in 
        /// <paramref name="otherSet"/>.</remarks>
        /// <param name="otherSet">OrderedSet 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(OrderedSet<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 log M), where M is the size of the 
        /// <paramref name="otherSet"/>, and 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(OrderedSet<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>IsSubsetOf is computed in time O(N log M), where M is the size of the 
        /// <paramref name="otherSet"/>, and 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(OrderedSet<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(OrderedSet<T> otherSet)
        {
            CheckConsistentComparison(otherSet);

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

            // Since both sets are ordered, we can simply compare items in order.
            using (IEnumerator<T> enum1 = this.GetEnumerator(), enum2 = otherSet.GetEnumerator()) {
                bool continue1, continue2;

                for (; ; ) {
                    continue1 = enum1.MoveNext(); continue2 = enum2.MoveNext();
                    if (!continue1 || !continue2)
                        break;

                    if (comparer.Compare(enum1.Current, enum2.Current) != 0)
                        return false;     // the two items are not equal.
                }

                // If both continue1 and continue2 are false, we reached the end of both sequences at the same
                // time and found success. If one is true and one is false, the sequences were of difference lengths -- failure.
                return (continue1 == continue2);
            }
        }

        /// <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 log M), 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(OrderedSet<T> otherSet)
        {
            CheckConsistentComparison(otherSet);

            AddMany(otherSet);

            // CONSIDER: if RedBlackTree cloning is O(N), then if otherSet is much larger, better to clone it,
            // add all of the current into it, and replace.
        }

        /// <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 log M), 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 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(OrderedSet<T> otherSet)
        {
            CheckConsistentComparison(otherSet);
            OrderedSet<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. 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 log M), 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>
        /// <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 OrderedSet<T> Union(OrderedSet<T> otherSet)
        {
            CheckConsistentComparison(otherSet);
            OrderedSet<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 log M), 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 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(OrderedSet<T> otherSet)
        {
            CheckConsistentComparison(otherSet);
            tree.StopEnumerations();

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

            T dummy;
            RedBlackTree<T> newTree = new RedBlackTree<T>(comparer);

            foreach (T item in smaller) {
                if (larger.Contains(item))
                    newTree.Insert(item, DuplicatePolicy.ReplaceFirst, out dummy);
            }

            tree = newTree;
        }

        /// <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 log M), 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 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 OrderedSet<T> Intersection(OrderedSet<T> otherSet)
        {
            CheckConsistentComparison(otherSet);
            OrderedSet<T> smaller, larger, result;
            if (otherSet.Count > this.Count) {
                smaller = this; larger = otherSet;
            }
            else {
                smaller = otherSet; larger = this;
            }

            result = new OrderedSet<T>(comparer);
            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(M + N log M), 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 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(OrderedSet<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(M + N log M), 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 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 OrderedSet<T> Difference(OrderedSet<T> otherSet)
        {
            CheckConsistentComparison(otherSet);
            OrderedSet<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(M + N log M), 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 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(OrderedSet<T> otherSet)
        {
            // Symmetric difference with myself is nothing. This check is needed because the
            // main algorithm doesn't work correctly otherwise.
            if (this == otherSet)
                Clear();

            CheckConsistentComparison(otherSet);

            // CONSIDER: if otherSet is larger, better to clone it and reverse the below?
            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(M + N log M), 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 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 OrderedSet<T> SymmetricDifference(OrderedSet<T> otherSet)
        {
            CheckConsistentComparison(otherSet);
            OrderedSet<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

        #region Read-only list view

        /// <summary>
        /// Get a read-only list view of the items in this ordered set. The
        /// items in the list are in sorted order, with the smallest item
        /// at index 0. This view does not copy any data, and reflects any
        /// changes to the underlying OrderedSet.
        /// </summary>
        /// <returns>A read-only IList&lt;T&gt; view onto this OrderedSet.</returns>
        public IList<T> AsList()
        {
            return new ListView(this, tree.EntireRangeTester, true, false);
        }

        /// <summary>
        /// The nested class that provides a read-only list view
        /// of all or part of the collection.
        /// </summary>
        [Serializable]
        private class ListView : ReadOnlyListBase<T>
        {
            private OrderedSet<T> mySet;
            private RedBlackTree<T>.RangeTester rangeTester;   // range tester for the range being used.
            private bool entireTree;                   // is the view the whole tree?
            private bool reversed;                     // is the view reversed?

