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<div class="subTitle">edu.emory.mathcs.backport.java.util</div>
<h2 title="Interface NavigableSet" class="title">Interface NavigableSet</h2>
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<dl>
<dt>All Superinterfaces:</dt>
<dd>java.util.Collection, java.lang.Iterable, java.util.Set, java.util.SortedSet</dd>
</dl>
<dl>
<dt>All Known Implementing Classes:</dt>
<dd><a href="../../../../../../edu/emory/mathcs/backport/java/util/concurrent/ConcurrentSkipListSet.html" title="class in edu.emory.mathcs.backport.java.util.concurrent">ConcurrentSkipListSet</a>, <a href="../../../../../../edu/emory/mathcs/backport/java/util/TreeSet.html" title="class in edu.emory.mathcs.backport.java.util">TreeSet</a></dd>
</dl>
<hr>
<br>
<pre>public interface <span class="strong">NavigableSet</span>
extends java.util.SortedSet</pre>
<div class="block">A <code>SortedSet</code> extended with navigation methods reporting
closest matches for given search targets. Methods <code>lower</code>,
<code>floor</code>, <code>ceiling</code>, and <code>higher</code> return elements
respectively less than, less than or equal, greater than or equal,
and greater than a given element, returning <code>null</code> if there
is no such element. A <code>NavigableSet</code> may be accessed and
traversed in either ascending or descending order. The <code>descendingSet</code> method returns a view of the set with the senses of
all relational and directional methods inverted. The performance of
ascending operations and views is likely to be faster than that of
descending ones. This interface additionally defines methods
<code>pollFirst</code> and <code>pollLast</code> that return and remove the
lowest and highest element, if one exists, else returning <code>null</code>. Methods <code>subSet</code>, <code>headSet</code>,
and <code>tailSet</code> differ from the like-named <code>SortedSet</code> methods in accepting additional arguments describing
whether lower and upper bounds are inclusive versus exclusive.
Subsets of any <code>NavigableSet</code> must implement the <code>NavigableSet</code> interface.
<p> The return values of navigation methods may be ambiguous in
implementations that permit <code>null</code> elements. However, even
in this case the result can be disambiguated by checking
<code>contains(null)</code>. To avoid such issues, implementations of
this interface are encouraged to <em>not</em> permit insertion of
<code>null</code> elements. (Note that sorted sets of <code>Comparable</code> elements intrinsically do not permit <code>null</code>.)
<p>Methods
<a href="../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#subSet(java.lang.Object, java.lang.Object)"><code>subSet(E, E)</code></a>,
<a href="../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#headSet(java.lang.Object)"><code>headSet(E)</code></a>, and
<a href="../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#tailSet(java.lang.Object)"><code>tailSet(E)</code></a>
are specified to return <code>SortedSet</code> to allow existing
implementations of <code>SortedSet</code> to be compatibly retrofitted to
implement <code>NavigableSet</code>, but extensions and implementations
of this interface are encouraged to override these methods to return
<code>NavigableSet</code>.
<p>This interface 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, Josh Bloch</dd></dl>
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<h3>Method Summary</h3>
<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Method Summary table, listing methods, and an explanation">
<caption><span>Methods</span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
</tr>
<tr class="altColor">
<td class="colFirst"><code>java.lang.Object</code></td>
<td class="colLast"><code><strong><a href="../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#ceiling(java.lang.Object)">ceiling</a></strong>(java.lang.Object 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="rowColor">
<td class="colFirst"><code>java.util.Iterator</code></td>
<td class="colLast"><code><strong><a href="../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#descendingIterator()">descendingIterator</a></strong>()</code>
<div class="block">Returns an iterator over the elements in this set, in descending order.</div>
</td>
</tr>
<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/NavigableSet.html#descendingSet()">descendingSet</a></strong>()</code>
<div class="block">Returns a reverse order view of the elements contained in 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/NavigableSet.html#floor(java.lang.Object)">floor</a></strong>(java.lang.Object e)</code>
<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>
</td>
</tr>
<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/NavigableSet.html#headSet(java.lang.Object)">headSet</a></strong>(java.lang.Object toElement)</code></td>
</tr>
<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/NavigableSet.html#headSet(java.lang.Object, boolean)">headSet</a></strong>(java.lang.Object toElement,
boolean inclusive)</code>
<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>.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>java.lang.Object</code></td>
<td class="colLast"><code><strong><a href="../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#higher(java.lang.Object)">higher</a></strong>(java.lang.Object e)</code>
<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>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>java.util.Iterator</code></td>
<td class="colLast"><code><strong><a href="../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#iterator()">iterator</a></strong>()</code>
<div class="block">Returns an iterator over the elements in this set, in ascending order.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>java.lang.Object</code></td>
<td class="colLast"><code><strong><a href="../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#lower(java.lang.Object)">lower</a></strong>(java.lang.Object e)</code>
<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>
</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/NavigableSet.html#pollFirst()">pollFirst</a></strong>()</code>
<div class="block">Retrieves and removes the first (lowest) element,
or returns <code>null</code> if this set is empty.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>java.lang.Object</code></td>
<td class="colLast"><code><strong><a href="../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html#pollLast()">pollLast</a></strong>()</code>
<div class="block">Retrieves and removes the last (highest) element,
or returns <code>null</code> if this set is empty.</div>
</td>
</tr>
<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/NavigableSet.html#subSet(java.lang.Object, boolean, java.lang.Object, boolean)">subSet</a></strong>(java.lang.Object fromElement,
boolean fromInclusive,
java.lang.Object toElement,
boolean toInclusive)</code>
<div class="block">Returns a view of the portion of this set whose elements range from
<code>fromElement</code> to <code>toElement</code>.</div>
</td>
</tr>
<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/NavigableSet.html#subSet(java.lang.Object, java.lang.Object)">subSet</a></strong>(java.lang.Object fromElement,
java.lang.Object toElement)</code></td>
</tr>
<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/NavigableSet.html#tailSet(java.lang.Object)">tailSet</a></strong>(java.lang.Object fromElement)</code></td>
