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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<div class="subTitle">edu.emory.mathcs.backport.java.util.concurrent</div>
<h2 title="Class ConcurrentSkipListSet" class="title">Class ConcurrentSkipListSet</h2>
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<div class="contentContainer">
<ul class="inheritance">
<li>java.lang.Object</li>
<li>
<ul class="inheritance">
<li>java.util.AbstractCollection</li>
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<ul class="inheritance">
<li>java.util.AbstractSet</li>
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<ul class="inheritance">
<li><a href="../../../../../../../edu/emory/mathcs/backport/java/util/AbstractSet.html" title="class in edu.emory.mathcs.backport.java.util">edu.emory.mathcs.backport.java.util.AbstractSet</a></li>
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<li>edu.emory.mathcs.backport.java.util.concurrent.ConcurrentSkipListSet</li>
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<dt>All Implemented Interfaces:</dt>
<dd><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a>, java.io.Serializable, java.lang.Cloneable, java.lang.Iterable, java.util.Collection, java.util.Set, java.util.SortedSet</dd>
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<pre>public class <span class="strong">ConcurrentSkipListSet</span>
extends <a href="../../../../../../../edu/emory/mathcs/backport/java/util/AbstractSet.html" title="class in edu.emory.mathcs.backport.java.util">AbstractSet</a>
implements <a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a>, java.lang.Cloneable, java.io.Serializable</pre>
<div class="block">A scalable concurrent <a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util"><code>NavigableSet</code></a> implementation based on
 a <a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListMap.html" title="class in edu.emory.mathcs.backport.java.util.concurrent"><code>ConcurrentSkipListMap</code></a>.  The elements of the set are kept
 sorted according to their natural ordering,
 or by a <code>Comparator</code> provided at set creation time, depending
 on which constructor is used.

 <p>This implementation provides expected average <i>log(n)</i> time
 cost for the <tt>contains</tt>, <tt>add</tt>, and <tt>remove</tt>
 operations and their variants.  Insertion, removal, and access
 operations safely execute concurrently by multiple threads.
 Iterators are <i>weakly consistent</i>, returning elements
 reflecting the state of the set at some point at or since the
 creation of the iterator.  They do <em>not</em> throw <code>ConcurrentModificationException</code>, and may proceed concurrently with
 other operations.  Ascending ordered views and their iterators are
 faster than descending ones.

 <p>Beware that, unlike in most collections, the <tt>size</tt>
 method is <em>not</em> a constant-time operation. Because of the
 asynchronous nature of these sets, determining the current number
 of elements requires a traversal of the elements. Additionally, the
 bulk operations <tt>addAll</tt>, <tt>removeAll</tt>,
 <tt>retainAll</tt>, and <tt>containsAll</tt> are <em>not</em>
 guaranteed to be performed atomically. For example, an iterator
 operating concurrently with an <tt>addAll</tt> operation might view
 only some of the added elements.

 <p>This class and its iterators implement all of the
 <em>optional</em> methods of the <code>Set</code> and <code>Iterator</code>
 interfaces. Like most other concurrent collection implementations,
 this class does not permit the use of <tt>null</tt> elements,
 because <tt>null</tt> arguments and return values cannot be reliably
 distinguished from the absence of elements.

