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| <H2>14.4 Binary Search</H2> |
| <A NAME="idx356"><!></A> |
| <P>The C++ Standard Library provides a number of different variations on binary search algorithms. All perform only approximately <SAMP>log N</SAMP> comparisons, where <SAMP>N</SAMP> is the number of elements in the range described by the arguments. The algorithms work best with random access <B><I><A HREF="../stdlibref/iterator.html">iterator</A></I></B>s, such as those generated by <B><I><A HREF="../stdlibref/vector.html">vector</A></I></B>s or <B><I><A HREF="../stdlibref/deque.html">deque</A></I></B>s. In this case they perform approximately <SAMP>log N</SAMP> operations in total. However, these algorithms also work with non-random access <B><I>iterator</I></B>s, such as those generated by <B><I><A HREF="../stdlibref/list.html">list</A></I></B>s, in which case they perform a linear number of steps. Although possible, it is not worthwhile to perform a binary search on a <B><I><A HREF="../stdlibref/set.html">set</A></I></B> or <B><I><A HREF="../stdlibref/multiset.html">multiset</A></I></B> data structure, since those container classes provide their own search methods, which are more efficient.</P> |
| <A NAME="idx357"><!></A> |
| <P>The generic algorithm <SAMP>std::binary_search()</SAMP> returns <SAMP>true</SAMP> if the sequence contains a value that is equivalent to the argument. Recall that to be equivalent means that both <SAMP>Compare(value, arg)</SAMP> and <SAMP>Compare(arg, value)</SAMP> are <SAMP>false</SAMP>. The algorithm is declared as follows:</P> |
| |
| <UL><PRE> |
| namespace std { |
| bool binary_search(ForwardIterator first, ForwardIterator last, |
| const T& value [, Compare ] ); |
| } |
| </PRE></UL> |
| <P>In other situations it is important to know the position of the matching value. This information is returned by a collection of algorithms, defined as follows:</P> |
| |
| <UL><PRE> |
| namespace std { |
| ForwardIterator lower_bound(ForwardIterator first, |
| ForwardIterator last, const T& value [, Compare ] ); |
| |
| ForwardIterator upper_bound (ForwardIterator first, |
| ForwardIterator last, const T& value [, Compare ] ); |
| |
| pair<ForwardIterator, ForwardIterator> equal_range |
| (ForwardIterator first, ForwardIterator last, |
| const T& value [, Compare ] ); |
| } |
| </PRE></UL> |
| <A NAME="idx358"><!></A> |
| <P>The algorithm <SAMP>std::lower_bound()</SAMP> returns, as an <B><I><A HREF="../stdlibref/iterator.html">iterator</A></I></B>, the first position into which the argument could be inserted without violating the ordering, whereas the algorithm <SAMP>std::upper_bound()</SAMP> finds the last such position. These match only when the element is not currently found in the sequence. Both can be executed together in the algorithm <SAMP>std::equal_range()</SAMP>, which returns a pair of <B><I>iterator</I></B>s.</P> |
| <P>Our example program shows these functions being used with a <B><I><A HREF="../stdlibref/vector.html">vector</A></I></B> of random integers.</P> |
| |
| <A NAME="idx359"><!></A> |
| <UL><PRE> |
| void binary_search_example() |
| // illustrates the use of the binary search algorithm |
| // see alg7.cpp for complete source code |
| { |
| // make an ordered vector of 15 random integers |
| std::vector<int> aVec(15); |
| std::generate(aVec.begin(), aVec.end(), randomValue); |
| std::sort(aVec.begin(), aVec.end()); |
| |
| // see if it contains an eleven |
| if (binary_search(aVec.begin(), aVec.end(), 11)) |
| std::cout << "contains an 11" << std::endl; |
| else |
| std::cout << "does not contain an 11" << std::endl; |
| |
| // insert an 11 and a 14 |
| std::vector<int>::iterator where; |
| where = std::lower_bound(aVec.begin(), aVec.end(), 11); |
| aVec.insert(where, 11); |
| |
| where = std::upper_bound(aVec.begin(), aVec.end(), 14); |
| aVec.insert(where, 14); |
| } |
| </PRE></UL> |
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