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 <H2>binary_search()</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>Algorithm that performs a binary search for a value</P>
 <A NAME="sec3"><H3>Synopsis</H3></A>

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

 namespace std {
   template &lt;class ForwardIterator, class T&gt;
   bool
   binary_search(ForwardIterator start, ForwardIterator finish,
                 const T&amp; value);
   template &lt;class ForwardIterator, class T, class Compare&gt;
   bool
   binary_search(ForwardIterator start, ForwardIterator finish,
                 const T&amp; value, Compare comp);
 }
 </PRE>
 <A NAME="sec4"><H3>Description</H3></A>
 <P>The <SAMP>binary_search()</SAMP> algorithm, like the related algorithms <SAMP><A HREF="equal-range.html">equal_range()</A></SAMP>, <SAMP><A HREF="lower-bound.html">lower_bound()</A></SAMP>, and <SAMP><A HREF="upper-bound.html">upper_bound()</A></SAMP>, performs a binary search on a range of ordered values. All binary search algorithms have two variations. The first variation uses the <SAMP>operator&lt;</SAMP> to perform the comparison, and assumes that the sequence has been sorted using that operator. The second variation allows you to specify a function object of type <SAMP>Compare</SAMP>, which it assumes was the function used to sort the sequence. The function object must be a binary predicate. </P>
 <P>The <SAMP>binary_search()</SAMP> algorithm returns <SAMP>true</SAMP> if a sequence contains an element equivalent to the argument <SAMP>value</SAMP>. The first variation of <SAMP>binary_search()</SAMP> returns <SAMP>true</SAMP> if the sequence contains at least one element that is equal to the search value. The second variation of the <SAMP>binary_search()</SAMP> algorithm returns <SAMP>true</SAMP> if the sequence contains at least one element that satisfies the conditions of the comparison function. Formally, <SAMP>binary_search()</SAMP> returns <SAMP>true</SAMP> if there is an iterator <SAMP>i</SAMP> in the range <SAMP>[start, finish)</SAMP> that satisfies the corresponding conditions:</P>
 <P><SAMP>!(*i &lt; value) &amp;&amp; !(value &lt; *i) </SAMP></P>
 <P>or </P>
 <P><SAMP>comp(*i, value) == false &amp;&amp; comp(value, *i) == false</SAMP></P>
 <A NAME="sec5"><H3>Complexity</H3></A>
 <P><SAMP>binary_search()</SAMP> performs at most <SAMP>log(finish - start) + 2 </SAMP>comparisons.</P>
 <A NAME="sec6"><H3>Example</H3></A>

 <UL><PRE>//
 // b_search.cpp
 //

 #include &lt;algorithm&gt;    // for copy, sort
 #include &lt;deque&gt;        // for deque
 #include &lt;functional&gt;   // for less
 #include &lt;iostream&gt;     // for cout, endl, ostream_iterator


 int main ()
 {
     // Typedefs for convenience.
     typedef std::deque&lt;short, std::allocator&lt;short&gt; &gt; deque;

     typedef std::ostream_iterator&lt;deque::value_type, char,
                            std::char_traits&lt;char&gt; &gt; os_iter;

     const deque::value_type arr[] = {
       0, 1, 2, 2, 3, 4, 2, 2, 6, 7
     };

     // Populate and sort the container.
     deque d (arr + 0, arr + sizeof arr / sizeof *arr);
     std::sort (d.begin (), d.end ());

     // Try binary_search variants.
     bool b1 = std::binary_search (d.begin (), d.end (), 3);
     bool b2 = std::binary_search (d.begin (), d.end (), 11,
                                   std::less&lt;int&gt;());

     // Output results.
     std::cout &lt;&lt; "Container contents: ";
     std::copy (d.begin (), d.end (),
                os_iter (std::cout, " "));

     std::cout &lt;&lt; "\nThe number 3 was "
               &lt;&lt; ("NOT found" + b1 * 4);

     std::cout &lt;&lt; "\nThe number 11 was "
               &lt;&lt; ("NOT found" + b2 * 4) &lt;&lt; std::endl;

     return 0;
 }

 Program Output:
 Container contents: 0 1 2 2 2 2 3 4 6 7
 The number 3 was found
 The number 11 was NOT found
 </PRE></UL>
 <A NAME="sec7"><H3>See Also</H3></A>
 <P><SAMP><A HREF="equal-range.html">equal_range()</A></SAMP>, <SAMP><A HREF="lower-bound.html">lower_bound()</A></SAMP>, <SAMP><A HREF="upper-bound.html">upper_bound()</A></SAMP></P>
 <A NAME="sec8"><H3>Standards Conformance</H3></A>
 <P><I>ISO/IEC 14882:1998 -- International Standard for Information Systems -- Programming Language C++, Section 25.3.3.4</I></P>