 <p>This class is a member of the
 <a href="../../../../../../../../technotes/guides/collections/index.html">
 Java Collections Framework</a>.</div>
<dl><dt><span class="strong">Since:</span></dt>
  <dd>1.6</dd>
<dt><span class="strong">Author:</span></dt>
  <dd>Doug Lea</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../../serialized-form.html#edu.emory.mathcs.backport.java.util.concurrent.ConcurrentSkipListSet">Serialized Form</a></dd></dl>
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<h3>Constructor Summary</h3>
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<caption><span>Constructors</span><span class="tabEnd">&nbsp;</span></caption>
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<th class="colOne" scope="col">Constructor and Description</th>
</tr>
<tr class="altColor">
<td class="colOne"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#ConcurrentSkipListSet()">ConcurrentSkipListSet</a></strong>()</code>
<div class="block">Constructs a new, empty set that orders its elements according to
 their natural ordering.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colOne"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#ConcurrentSkipListSet(java.util.Collection)">ConcurrentSkipListSet</a></strong>(java.util.Collection&nbsp;c)</code>
<div class="block">Constructs a new set containing the elements in the specified
 collection, that orders its elements according to their
 natural ordering.</div>
</td>
</tr>
<tr class="altColor">
<td class="colOne"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#ConcurrentSkipListSet(java.util.Comparator)">ConcurrentSkipListSet</a></strong>(java.util.Comparator&nbsp;comparator)</code>
<div class="block">Constructs a new, empty set that orders its elements according to
 the specified comparator.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colOne"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#ConcurrentSkipListSet(java.util.SortedSet)">ConcurrentSkipListSet</a></strong>(java.util.SortedSet&nbsp;s)</code>
<div class="block">Constructs a new set containing the same elements and using the
 same ordering as the specified sorted set.</div>
</td>
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<caption><span>Methods</span><span class="tabEnd">&nbsp;</span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
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<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#add(java.lang.Object)">add</a></strong>(java.lang.Object&nbsp;e)</code>
<div class="block">Adds the specified element to this set if it is not already present.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>java.lang.Object</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#ceiling(java.lang.Object)">ceiling</a></strong>(java.lang.Object&nbsp;e)</code>
<div class="block">Returns the least element in this set greater than or equal to
 the given element, or <code>null</code> if there is no such element.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#clear()">clear</a></strong>()</code>
<div class="block">Removes all of the elements from this set.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>java.lang.Object</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#clone()">clone</a></strong>()</code>
<div class="block">Returns a shallow copy of this <tt>ConcurrentSkipListSet</tt>
 instance.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>java.util.Comparator</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#comparator()">comparator</a></strong>()</code>&nbsp;</td>
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<tr class="rowColor">
<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#contains(java.lang.Object)">contains</a></strong>(java.lang.Object&nbsp;o)</code>
<div class="block">Returns <tt>true</tt> if this set contains the specified element.</div>
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<tr class="altColor">
<td class="colFirst"><code>java.util.Iterator</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#descendingIterator()">descendingIterator</a></strong>()</code>
<div class="block">Returns an iterator over the elements in this set in descending order.</div>
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<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#descendingSet()">descendingSet</a></strong>()</code>
<div class="block">Returns a reverse order view of the elements contained in this set.</div>
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<tr class="altColor">
<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#equals(java.lang.Object)">equals</a></strong>(java.lang.Object&nbsp;o)</code>
<div class="block">Compares the specified object with this set for equality.</div>
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<tr class="rowColor">
<td class="colFirst"><code>java.lang.Object</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#first()">first</a></strong>()</code>&nbsp;</td>
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<td class="colFirst"><code>java.lang.Object</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#floor(java.lang.Object)">floor</a></strong>(java.lang.Object&nbsp;e)</code>
<div class="block">Returns the greatest element in this set less than or equal to
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<td class="colFirst"><code>java.util.SortedSet</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#headSet(java.lang.Object)">headSet</a></strong>(java.lang.Object&nbsp;toElement)</code></td>
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<tr class="altColor">
<td class="colFirst"><code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a></code></td>
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<div class="block">Returns a view of the portion of this set whose elements are less than
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<td class="colFirst"><code>java.lang.Object</code></td>
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<div class="block">Returns the least element in this set strictly greater than the
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<tr class="altColor">
<td class="colFirst"><code>boolean</code></td>
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<td class="colFirst"><code>java.util.Iterator</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#iterator()">iterator</a></strong>()</code>
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<tr class="altColor">
<td class="colFirst"><code>java.lang.Object</code></td>
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<td class="colFirst"><code>java.lang.Object</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#lower(java.lang.Object)">lower</a></strong>(java.lang.Object&nbsp;e)</code>
<div class="block">Returns the greatest element in this set strictly less than the
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<tr class="altColor">