            /// <summary>
            /// Create a new list view wrapped the given set.
            /// </summary>
            /// <param name="mySet"></param>
            /// <param name="rangeTester">Range tester that defines the range being used.</param>
            /// <param name="entireTree">If true, then rangeTester defines the entire tree. Used to optimize some operations.</param>
            /// <param name="reversed">Is the view enuemerated in reverse order?</param>
            public ListView(OrderedSet<T> mySet, RedBlackTree<T>.RangeTester rangeTester, bool entireTree, bool reversed)
            {
                this.mySet = mySet;
                this.rangeTester = rangeTester;
                this.entireTree = entireTree;
                this.reversed = reversed;
            }

            public override int Count
            {
                get
                {
                    if (entireTree)
                        return mySet.Count;
                    else {
                        // Note: we can't cache the result of this call because the underlying
                        // set can change, which would make the cached value incorrect.
                        return mySet.tree.CountRange(rangeTester);
                    }
                }
            }

            public override T this[int index]
            {
                get
                {
                    if (entireTree) {
                        if (reversed)
                            return mySet[mySet.Count - 1 - index];
                        else
                            return mySet[index];
                    }
                    else {
                        T dummy;
                        int firstIndex = mySet.tree.FirstItemInRange(rangeTester, out dummy);
                        int lastIndex = mySet.tree.LastItemInRange(rangeTester, out dummy);
                        if (firstIndex < 0 || lastIndex < 0 || index < 0 || index >= (lastIndex - firstIndex + 1))
                            throw new ArgumentOutOfRangeException("index");

                        if (reversed) 
                            return mySet[lastIndex - index];
                        else 
                            return mySet[firstIndex + index];
                    }
                }
            }

            public override int IndexOf(T item)
            {
                if (entireTree) {
                    if (reversed)
                        return mySet.Count - 1 - mySet.IndexOf(item);
                    else
                        return mySet.IndexOf(item);
                }
                else {
                    T dummy;

                    if (rangeTester(item) != 0)
                        return -1;

                    if (reversed) {
                        int indexInSet = mySet.tree.FindIndex(item, false);
                        if (indexInSet < 0)
                            return -1;
                        int indexOfEnd = mySet.tree.LastItemInRange(rangeTester, out dummy);
                        return indexOfEnd - indexInSet;

                    }
                    else {
                        int indexInSet = mySet.tree.FindIndex(item, true);
                        if (indexInSet < 0)
                            return -1;
                        int indexOfStart = mySet.tree.FirstItemInRange(rangeTester, out dummy);
                        return indexInSet - indexOfStart;
                    }
                }
            }
        }

        #endregion Read-only list view

        #region Sub-views

        /// <summary>
        /// Returns a View collection that can be used for enumerating the items in the set in 
        /// reversed order.
        /// </summary>
        ///<remarks>
        ///<p>Typically, this method is used in conjunction with a foreach statement. For example:
        ///<code>
        /// foreach(T item in set.Reversed()) {
        ///    // process item
        /// }
        ///</code></p>
        /// <p>If an item is added to or deleted from the set while the View is being enumerated, then 
        /// the enumeration will end with an InvalidOperationException.</p>
        ///<p>Calling Reverse does not copy the data in the tree, and the operation takes constant time.</p>
        ///</remarks>
        /// <returns>An OrderedSet.View of items in reverse order.</returns>
        public View Reversed()   // A reversed view that can be enumerated
        {
            return new View(this, tree.EntireRangeTester, true, true);
        }

        /// <summary>
        /// Returns a View collection that can be used for enumerating a range of the items in the set..
        /// Only items that are greater than <paramref name="from"/> and 
        /// less than <paramref name="to"/> are included. The items are enumerated in sorted order.
        /// Items equal to the end points of the range can be included or excluded depending on the
        /// <paramref name="fromInclusive"/> and <paramref name="toInclusive"/> parameters.
        /// </summary>
        ///<remarks>
        ///<p>If <paramref name="from"/> is greater than <paramref name="to"/>, the returned collection is empty. </p>
        ///<p>Typically, this method is used in conjunction with a foreach statement. For example:
        ///<code>
        /// foreach(T item in set.Range(from, true, to, false)) {
        ///    // process item
        /// }
        ///</code></p>
        /// <p>If an item is added to or deleted from the set while the View is being enumerated, then 
        /// the enumeration will end with an InvalidOperationException.</p>
        ///<p>Calling Range does not copy the data in the tree, and the operation takes constant time.</p>
        ///</remarks>
        /// <param name="from">The lower bound of the range.</param>
        /// <param name="fromInclusive">If true, the lower bound is inclusive--items equal to the lower bound will
        /// be included in the range. If false, the lower bound is exclusive--items equal to the lower bound will not
        /// be included in the range.</param>
        /// <param name="to">The upper bound of the range. </param>
        /// <param name="toInclusive">If true, the upper bound is inclusive--items equal to the upper bound will
        /// be included in the range. If false, the upper bound is exclusive--items equal to the upper bound will not
        /// be included in the range.</param>
        /// <returns>An OrderedSet.View of items in the given range.</returns>
        public View Range(T from, bool fromInclusive, T to, bool toInclusive)  // A partial view that can be enumerated
        {
            return new View(this, tree.DoubleBoundedRangeTester(from, fromInclusive, to, toInclusive), false, false);
        }