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	<H2>binary_search()</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>Algorithm that performs a binary search for a value</P>
	<A NAME="sec3"><H3>Synopsis</H3></A>

	<PRE>#include <algorithm>

	namespace std {
	template <class ForwardIterator, class T>
	bool
	binary_search(ForwardIterator start, ForwardIterator finish,
	const T& value);
	template <class ForwardIterator, class T, class Compare>
	bool
	binary_search(ForwardIterator start, ForwardIterator finish,
	const T& value, Compare comp);
	}
	</PRE>
	<A NAME="sec4"><H3>Description</H3></A>
	<P>The <SAMP>binary_search()</SAMP> algorithm, like the related algorithms <SAMP><A HREF="equal-range.html">equal_range()</A></SAMP>, <SAMP><A HREF="lower-bound.html">lower_bound()</A></SAMP>, and <SAMP><A HREF="upper-bound.html">upper_bound()</A></SAMP>, performs a binary search on a range of ordered values. All binary search algorithms have two variations. The first variation uses the <SAMP>operator<</SAMP> to perform the comparison, and assumes that the sequence has been sorted using that operator. The second variation allows you to specify a function object of type <SAMP>Compare</SAMP>, which it assumes was the function used to sort the sequence. The function object must be a binary predicate. </P>
	<P>The <SAMP>binary_search()</SAMP> algorithm returns <SAMP>true</SAMP> if a sequence contains an element equivalent to the argument <SAMP>value</SAMP>. The first variation of <SAMP>binary_search()</SAMP> returns <SAMP>true</SAMP> if the sequence contains at least one element that is equal to the search value. The second variation of the <SAMP>binary_search()</SAMP> algorithm returns <SAMP>true</SAMP> if the sequence contains at least one element that satisfies the conditions of the comparison function. Formally, <SAMP>binary_search()</SAMP> returns <SAMP>true</SAMP> if there is an iterator <SAMP>i</SAMP> in the range <SAMP>[start, finish)</SAMP> that satisfies the corresponding conditions:</P>
	<P><SAMP>!(i < value) && !(value < i) </SAMP></P>
	<P>or </P>
	<P><SAMP>comp(i, value) == false && comp(value, i) == false</SAMP></P>
	<A NAME="sec5"><H3>Complexity</H3></A>
	<P><SAMP>binary_search()</SAMP> performs at most <SAMP>log(finish - start) + 2 </SAMP>comparisons.</P>
	<A NAME="sec6"><H3>Example</H3></A>

	<UL><PRE>//
	// b_search.cpp
	//

	#include <algorithm> // for copy, sort
	#include <deque> // for deque
	#include <functional> // for less
	#include <iostream> // for cout, endl, ostream_iterator



	int main ()
	{
	// Typedefs for convenience.
	typedef std::deque<short, std::allocator<short> > deque;

	typedef std::ostream_iterator<deque::value_type, char,
	std::char_traits<char> > os_iter;

	const deque::value_type arr[] = {
	0, 1, 2, 2, 3, 4, 2, 2, 6, 7
	};

	// Populate and sort the container.
	deque d (arr + 0, arr + sizeof arr / sizeof *arr);
	std::sort (d.begin (), d.end ());

	// Try binary_search variants.
	bool b1 = std::binary_search (d.begin (), d.end (), 3);
	bool b2 = std::binary_search (d.begin (), d.end (), 11,
	std::less<int>());

	// Output results.
	std::cout << "Container contents: ";
	std::copy (d.begin (), d.end (),
	os_iter (std::cout, " "));

	std::cout << "\nThe number 3 was "
	<< ("NOT found" + b1 * 4);

	std::cout << "\nThe number 11 was "
	<< ("NOT found" + b2 * 4) << std::endl;

	return 0;
	}

	Program Output:
	Container contents: 0 1 2 2 2 2 3 4 6 7
	The number 3 was found
	The number 11 was NOT found
	</PRE></UL>
	<A NAME="sec7"><H3>See Also</H3></A>
	<P><SAMP><A HREF="equal-range.html">equal_range()</A></SAMP>, <SAMP><A HREF="lower-bound.html">lower_bound()</A></SAMP>, <SAMP><A HREF="upper-bound.html">upper_bound()</A></SAMP></P>
	<A NAME="sec8"><H3>Standards Conformance</H3></A>
	<P><I>ISO/IEC 14882:1998 -- International Standard for Information Systems -- Programming Language C++, Section 25.3.3.4</I></P>

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