<td class="colFirst"><code>java.lang.Object</code></td>
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<div class="block">Retrieves and removes the first (lowest) element,
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<tr class="rowColor">
<td class="colFirst"><code>java.lang.Object</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#pollLast()">pollLast</a></strong>()</code>
<div class="block">Retrieves and removes the last (highest) element,
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<tr class="altColor">
<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#remove(java.lang.Object)">remove</a></strong>(java.lang.Object&nbsp;o)</code>
<div class="block">Removes the specified element from this set if it is present.</div>
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<tr class="rowColor">
<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#removeAll(java.util.Collection)">removeAll</a></strong>(java.util.Collection&nbsp;c)</code>
<div class="block">Removes from this set all of its elements that are contained in
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<tr class="altColor">
<td class="colFirst"><code>int</code></td>
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<div class="block">Returns the number of elements in this set.</div>
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<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#subSet(java.lang.Object, boolean, java.lang.Object, boolean)">subSet</a></strong>(java.lang.Object&nbsp;fromElement,
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<div class="block">Returns a view of the portion of this set whose elements range from
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<tr class="altColor">
<td class="colFirst"><code>java.util.SortedSet</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#subSet(java.lang.Object, java.lang.Object)">subSet</a></strong>(java.lang.Object&nbsp;fromElement,
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<tr class="rowColor">
<td class="colFirst"><code>java.util.SortedSet</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#tailSet(java.lang.Object)">tailSet</a></strong>(java.lang.Object&nbsp;fromElement)</code></td>
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<tr class="altColor">
<td class="colFirst"><code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html#tailSet(java.lang.Object, boolean)">tailSet</a></strong>(java.lang.Object&nbsp;fromElement,
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<div class="block">Returns a view of the portion of this set whose elements are greater
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<pre>public&nbsp;ConcurrentSkipListSet()</pre>
<div class="block">Constructs a new, empty set that orders its elements according to
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<pre>public&nbsp;ConcurrentSkipListSet(java.util.Comparator&nbsp;comparator)</pre>
<div class="block">Constructs a new, empty set that orders its elements according to
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>comparator</code> - the comparator that will be used to order this set.
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<pre>public&nbsp;ConcurrentSkipListSet(java.util.Collection&nbsp;c)</pre>
<div class="block">Constructs a new set containing the elements in the specified
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 natural ordering.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>c</code> - The elements that will comprise the new set</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code>java.lang.ClassCastException</code> - if the elements in <tt>c</tt> are
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<dd><code>java.lang.NullPointerException</code> - if the specified collection or any
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<pre>public&nbsp;ConcurrentSkipListSet(java.util.SortedSet&nbsp;s)</pre>
<div class="block">Constructs a new set containing the same elements and using the
 same ordering as the specified sorted set.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>s</code> - sorted set whose elements will comprise the new set</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code>java.lang.NullPointerException</code> - if the specified sorted set or any
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<pre>public&nbsp;java.lang.Object&nbsp;clone()</pre>
<div class="block">Returns a shallow copy of this <tt>ConcurrentSkipListSet</tt>
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<dl>
<dt><strong>Overrides:</strong></dt>
<dd><code>clone</code>&nbsp;in class&nbsp;<code>java.lang.Object</code></dd>
<dt><span class="strong">Returns:</span></dt><dd>a shallow copy of this set</dd></dl>
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<pre>public&nbsp;int&nbsp;size()</pre>
<div class="block">Returns the number of elements in this set.  If this set
 contains more than <tt>Integer.MAX_VALUE</tt> elements, it
 returns <tt>Integer.MAX_VALUE</tt>.

 <p>Beware that, unlike in most collections, this method is
 <em>NOT</em> a constant-time operation. Because of the
 asynchronous nature of these sets, determining the current
 number of elements requires traversing them all to count them.
 Additionally, it is possible for the size to change during
 execution of this method, in which case the returned result
 will be inaccurate. Thus, this method is typically not very
 useful in concurrent applications.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code>size</code>&nbsp;in interface&nbsp;<code>java.util.Collection</code></dd>
<dt><strong>Specified by:</strong></dt>
<dd><code>size</code>&nbsp;in interface&nbsp;<code>java.util.Set</code></dd>
<dt><strong>Specified by:</strong></dt>
<dd><code>size</code>&nbsp;in class&nbsp;<code>java.util.AbstractCollection</code></dd>
<dt><span class="strong">Returns:</span></dt><dd>the number of elements in this set</dd></dl>
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<pre>public&nbsp;boolean&nbsp;isEmpty()</pre>
<div class="block">Returns <tt>true</tt> if this set contains no elements.</div>
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<dt><strong>Specified by:</strong></dt>
<dd><code>isEmpty</code>&nbsp;in interface&nbsp;<code>java.util.Collection</code></dd>
<dt><strong>Specified by:</strong></dt>
<dd><code>isEmpty</code>&nbsp;in interface&nbsp;<code>java.util.Set</code></dd>
<dt><strong>Overrides:</strong></dt>
<dd><code>isEmpty</code>&nbsp;in class&nbsp;<code>java.util.AbstractCollection</code></dd>
<dt><span class="strong">Returns:</span></dt><dd><tt>true</tt> if this set contains no elements</dd></dl>
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<pre>public&nbsp;boolean&nbsp;contains(java.lang.Object&nbsp;o)</pre>
<div class="block">Returns <tt>true</tt> if this set contains the specified element.