</tr>
<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/NavigableSet.html#tailSet(java.lang.Object, boolean)">tailSet</a></strong>(java.lang.Object fromElement,
boolean inclusive)</code>
<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>.</div>
</td>
</tr>
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<h3>Methods inherited from interface java.util.SortedSet</h3>
<code>comparator, first, last</code></li>
</ul>
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<h3>Methods inherited from interface java.util.Set</h3>
<code>add, addAll, clear, contains, containsAll, equals, hashCode, isEmpty, remove, removeAll, retainAll, size, toArray, toArray</code></li>
</ul>
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<h3>Method Detail</h3>
<a name="lower(java.lang.Object)">
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<h4>lower</h4>
<pre>java.lang.Object lower(java.lang.Object e)</pre>
<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><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
and this set does not permit null elements</dd></dl>
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<a name="floor(java.lang.Object)">
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<h4>floor</h4>
<pre>java.lang.Object floor(java.lang.Object e)</pre>
<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><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
and this set does not permit null elements</dd></dl>
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<a name="ceiling(java.lang.Object)">
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<h4>ceiling</h4>
<pre>java.lang.Object ceiling(java.lang.Object e)</pre>
<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><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
and this set does not permit null elements</dd></dl>
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<h4>higher</h4>
<pre>java.lang.Object higher(java.lang.Object e)</pre>
<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><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
and this set does not permit null elements</dd></dl>
</li>
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<a name="pollFirst()">
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<h4>pollFirst</h4>
<pre>java.lang.Object pollFirst()</pre>
<div class="block">Retrieves and removes the first (lowest) element,
or returns <code>null</code> if this set is empty.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the first element, or <code>null</code> if this set is empty</dd></dl>
</li>
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<a name="pollLast()">
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<h4>pollLast</h4>
<pre>java.lang.Object pollLast()</pre>
<div class="block">Retrieves and removes the last (highest) element,
or returns <code>null</code> if this set is empty.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the last element, or <code>null</code> if this set is empty</dd></dl>
</li>
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<a name="iterator()">
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<h4>iterator</h4>
<pre>java.util.Iterator 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>
<dd><code>iterator</code> in interface <code>java.util.Collection</code></dd>
<dt><strong>Specified by:</strong></dt>
<dd><code>iterator</code> in interface <code>java.lang.Iterable</code></dd>
<dt><strong>Specified by:</strong></dt>
<dd><code>iterator</code> in interface <code>java.util.Set</code></dd>
<dt><span class="strong">Returns:</span></dt><dd>an iterator over the elements in this set, in ascending order</dd></dl>
</li>
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<a name="descendingSet()">
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<h4>descendingSet</h4>
<pre><a href="../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a> 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. If either set is
modified while an iteration over either set is in progress (except
through the iterator's own <code>remove</code> operation), the results of
the iteration are undefined.
<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><span class="strong">Returns:</span></dt><dd>a reverse order view of this set</dd></dl>
</li>
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<a name="descendingIterator()">
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<h4>descendingIterator</h4>
<pre>java.util.Iterator descendingIterator()</pre>
<div class="block">Returns an iterator over the elements in this set, in descending order.
Equivalent in effect to <code>descendingSet().iterator()</code>.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>an iterator over the elements in this set, in descending order</dd></dl>
</li>
</ul>
<a name="subSet(java.lang.Object, boolean, java.lang.Object, boolean)">
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<h4>subSet</h4>
<pre><a href="../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a> subSet(java.lang.Object fromElement,
boolean fromInclusive,
java.lang.Object toElement,
boolean toInclusive)</pre>
<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><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 and this set does
not permit null elements</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>
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<h4>headSet</h4>
<pre><a href="../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a> headSet(java.lang.Object toElement,
boolean inclusive)</pre>
<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><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 and
this set does not permit null elements</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><a href="../../../../../../edu/emory/mathcs/backport/java/util/NavigableSet.html" title="interface in edu.emory.mathcs.backport.java.util">NavigableSet</a> tailSet(java.lang.Object fromElement,
boolean inclusive)</pre>
<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><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
and this set does not permit null elements</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>java.util.SortedSet subSet(java.lang.Object fromElement,
java.lang.Object toElement)</pre>
<div class="block">
<p>Equivalent to <code>subSet(fromElement, true, toElement, false)</code>.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code>subSet</code> in interface <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></dd>
<dd><code>java.lang.IllegalArgumentException</code></dd></dl>
</li>
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<h4>headSet</h4>
<pre>java.util.SortedSet headSet(java.lang.Object toElement)</pre>
<div class="block">
<p>Equivalent to <code>headSet(toElement, false)</code>.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code>headSet</code> in interface <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></dd>
<dd><code>java.lang.IllegalArgumentException</code></dd></dl>
</li>
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<h4>tailSet</h4>
<pre>java.util.SortedSet tailSet(java.lang.Object fromElement)</pre>
<div class="block">
<p>Equivalent to <code>tailSet(fromElement, true)</code>.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code>tailSet</code> in interface <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></dd>
<dd><code>java.lang.IllegalArgumentException</code></dd></dl>
</li>
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