        /// <summary>
        /// Returns a View collection that can be used for enumerating a range of the items in the set..
        /// Only items that are greater than (and optionally, equal to) <paramref name="from"/> are included. 
        /// The items are enumerated in sorted order. Items equal to <paramref name="from"/> can be included
        /// or excluded depending on the <paramref name="fromInclusive"/> parameter.
        /// </summary>
        ///<remarks>
        ///<p>Typically, this method is used in conjunction with a foreach statement. For example:
        ///<code>
        /// foreach(T item in set.RangeFrom(from, true)) {
        ///    // process item
        /// }
        ///</code></p>
        /// <p>If an item is added to or deleted from the set while the View is being enumerated, then 
        /// the enumeration will end with an InvalidOperationException.</p>
        ///<p>Calling RangeFrom does not copy the data in the tree, and the operation takes constant time.</p>
        ///</remarks>
        /// <param name="from">The lower bound of the range.</param>
        /// <param name="fromInclusive">If true, the lower bound is inclusive--items equal to the lower bound will
        /// be included in the range. If false, the lower bound is exclusive--items equal to the lower bound will not
        /// be included in the range.</param>
        /// <returns>An OrderedSet.View of items in the given range.</returns>
        public View RangeFrom(T from, bool fromInclusive)  // A partial view that can be enumerated
        {
            return new View(this, tree.LowerBoundedRangeTester(from, fromInclusive), false, false);
        }

        /// <summary>
        /// Returns a View collection that can be used for enumerating a range of the items in the set..
        /// Only items that are less than (and optionally, equal to) <paramref name="to"/> are included. 
        /// The items are enumerated in sorted order. Items equal to <paramref name="to"/> can be included
        /// or excluded depending on the <paramref name="toInclusive"/> parameter.
        /// </summary>
        ///<remarks>
        ///<p>Typically, this method is used in conjunction with a foreach statement. For example:
        ///<code>
        /// foreach(T item in set.RangeTo(to, false)) {
        ///    // process item
        /// }
        ///</code></p>
        /// <p>If an item is added to or deleted from the set while the View is being enumerated, then 
        /// the enumeration will end with an InvalidOperationException.</p>
        ///<p>Calling RangeTo does not copy the data in the tree, and the operation takes constant time.</p>
        ///</remarks>
        /// <param name="to">The upper bound of the range. </param>
        /// <param name="toInclusive">If true, the upper bound is inclusive--items equal to the upper bound will
        /// be included in the range. If false, the upper bound is exclusive--items equal to the upper bound will not
        /// be included in the range.</param>
        /// <returns>An OrderedSet.View of items in the given range.</returns>
        public View RangeTo(T to, bool toInclusive)  // A partial view that can be enumerated
        {
            return new View(this, tree.UpperBoundedRangeTester(to, toInclusive), false, false);
        }

        #endregion
        
        #region View nested class
   
        /// <summary>
        /// The OrderedSet&lt;T&gt;.View class is used to look at a subset of the Items
        /// inside an ordered set. It is returned from the Range, RangeTo, RangeFrom, and Reversed methods. 
        /// </summary>
        ///<remarks>
        /// <p>Views are dynamic. If the underlying set changes, the view changes in sync. If a change is made
        /// to the view, the underlying set changes accordingly.</p>
        ///<p>Typically, this class is used in conjunction with a foreach statement to enumerate the items 
        /// in a subset of the OrderedSet. For example:</p>
        ///<code>
        /// foreach(T item in set.Range(from, to)) {
        ///    // process item
        /// }
        ///</code>
        ///</remarks>
        [Serializable]
        public class View : CollectionBase<T>, ICollection<T>
        {
            private OrderedSet<T> mySet;
            private RedBlackTree<T>.RangeTester rangeTester;   // range tester for the range being used.
            private bool entireTree;                   // is the view the whole tree?
            private bool reversed;                     // is the view reversed?

