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 <H2>nth_element()</H2>
 <P><B>Library:</B>&nbsp;&nbsp;<A HREF="2-9.html">Algorithms</A></P>

 <PRE><HR><B><I>Function</I></B><HR></PRE>

 <UL>
 <LI><A HREF="#sec1">Local Index</A></LI>
 <LI><A HREF="#sec2">Summary</A></LI>
 <LI><A HREF="#sec3">Synopsis</A></LI>
 <LI><A HREF="#sec4">Description</A></LI>
 <LI><A HREF="#sec5">Complexity</A></LI>
 <LI><A HREF="#sec6">Example</A></LI>
 <LI><A HREF="#sec7">See Also</A></LI>
 <LI><A HREF="#sec8">Standards Conformance</A></LI>
 </UL>
 <A NAME="sec1"><H3>Local Index</H3></A>
 No Entries
 <A NAME="sec2"><H3>Summary</H3></A>
 <P>An algorithm that rearranges a collection so that all elements lower in sorted order than the <SAMP>nth</SAMP> element come before it, and all elements higher in sorted order than the <SAMP>nth</SAMP> element come after it</P>
 <A NAME="sec3"><H3>Synopsis</H3></A>

 <PRE>#include &lt;algorithm&gt;

 namespace std {
   template &lt;class RandomAccessIterator&gt;
   void nth_element(RandomAccessIterator start,
                    RandomAccessIterator nth,
                    RandomAccessIterator finish);

   template &lt;class RandomAccessIterator, class Compare&gt;
   void nth_element(RandomAccessIterator start,
                    RandomAccessIterator nth,
                    RandomAccessIterator finish,
                    Compare comp);
 }
 </PRE>
 <A NAME="sec4"><H3>Description</H3></A>
 <P>The <SAMP>nth_element()</SAMP> algorithm rearranges a collection according to either  <SAMP>operator&lt;()</SAMP> or the function object <SAMP>comp</SAMP>. After the algorithm is applied, the follwoing hold:</P>
 <UL>
 <LI><P CLASS="LIST">The element that would be in the <SAMP>nth</SAMP> position if the sequence were completely sorted is in the <SAMP>nth</SAMP> position</P></LI>
 <LI><P CLASS="LIST">All elements prior to the <SAMP>nth</SAMP> position would also precede that position in an ordered sequence</P></LI>
 <LI><P CLASS="LIST">All elements following the <SAMP>nth</SAMP> position would also follow that position in an ordered sequence</P></LI>
 </UL>
 <P>That is, for any iterator <SAMP>i</SAMP> in the range <SAMP>[start, nth)</SAMP> and any iterator <SAMP>j</SAMP> in the range <SAMP>[nth, finish)</SAMP>, it holds that <SAMP>!(*i &gt; *j)</SAMP> or <SAMP>comp(*i, *j) == false</SAMP>. </P>
 <P>Note that the elements that precede or follow the <SAMP>nth</SAMP> position are not necessarily sorted relative to each other. The <SAMP>nth_element()</SAMP> algorithm does<I> not </I>sort the entire collection.</P>
 <A NAME="sec5"><H3>Complexity</H3></A>
 <P>The algorithm is linear, on average, where <SAMP>N</SAMP> is the size of the range <SAMP>[start, finish)</SAMP>.</P>
 <A NAME="sec6"><H3>Example</H3></A>

 <UL><PRE>//
 //  nthelem.cpp
 //

 #include &lt;algorithm&gt;   // for swap
 #include &lt;vector&gt;      // for vector
 #include &lt;iostream&gt;    // for cout, endl


 template&lt;class RandomAccessIterator&gt;
 void quik_sort (RandomAccessIterator start, RandomAccessIterator end)
 {
     size_t dist = end - start;

     // Stop condition for recursion.
     if (dist &gt; 2) {
         // Use nth_element to do all the work for quik_sort.
         std::nth_element (start, start + (dist / 2), end);

         // Recursive calls to each remaining unsorted portion.
         quik_sort (start, start + (dist / 2 - 1));
         quik_sort (start + (dist / 2 + 1), end);
     }

     if (2 == dist &amp;&amp; *(end - 1) &lt; *start)
         std::swap (start, end);
 }


 int main ()
 {
     typedef std::vector&lt;int, std::allocator&lt;int&gt; &gt; Vector;

     // Initialize a vector using an array of integers.
     Vector::value_type arr[] = { 37, 12,  2, -5, 14,
                                   1,  0, -1, 14, 32 };

     Vector v (arr + 0, arr + sizeof arr / sizeof *arr);

     // Print the initial vector.
     std::cout &lt;&lt; "The unsorted values are: \n     ";

     for (Vector::iterator i = v.begin (); i != v.end (); ++i)
         std::cout &lt;&lt; *i &lt;&lt; ", ";

     std::cout &lt;&lt; "\n\n";

     // Use the new sort algorithm.
     quik_sort (v.begin (), v.end ());

     // Output the sorted vector.
     std::cout &lt;&lt; "The sorted values are: \n     ";
     for (Vector::iterator i = v.begin (); i != v.end (); ++i)
         std::cout &lt;&lt; *i &lt;&lt; ", ";

     std::cout &lt;&lt; std::endl &lt;&lt; std::endl;

     return 0;
 }


 Program Output:
 The unsorted values are:
      37, 12, 2, -5, 14, 1, 0, -1, 14, 32,

 The sorted values are:
      -5, -1, 0, 1, 2, 12, 14, 14, 32, 37,
 </PRE></UL>
 <UL><PRE></PRE></UL>
 <A NAME="sec7"><H3>See Also</H3></A>
 <P><A HREF="algorithms.html">Algorithms</A></P>
 <A NAME="sec8"><H3>Standards Conformance</H3></A>
 <P><I>ISO/IEC 14882:1998 -- International Standard for Information Systems -- Programming Language C++, Section 25.3.2</I></P>