 More formally, returns <tt>true</tt> if and only if this set
 contains an element <tt>e</tt> such that <tt>o.equals(e)</tt>.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code>contains</code>&nbsp;in interface&nbsp;<code>java.util.Collection</code></dd>
<dt><strong>Specified by:</strong></dt>
<dd><code>contains</code>&nbsp;in interface&nbsp;<code>java.util.Set</code></dd>
<dt><strong>Overrides:</strong></dt>
<dd><code>contains</code>&nbsp;in class&nbsp;<code>java.util.AbstractCollection</code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>o</code> - object to be checked for containment in this set</dd>
<dt><span class="strong">Returns:</span></dt><dd><tt>true</tt> if this set contains the specified element</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code>java.lang.ClassCastException</code> - if the specified element cannot be
         compared with the elements currently in this set</dd>
<dd><code>java.lang.NullPointerException</code> - if the specified element is null</dd></dl>
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<pre>public&nbsp;boolean&nbsp;add(java.lang.Object&nbsp;e)</pre>
<div class="block">Adds the specified element to this set if it is not already present.
 More formally, adds the specified element <tt>e</tt> to this set if
 the set contains no element <tt>e2</tt> such that <tt>e.equals(e2)</tt>.
 If this set already contains the element, the call leaves the set
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<dl>
<dt><strong>Specified by:</strong></dt>
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<dt><strong>Specified by:</strong></dt>
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<dt><strong>Overrides:</strong></dt>
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<dt><span class="strong">Returns:</span></dt><dd><tt>true</tt> if this set did not already contain the
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<dt><span class="strong">Throws:</span></dt>
<dd><code>java.lang.ClassCastException</code> - if <tt>e</tt> cannot be compared
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<dd><code>java.lang.NullPointerException</code> - if the specified element is null</dd></dl>
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<pre>public&nbsp;boolean&nbsp;remove(java.lang.Object&nbsp;o)</pre>
<div class="block">Removes the specified element from this set if it is present.
 More formally, removes an element <tt>e</tt> such that
 <tt>o.equals(e)</tt>, if this set contains such an element.
 Returns <tt>true</tt> if this set contained the element (or
 equivalently, if this set changed as a result of the call).
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<dt><strong>Overrides:</strong></dt>
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<dt><span class="strong">Parameters:</span></dt><dd><code>o</code> - object to be removed from this set, if present</dd>
<dt><span class="strong">Returns:</span></dt><dd><tt>true</tt> if this set contained the specified element</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code>java.lang.ClassCastException</code> - if <tt>o</tt> cannot be compared
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<dd><code>java.lang.NullPointerException</code> - if the specified element is null</dd></dl>
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<pre>public&nbsp;void&nbsp;clear()</pre>
<div class="block">Removes all of the elements from this set.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code>clear</code>&nbsp;in interface&nbsp;<code>java.util.Collection</code></dd>
<dt><strong>Specified by:</strong></dt>
<dd><code>clear</code>&nbsp;in interface&nbsp;<code>java.util.Set</code></dd>
<dt><strong>Overrides:</strong></dt>
<dd><code>clear</code>&nbsp;in class&nbsp;<code>java.util.AbstractCollection</code></dd>
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<h4>iterator</h4>
<pre>public&nbsp;java.util.Iterator&nbsp;iterator()</pre>
<div class="block">Returns an iterator over the elements in this set in ascending order.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
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<dt><strong>Specified by:</strong></dt>
<dd><code>iterator</code>&nbsp;in interface&nbsp;<code>java.lang.Iterable</code></dd>
<dt><strong>Specified by:</strong></dt>
<dd><code>iterator</code>&nbsp;in interface&nbsp;<code>java.util.Collection</code></dd>
<dt><strong>Specified by:</strong></dt>
<dd><code>iterator</code>&nbsp;in interface&nbsp;<code>java.util.Set</code></dd>
<dt><strong>Specified by:</strong></dt>
<dd><code>iterator</code>&nbsp;in class&nbsp;<code>java.util.AbstractCollection</code></dd>
<dt><span class="strong">Returns:</span></dt><dd>an iterator over the elements in this set in ascending order</dd></dl>
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<pre>public&nbsp;java.util.Iterator&nbsp;descendingIterator()</pre>
<div class="block">Returns an iterator over the elements in this set in descending order.</div>
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<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#descendingIterator()">descendingIterator</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a></code></dd>
<dt><span class="strong">Returns:</span></dt><dd>an iterator over the elements in this set in descending order</dd></dl>