            /// <summary>
            /// Initialize the view.
            /// </summary>
            /// <param name="mySet">OrderedSet being viewed</param>
            /// <param name="rangeTester">Range tester that defines the range being used.</param>
            /// <param name="entireTree">If true, then rangeTester defines the entire tree. Used to optimize some operations.</param>
            /// <param name="reversed">Is the view enuemerated in reverse order?</param>
            internal View(OrderedSet<T> mySet, RedBlackTree<T>.RangeTester rangeTester, bool entireTree, bool reversed)
            {
                this.mySet = mySet;
                this.rangeTester = rangeTester;
                this.entireTree = entireTree;
                this.reversed = reversed;
            }

            /// <summary>
            /// Determine if the given item lies within the bounds of this view.
            /// </summary>
            /// <param name="item">Item to test.</param>
            /// <returns>True if the item is within the bounds of this view.</returns>
            private bool ItemInView(T item)
            {
                return rangeTester(item) == 0;
            }

            /// <summary>
            /// Enumerate all the items in this view.
            /// </summary>
            /// <returns>An IEnumerator&lt;T&gt; with the items in this view.</returns>
            public sealed override IEnumerator<T> GetEnumerator()
            {
                if (reversed)
                    return mySet.tree.EnumerateRangeReversed(rangeTester).GetEnumerator();
                else
                    return mySet.tree.EnumerateRange(rangeTester).GetEnumerator();
            }

            /// <summary>
            /// Number of items in this view.
            /// </summary>
            /// <value>Number of items that lie within the bounds the view.</value>
            public sealed override int Count
            {
                get {
                    if (entireTree)
                        return mySet.Count;
                    else {
                        // Note: we can't cache the result of this call because the underlying
                        // set can change, which would make the cached value incorrect.
                        return mySet.tree.CountRange(rangeTester);
                    }
                }
            }

            /// <summary>
            /// Removes all the items within this view from the underlying set.
            /// </summary>
            /// <example>The following removes all the items that start with "A" from an OrderedSet.
            /// <code>
            /// set.Range("A", "B").Clear();
            /// </code>
            /// </example>
            public sealed override void Clear()
            {
                if (entireTree) {
                    mySet.Clear();   // much faster than DeleteRange
                }
                else {
                    mySet.tree.DeleteRange(rangeTester);
                }
            }

            /// <summary>
            /// Adds a new item to the set underlying this View. If the set already contains an item equal to
            /// <paramref name="item"/>, that item is replaces with <paramref name="item"/>. If
            /// <paramref name="item"/> is outside the range of this view, an InvalidOperationException
            /// is thrown.
            /// </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 time O(log N), where N is the number of items in the set.</para></remarks>
            /// <param name="item">The item to add.</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)
            {
                if (!ItemInView(item))
                    throw new ArgumentException(Strings.OutOfViewRange, "item");
                else
                    return mySet.Add(item);
            }

            /// <summary>
            /// Adds a new item to the set underlying this View. If the set already contains an item equal to
            /// <paramref name="item"/>, that item is replaces with <paramref name="item"/>. If
            /// <paramref name="item"/> is outside the range of this view, an InvalidOperationException
            /// is thrown.
            /// </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 time O(log N), where N is the number of items in the set.</para></remarks>
            /// <param name="item">The item to add.</param>
            void ICollection<T>.Add(T item)
            {
                Add(item);
            }

            /// <summary>
            /// Searches the underlying set for an item equal to <paramref name="item"/>, and if found,
            /// removes it from the set. If not found, the set is unchanged. If the item is outside
            /// the range of this view, 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 time O(log N), where N is the number of items in 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, or
            /// was outside the range of this view.</returns>
            public sealed override bool Remove(T item)
            {
                if (!ItemInView(item))
                    return false;
                else
                    return mySet.Remove(item);
            }

            /// <summary>
            /// Determines if this view of the set contains an item equal to <paramref name="item"/>. The set
            /// is not changed. If 
            /// </summary>
            /// <remarks>Searching the set for an item takes time O(log N), where N is 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"/>, and <paramref name="item"/> is within
            /// the range of this view. False otherwise.</returns>
            public sealed override bool Contains(T item)
            {
                if (!ItemInView(item))
                    return false;
                else
                    return mySet.Contains(item);
            }

            /// <summary>
            /// Get the index of the given item in the view. The smallest item in the view has index 0,
            /// the next smallest item has index 1, and the largest item has index Count-1. 
            /// </summary>
            /// <remarks>Finding the index takes time O(log N), which N is the number of items in 
            /// the set.</remarks>
            /// <param name="item">The item to get the index of.</param>
            /// <returns>The index of the item in the view, or -1 if the item is not present
            /// in the view.</returns>
            public int IndexOf(T item)
            {
                if (entireTree) {
                    if (reversed) {
                        int indexInSet = mySet.tree.FindIndex(item, false);
                        if (indexInSet < 0)
                            return -1;