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	<H2>nth_element()</H2>
	<P><B>Library:</B>  <A HREF="2-9.html">Algorithms</A></P>

	<PRE><HR><B><I>Function</I></B><HR></PRE>

	<UL>
	<LI><A HREF="#sec1">Local Index</A></LI>
	<LI><A HREF="#sec2">Summary</A></LI>
	<LI><A HREF="#sec3">Synopsis</A></LI>
	<LI><A HREF="#sec4">Description</A></LI>
	<LI><A HREF="#sec5">Complexity</A></LI>
	<LI><A HREF="#sec6">Example</A></LI>
	<LI><A HREF="#sec7">See Also</A></LI>
	<LI><A HREF="#sec8">Standards Conformance</A></LI>
	</UL>
	<A NAME="sec1"><H3>Local Index</H3></A>
	No Entries
	<A NAME="sec2"><H3>Summary</H3></A>
	<P>An algorithm that rearranges a collection so that all elements lower in sorted order than the <SAMP>nth</SAMP> element come before it, and all elements higher in sorted order than the <SAMP>nth</SAMP> element come after it</P>
	<A NAME="sec3"><H3>Synopsis</H3></A>

	<PRE>#include <algorithm>

	namespace std {
	template <class RandomAccessIterator>
	void nth_element(RandomAccessIterator start,
	RandomAccessIterator nth,
	RandomAccessIterator finish);

	template <class RandomAccessIterator, class Compare>
	void nth_element(RandomAccessIterator start,
	RandomAccessIterator nth,
	RandomAccessIterator finish,
	Compare comp);
	}
	</PRE>
	<A NAME="sec4"><H3>Description</H3></A>
	<P>The <SAMP>nth_element()</SAMP> algorithm rearranges a collection according to either <SAMP>operator<()</SAMP> or the function object <SAMP>comp</SAMP>. After the algorithm is applied, the follwoing hold:</P>
	<UL>
	<LI><P CLASS="LIST">The element that would be in the <SAMP>nth</SAMP> position if the sequence were completely sorted is in the <SAMP>nth</SAMP> position</P></LI>
	<LI><P CLASS="LIST">All elements prior to the <SAMP>nth</SAMP> position would also precede that position in an ordered sequence</P></LI>
	<LI><P CLASS="LIST">All elements following the <SAMP>nth</SAMP> position would also follow that position in an ordered sequence</P></LI>
	</UL>
	<P>That is, for any iterator <SAMP>i</SAMP> in the range <SAMP>[start, nth)</SAMP> and any iterator <SAMP>j</SAMP> in the range <SAMP>[nth, finish)</SAMP>, it holds that <SAMP>!(i > j)</SAMP> or <SAMP>comp(i, j) == false</SAMP>. </P>
	<P>Note that the elements that precede or follow the <SAMP>nth</SAMP> position are not necessarily sorted relative to each other. The <SAMP>nth_element()</SAMP> algorithm does<I> not </I>sort the entire collection.</P>
	<A NAME="sec5"><H3>Complexity</H3></A>
	<P>The algorithm is linear, on average, where <SAMP>N</SAMP> is the size of the range <SAMP>[start, finish)</SAMP>.</P>
	<A NAME="sec6"><H3>Example</H3></A>

	<UL><PRE>//
	// nthelem.cpp
	//

	#include <algorithm> // for swap
	#include <vector> // for vector
	#include <iostream> // for cout, endl



	template<class RandomAccessIterator>
	void quik_sort (RandomAccessIterator start, RandomAccessIterator end)
	{
	size_t dist = end - start;

	// Stop condition for recursion.
	if (dist > 2) {
	// Use nth_element to do all the work for quik_sort.
	std::nth_element (start, start + (dist / 2), end);

	// Recursive calls to each remaining unsorted portion.
	quik_sort (start, start + (dist / 2 - 1));
	quik_sort (start + (dist / 2 + 1), end);
	}

	if (2 == dist && (end - 1) < start)
	std::swap (start, end);
	}


	int main ()
	{
	typedef std::vector<int, std::allocator<int> > Vector;

	// Initialize a vector using an array of integers.
	Vector::value_type arr[] = { 37, 12, 2, -5, 14,
	1, 0, -1, 14, 32 };

	Vector v (arr + 0, arr + sizeof arr / sizeof *arr);

	// Print the initial vector.
	std::cout << "The unsorted values are: \n ";

	for (Vector::iterator i = v.begin (); i != v.end (); ++i)
	std::cout << *i << ", ";

	std::cout << "\n\n";

	// Use the new sort algorithm.
	quik_sort (v.begin (), v.end ());

	// Output the sorted vector.
	std::cout << "The sorted values are: \n ";
	for (Vector::iterator i = v.begin (); i != v.end (); ++i)
	std::cout << *i << ", ";

	std::cout << std::endl << std::endl;

	return 0;
	}


	Program Output:
	The unsorted values are:
	37, 12, 2, -5, 14, 1, 0, -1, 14, 32,

	The sorted values are:
	-5, -1, 0, 1, 2, 12, 14, 14, 32, 37,
	</PRE></UL>
	<UL><PRE></PRE></UL>
	<A NAME="sec7"><H3>See Also</H3></A>
	<P><A HREF="algorithms.html">Algorithms</A></P>
	<A NAME="sec8"><H3>Standards Conformance</H3></A>
	<P><I>ISO/IEC 14882:1998 -- International Standard for Information Systems -- Programming Language C++, Section 25.3.2</I></P>

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