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<pre>public&nbsp;boolean&nbsp;equals(java.lang.Object&nbsp;o)</pre>
<div class="block">Compares the specified object with this set for equality.  Returns
 <tt>true</tt> if the specified object is also a set, the two sets
 have the same size, and every member of the specified set is
 contained in this set (or equivalently, every member of this set is
 contained in the specified set).  This definition ensures that the
 equals method works properly across different implementations of the
 set interface.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code>equals</code>&nbsp;in interface&nbsp;<code>java.util.Collection</code></dd>
<dt><strong>Specified by:</strong></dt>
<dd><code>equals</code>&nbsp;in interface&nbsp;<code>java.util.Set</code></dd>
<dt><strong>Overrides:</strong></dt>
<dd><code>equals</code>&nbsp;in class&nbsp;<code>java.util.AbstractSet</code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>o</code> - the object to be compared for equality with this set</dd>
<dt><span class="strong">Returns:</span></dt><dd><tt>true</tt> if the specified object is equal to this set</dd></dl>
</li>
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<a name="removeAll(java.util.Collection)">
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<h4>removeAll</h4>
<pre>public&nbsp;boolean&nbsp;removeAll(java.util.Collection&nbsp;c)</pre>
<div class="block">Removes from this set all of its elements that are contained in
 the specified collection.  If the specified collection is also
 a set, this operation effectively modifies this set so that its
 value is the <i>asymmetric set difference</i> of the two sets.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code>removeAll</code>&nbsp;in interface&nbsp;<code>java.util.Collection</code></dd>
<dt><strong>Specified by:</strong></dt>
<dd><code>removeAll</code>&nbsp;in interface&nbsp;<code>java.util.Set</code></dd>
<dt><strong>Overrides:</strong></dt>
<dd><code>removeAll</code>&nbsp;in class&nbsp;<code>java.util.AbstractSet</code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>c</code> - collection containing elements to be removed from this set</dd>
<dt><span class="strong">Returns:</span></dt><dd><tt>true</tt> if this set changed as a result of the call</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code>java.lang.ClassCastException</code> - if the types of one or more elements in this
         set are incompatible with the specified collection</dd>
<dd><code>java.lang.NullPointerException</code> - if the specified collection or any
         of its elements are null</dd></dl>
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<a name="lower(java.lang.Object)">
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<h4>lower</h4>
<pre>public&nbsp;java.lang.Object&nbsp;lower(java.lang.Object&nbsp;e)</pre>
<div class="block"><strong>Description copied from interface:&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#lower(java.lang.Object)">NavigableSet</a></code></strong></div>
<div class="block">Returns the greatest element in this set strictly less than the
 given element, or <code>null</code> if there is no such element.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#lower(java.lang.Object)">lower</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>e</code> - the value to match</dd>
<dt><span class="strong">Returns:</span></dt><dd>the greatest element less than <code>e</code>,
         or <code>null</code> if there is no such element</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code>java.lang.ClassCastException</code> - if the specified element cannot be
         compared with the elements currently in the set</dd>
<dd><code>java.lang.NullPointerException</code> - if the specified element is null</dd></dl>
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<h4>floor</h4>
<pre>public&nbsp;java.lang.Object&nbsp;floor(java.lang.Object&nbsp;e)</pre>
<div class="block"><strong>Description copied from interface:&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#floor(java.lang.Object)">NavigableSet</a></code></strong></div>
<div class="block">Returns the greatest element in this set less than or equal to
 the given element, or <code>null</code> if there is no such element.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#floor(java.lang.Object)">floor</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>e</code> - the value to match</dd>
<dt><span class="strong">Returns:</span></dt><dd>the greatest element less than or equal to <code>e</code>,
         or <code>null</code> if there is no such element</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code>java.lang.ClassCastException</code> - if the specified element cannot be
         compared with the elements currently in the set</dd>
<dd><code>java.lang.NullPointerException</code> - if the specified element is null</dd></dl>
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<pre>public&nbsp;java.lang.Object&nbsp;ceiling(java.lang.Object&nbsp;e)</pre>
<div class="block"><strong>Description copied from interface:&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#ceiling(java.lang.Object)">NavigableSet</a></code></strong></div>
<div class="block">Returns the least element in this set greater than or equal to
 the given element, or <code>null</code> if there is no such element.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#ceiling(java.lang.Object)">ceiling</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>e</code> - the value to match</dd>