                        return mySet.Count - 1 - indexInSet;
                    }
                    else {
                        return mySet.tree.FindIndex(item, true);
                    }
                }
                else {
                    T dummy;

                    if (!ItemInView(item))
                        return -1;

                    if (reversed) {
                        int indexInSet = mySet.tree.FindIndex(item, false);
                        if (indexInSet < 0)
                            return -1;
                        int indexOfEnd = mySet.tree.LastItemInRange(rangeTester, out dummy);
                        return indexOfEnd - indexInSet;

                    }
                    else {
                        int indexInSet = mySet.tree.FindIndex(item, true);
                        if (indexInSet < 0)
                            return -1;
                        int indexOfStart = mySet.tree.FirstItemInRange(rangeTester, out dummy);
                        return indexInSet - indexOfStart;
                    }
                }
            }

            /// <summary>
            /// Get the item by its index in the sorted order. The smallest item in the view has index 0,
            /// the next smallest item has index 1, and the largest item has index Count-1. 
            /// </summary>
            /// <remarks>The indexer takes time O(log N), which N is the number of items in 
            /// the set.</remarks>
            /// <param name="index">The index to get the item by.</param>
            /// <returns>The item at the given index.</returns>
            /// <exception cref="ArgumentOutOfRangeException"><paramref name="index"/> is
            /// less than zero or greater than or equal to Count.</exception>
            public T this[int index]
            {
                get
                {
                    if (entireTree) {
                        if (reversed) {
                            return mySet[mySet.Count - 1 - index];
                        }
                        else {
                            return mySet[index];
                        }
                    }
                    else {
                        T dummy;
                        int firstIndex = mySet.tree.FirstItemInRange(rangeTester, out dummy);
                        int lastIndex = mySet.tree.LastItemInRange(rangeTester, out dummy);
                        if (firstIndex < 0 || lastIndex < 0 || index < 0 || index >= (lastIndex - firstIndex + 1))
                            throw new ArgumentOutOfRangeException("index");

                        if (reversed) 
                            return mySet[lastIndex - index];
                        else 
                            return mySet[firstIndex + index];
                    }
                }
            }

            /// <summary>
            /// Get a read-only list view of the items in this view. The
            /// items in the list are in sorted order, with the smallest item
            /// at index 0. This view does not copy any data, and reflects any
            /// changes to the underlying OrderedSet.
            /// </summary>
            /// <returns>A read-only IList&lt;T&gt; view onto this view.</returns>
            public IList<T> AsList()
            {
                return new ListView(mySet, rangeTester, entireTree, reversed);
            }

            /// <summary>
            /// Creates a new View that has the same items as this view, in the reversed order.
            /// </summary>
            /// <returns>A new View that has the reversed order of this view, with the same upper 
            /// and lower bounds.</returns>
            public View Reversed()
            {
                return new View(mySet, rangeTester, entireTree, !reversed);
            }

            /// <summary>
            /// Returns the first item in this view: the item
            /// that would appear first if the view was enumerated. 
            /// </summary>
            /// <remarks>GetFirst() takes time O(log N), where N is the number of items in the set.</remarks>
            /// <returns>The first item in the view. </returns>
            /// <exception cref="InvalidOperationException">The view has no items in it.</exception>
            public T GetFirst()
            {
                T item;
                int found;

                if (reversed)
                    found = mySet.tree.LastItemInRange(rangeTester, out item);
                else
                    found = mySet.tree.FirstItemInRange(rangeTester, out item);

                if (found < 0)
                    throw new InvalidOperationException(Strings.CollectionIsEmpty);

                return item;
            }

            /// <summary>
            /// Returns the last item in the view: the item
            /// that would appear last if the view was enumerated. 
            /// </summary>
            /// <remarks>GetLast() takes time O(log N), where N is the number of items in the set.</remarks>
            /// <returns>The last item in the view. </returns>
            /// <exception cref="InvalidOperationException">The view has no items in it.</exception>
            public T GetLast()
            {
                T item;
                int found;

                if (reversed)
                    found = mySet.tree.FirstItemInRange(rangeTester, out item);
                else
                    found = mySet.tree.LastItemInRange(rangeTester, out item);

                if (found < 0)
                    throw new InvalidOperationException(Strings.CollectionIsEmpty);

                return item;
            }
        }

        #endregion
    }
}