<dt><span class="strong">Returns:</span></dt><dd>the least element greater than or equal to <code>e</code>,
         or <code>null</code> if there is no such element</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code>java.lang.ClassCastException</code> - if the specified element cannot be
         compared with the elements currently in the set</dd>
<dd><code>java.lang.NullPointerException</code> - if the specified element is null</dd></dl>
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<h4>higher</h4>
<pre>public&nbsp;java.lang.Object&nbsp;higher(java.lang.Object&nbsp;e)</pre>
<div class="block"><strong>Description copied from interface:&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#higher(java.lang.Object)">NavigableSet</a></code></strong></div>
<div class="block">Returns the least element in this set strictly greater than the
 given element, or <code>null</code> if there is no such element.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#higher(java.lang.Object)">higher</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>e</code> - the value to match</dd>
<dt><span class="strong">Returns:</span></dt><dd>the least element greater than <code>e</code>,
         or <code>null</code> if there is no such element</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code>java.lang.ClassCastException</code> - if the specified element cannot be
         compared with the elements currently in the set</dd>
<dd><code>java.lang.NullPointerException</code> - if the specified element is null</dd></dl>
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<a name="pollFirst()">
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<h4>pollFirst</h4>
<pre>public&nbsp;java.lang.Object&nbsp;pollFirst()</pre>
<div class="block"><strong>Description copied from interface:&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#pollFirst()">NavigableSet</a></code></strong></div>
<div class="block">Retrieves and removes the first (lowest) element,
 or returns <code>null</code> if this set is empty.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#pollFirst()">pollFirst</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a></code></dd>
<dt><span class="strong">Returns:</span></dt><dd>the first element, or <code>null</code> if this set is empty</dd></dl>
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<a name="pollLast()">
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<h4>pollLast</h4>
<pre>public&nbsp;java.lang.Object&nbsp;pollLast()</pre>
<div class="block"><strong>Description copied from interface:&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#pollLast()">NavigableSet</a></code></strong></div>
<div class="block">Retrieves and removes the last (highest) element,
 or returns <code>null</code> if this set is empty.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#pollLast()">pollLast</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a></code></dd>
<dt><span class="strong">Returns:</span></dt><dd>the last element, or <code>null</code> if this set is empty</dd></dl>
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<a name="comparator()">
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<h4>comparator</h4>
<pre>public&nbsp;java.util.Comparator&nbsp;comparator()</pre>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code>comparator</code>&nbsp;in interface&nbsp;<code>java.util.SortedSet</code></dd>
</dl>
</li>
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<h4>first</h4>
<pre>public&nbsp;java.lang.Object&nbsp;first()</pre>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code>first</code>&nbsp;in interface&nbsp;<code>java.util.SortedSet</code></dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code>NoSuchElementException</code></dd></dl>
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<h4>last</h4>
<pre>public&nbsp;java.lang.Object&nbsp;last()</pre>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code>last</code>&nbsp;in interface&nbsp;<code>java.util.SortedSet</code></dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code>NoSuchElementException</code></dd></dl>
</li>
</ul>
<a name="subSet(java.lang.Object, boolean, java.lang.Object, boolean)">
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<h4>subSet</h4>
<pre>public&nbsp;<a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a>&nbsp;subSet(java.lang.Object&nbsp;fromElement,
                  boolean&nbsp;fromInclusive,
                  java.lang.Object&nbsp;toElement,
                  boolean&nbsp;toInclusive)</pre>
<div class="block"><strong>Description copied from interface:&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#subSet(java.lang.Object, boolean, java.lang.Object, boolean)">NavigableSet</a></code></strong></div>
<div class="block">Returns a view of the portion of this set whose elements range from
 <code>fromElement</code> to <code>toElement</code>.  If <code>fromElement</code> and
 <code>toElement</code> are equal, the returned set is empty unless <code>fromExclusive</code> and <code>toExclusive</code> are both true.  The returned set
 is backed by this set, so changes in the returned set are reflected in
 this set, and vice-versa.  The returned set supports all optional set
 operations that this set supports.

 <p>The returned set will throw an <code>IllegalArgumentException</code>
 on an attempt to insert an element outside its range.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#subSet(java.lang.Object, boolean, java.lang.Object, boolean)">subSet</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>fromElement</code> - low endpoint of the returned set</dd><dd><code>fromInclusive</code> - <code>true</code> if the low endpoint
        is to be included in the returned view</dd><dd><code>toElement</code> - high endpoint of the returned set</dd><dd><code>toInclusive</code> - <code>true</code> if the high endpoint
        is to be included in the returned view</dd>
<dt><span class="strong">Returns:</span></dt><dd>a view of the portion of this set whose elements range from
         <code>fromElement</code>, inclusive, to <code>toElement</code>, exclusive</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code>java.lang.ClassCastException</code> - if <code>fromElement</code> and
         <code>toElement</code> cannot be compared to one another using this
         set's comparator (or, if the set has no comparator, using
         natural ordering).  Implementations may, but are not required
         to, throw this exception if <code>fromElement</code> or
         <code>toElement</code> cannot be compared to elements currently in
         the set.</dd>
<dd><code>java.lang.NullPointerException</code> - if <code>fromElement</code> or
         <code>toElement</code> is null</dd>
<dd><code>java.lang.IllegalArgumentException</code> - if <code>fromElement</code> is
         greater than <code>toElement</code>; or if this set itself
         has a restricted range, and <code>fromElement</code> or
         <code>toElement</code> lies outside the bounds of the range.</dd></dl>
</li>
</ul>
<a name="headSet(java.lang.Object, boolean)">
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<li class="blockList">
<h4>headSet</h4>
<pre>public&nbsp;<a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a>&nbsp;headSet(java.lang.Object&nbsp;toElement,
                   boolean&nbsp;inclusive)</pre>
<div class="block"><strong>Description copied from interface:&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#headSet(java.lang.Object, boolean)">NavigableSet</a></code></strong></div>
<div class="block">Returns a view of the portion of this set whose elements are less than
 (or equal to, if <code>inclusive</code> is true) <code>toElement</code>.  The
 returned set is backed by this set, so changes in the returned set are
 reflected in this set, and vice-versa.  The returned set supports all
 optional set operations that this set supports.

 <p>The returned set will throw an <code>IllegalArgumentException</code>
 on an attempt to insert an element outside its range.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#headSet(java.lang.Object, boolean)">headSet</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>toElement</code> - high endpoint of the returned set</dd><dd><code>inclusive</code> - <code>true</code> if the high endpoint
        is to be included in the returned view</dd>
<dt><span class="strong">Returns:</span></dt><dd>a view of the portion of this set whose elements are less than
         (or equal to, if <code>inclusive</code> is true) <code>toElement</code></dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code>java.lang.ClassCastException</code> - if <code>toElement</code> is not compatible
         with this set's comparator (or, if the set has no comparator,
         if <code>toElement</code> does not implement <code>Comparable</code>).
         Implementations may, but are not required to, throw this
         exception if <code>toElement</code> cannot be compared to elements
         currently in the set.</dd>
<dd><code>java.lang.NullPointerException</code> - if <code>toElement</code> is null</dd>
<dd><code>java.lang.IllegalArgumentException</code> - if this set itself has a
         restricted range, and <code>toElement</code> lies outside the
         bounds of the range</dd></dl>
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<h4>tailSet</h4>
<pre>public&nbsp;<a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a>&nbsp;tailSet(java.lang.Object&nbsp;fromElement,
                   boolean&nbsp;inclusive)</pre>
<div class="block"><strong>Description copied from interface:&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#tailSet(java.lang.Object, boolean)">NavigableSet</a></code></strong></div>
<div class="block">Returns a view of the portion of this set whose elements are greater
 than (or equal to, if <code>inclusive</code> is true) <code>fromElement</code>.
 The returned set is backed by this set, so changes in the returned set
 are reflected in this set, and vice-versa.  The returned set supports
 all optional set operations that this set supports.

 <p>The returned set will throw an <code>IllegalArgumentException</code>
 on an attempt to insert an element outside its range.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#tailSet(java.lang.Object, boolean)">tailSet</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>fromElement</code> - low endpoint of the returned set</dd><dd><code>inclusive</code> - <code>true</code> if the low endpoint
        is to be included in the returned view</dd>
<dt><span class="strong">Returns:</span></dt><dd>a view of the portion of this set whose elements are greater
         than or equal to <code>fromElement</code></dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code>java.lang.ClassCastException</code> - if <code>fromElement</code> is not compatible
         with this set's comparator (or, if the set has no comparator,
         if <code>fromElement</code> does not implement <code>Comparable</code>).
         Implementations may, but are not required to, throw this
         exception if <code>fromElement</code> cannot be compared to elements
         currently in the set.</dd>
<dd><code>java.lang.NullPointerException</code> - if <code>fromElement</code> is null</dd>
<dd><code>java.lang.IllegalArgumentException</code> - if this set itself has a
         restricted range, and <code>fromElement</code> lies outside the
         bounds of the range</dd></dl>
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<h4>subSet</h4>
<pre>public&nbsp;java.util.SortedSet&nbsp;subSet(java.lang.Object&nbsp;fromElement,
                         java.lang.Object&nbsp;toElement)</pre>
<div class="block"><strong>Description copied from interface:&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#subSet(java.lang.Object, java.lang.Object)">NavigableSet</a></code></strong></div>
<div class="block">

 <p>Equivalent to <code>subSet(fromElement, true, toElement, false)</code>.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#subSet(java.lang.Object, java.lang.Object)">subSet</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a></code></dd>
<dt><strong>Specified by:</strong></dt>
<dd><code>subSet</code>&nbsp;in interface&nbsp;<code>java.util.SortedSet</code></dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code>java.lang.ClassCastException</code></dd>
<dd><code>java.lang.NullPointerException</code> - if <code>fromElement</code> or
         <code>toElement</code> is null</dd>
<dd><code>java.lang.IllegalArgumentException</code></dd></dl>
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<li class="blockList">
<h4>headSet</h4>
<pre>public&nbsp;java.util.SortedSet&nbsp;headSet(java.lang.Object&nbsp;toElement)</pre>
<div class="block"><strong>Description copied from interface:&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#headSet(java.lang.Object)">NavigableSet</a></code></strong></div>
<div class="block">

 <p>Equivalent to <code>headSet(toElement, false)</code>.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#headSet(java.lang.Object)">headSet</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a></code></dd>
<dt><strong>Specified by:</strong></dt>
<dd><code>headSet</code>&nbsp;in interface&nbsp;<code>java.util.SortedSet</code></dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code>java.lang.ClassCastException</code></dd>
<dd><code>java.lang.NullPointerException</code> - if <code>toElement</code> is null</dd>
<dd><code>java.lang.IllegalArgumentException</code></dd></dl>
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<h4>tailSet</h4>
<pre>public&nbsp;java.util.SortedSet&nbsp;tailSet(java.lang.Object&nbsp;fromElement)</pre>
<div class="block"><strong>Description copied from interface:&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#tailSet(java.lang.Object)">NavigableSet</a></code></strong></div>
<div class="block">

 <p>Equivalent to <code>tailSet(fromElement, true)</code>.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#tailSet(java.lang.Object)">tailSet</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a></code></dd>
<dt><strong>Specified by:</strong></dt>
<dd><code>tailSet</code>&nbsp;in interface&nbsp;<code>java.util.SortedSet</code></dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code>java.lang.ClassCastException</code></dd>
<dd><code>java.lang.NullPointerException</code> - if <code>fromElement</code> is null</dd>
<dd><code>java.lang.IllegalArgumentException</code></dd></dl>
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<h4>descendingSet</h4>
<pre>public&nbsp;<a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a>&nbsp;descendingSet()</pre>
<div class="block">Returns a reverse order view of the elements contained in this set.
 The descending set is backed by this set, so changes to the set are
 reflected in the descending set, and vice-versa.

 <p>The returned set has an ordering equivalent to
 <tt><a href="../../../../../../../edu/emory/mathcs/backport/java/util/Collections.html#reverseOrder(java.util.Comparator)"><code>Collections.reverseOrder</code></a>(comparator())</tt>.
 The expression <code>s.descendingSet().descendingSet()</code> returns a
 view of <code>s</code> essentially equivalent to <code>s</code>.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#descendingSet()">descendingSet</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a></code></dd>
<dt><span class="strong">Returns:</span></dt><dd>a reverse order view of this set</dd></dl>
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