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It is provided "as is" without express or implied warranty. -- --><Head><Title>next_permutation</Title><!-- Generated by htmldoc --></HEAD><BODY TEXT="#000000" LINK="#006600" ALINK="#003300" VLINK="#7C7F87" BGCOLOR="#FFFFFF"><A HREF="/"><IMG SRC="/images/common/sgilogo_small.gif" ALT="SGI Logo" WIDTH="80" HEIGHT="72" BORDER="0"></A><P><!--end header--><BR Clear><H1>next_permutation</H1><Table CellPadding=0 CellSpacing=0 width=100%><TR><TD Align=left><Img src = "algorithms.gif" Alt="" WIDTH = "194" HEIGHT = "38" ></TD><TD Align=right><Img src = "function.gif" Alt="" WIDTH = "194" HEIGHT = "38" ></TD></TR><TR><TD Align=left VAlign=top><b>Category</b>: algorithms</TD><TD Align=right VAlign=top><b>Component type</b>: function</TD></TR></Table><h3>Prototype</h3><tt>Next_permutation</tt> is an overloaded name; there are actually two <tt>next_permutation</tt>functions.<pre>template <class <A href="BidirectionalIterator.html">BidirectionalIterator</A>>bool next_permutation(BidirectionalIterator first, BidirectionalIterator last);template <class <A href="BidirectionalIterator.html">BidirectionalIterator</A>, class <A href="StrictWeakOrdering.html">StrictWeakOrdering</A>>bool next_permutation(BidirectionalIterator first, BidirectionalIterator last, <A href="StrictWeakOrdering.html">StrictWeakOrdering</A> comp);</pre> <h3>Description</h3><tt>Next_permutation</tt> transforms the range of elements <tt>[first, last)</tt>into the lexicographically next greater permutation of the elements.There is a finite number of distinct permutations (at most<tt>N!</tt> <A href="#1">[1]</A>, where <tt>N</tt> is <tt>last - first</tt>), so, if the permutations areordered by <tt><A href="lexicographical_compare.html">lexicographical_compare</A></tt>, there is an unambiguousdefinition of which permutation is lexicographically next. If sucha permutation exists, <tt>next_permutation</tt> transforms <tt>[first, last)</tt>into that permutation and returns <tt>true</tt>. Otherwise it transforms<tt>[first, last)</tt> into the lexicographically smallest permutation <A href="#2">[2]</A>and returns <tt>false</tt>. <P>The postcondition is that the new permutation of elements islexicographically greater than the old (as determined by<tt><A href="lexicographical_compare.html">lexicographical_compare</A></tt>) if and only if the return value is<tt>true</tt>.<P>The two versions of <tt>next_permutation</tt> differ in how they definewhether one element is less than another. The first version compares objects using <tt>operator<</tt>, and the second compares objectsusing a <A href="functors.html">function object</A> <tt>comp</tt>.<h3>Definition</h3>Defined in the standard header <A href="algorithm">algorithm</A>, and in the nonstandardbackward-compatibility header <A href="algo.h">algo.h</A>.<h3>Requirements on types</h3>For the first version, the one that takes two arguments:<UL><LI><tt>BidirectionalIterator</tt> is a model of <A href="BidirectionalIterator.html">Bidirectional Iterator</A>.<LI><tt>BidirectionalIterator</tt> is mutable.<LI><tt>BidirectionalIterator</tt>'s value type is <A href="LessThanComparable.html">LessThan Comparable</A>.<LI>The ordering relation on <tt>BidirectionalIterator</tt>'s value type is a <i>strict weak ordering</i>, as defined in the <A href="LessThanComparable.html">LessThan Comparable</A> requirements.</UL>For the second version, the one that takes three arguments:<UL><LI><tt>BidirectionalIterator</tt> is a model of <A href="BidirectionalIterator.html">Bidirectional Iterator</A>.<LI><tt>BidirectionalIterator</tt> is mutable.<LI><tt>StrictWeakOrdering</tt> is a model of <A href="StrictWeakOrdering.html">Strict Weak Ordering</A>.<LI><tt>BidirectionalIterator</tt>'s value type is convertible to <tt>StrictWeakOrdering</tt>'s argument type.</UL><h3>Preconditions</h3><UL><LI><tt>[first, last)</tt> is a valid range.</UL><h3>Complexity</h3>Linear. At most <tt>(last - first) / 2</tt> swaps.<h3>Example</h3>This example uses <tt>next_permutation</tt> to implement the worst knowndeterministic sorting algorithm. Most sorting algorithms are <tt>O(N log(N))</tt>, and even bubble sort is only <tt>O(N^2)</tt>. This algorithm is actually <tt>O(N!)</tt>.<pre>template <class BidirectionalIterator> void snail_sort(BidirectionalIterator first, BidirectionalIterator last){ while (next_permutation(first, last)) {}}int main(){ int A[] = {8, 3, 6, 1, 2, 5, 7, 4}; const int N = sizeof(A) / sizeof(int); snail_sort(A, A+N); <A href="copy.html">copy</A>(A, A+N, <A href="ostream_iterator.html">ostream_iterator</A><int>(cout, "\n"));}</pre><h3>Notes</h3><P><A name="1">[1]</A>If all of the elements in <tt>[first, last)</tt> are distinct from eachother, then there are exactly <tt>N!</tt> permutations. If some elements arethe same as each other, though, then there are fewer. There are, forexample, only three (<tt>3!/2!</tt>) permutations of the elements <tt>1 1 2</tt>.<P><A name="2">[2]</A>Note that the lexicographically smallest permutation is, bydefinition, sorted in nondecreasing order.<h3>See also</h3><tt><A href="prev_permutation.html">prev_permutation</A></tt>, <tt><A href="lexicographical_compare.html">lexicographical_compare</A></tt>, <A href="LessThanComparable.html">LessThan Comparable</A>, <A href="StrictWeakOrdering.html">Strict Weak Ordering</A>, <tt><A href="sort.html">sort</A></tt><!-- start footer --><!-- Footer Begins --><STYLE TYPE="text/css"><!--TD.footer, TD.footer A{ font-family: Arial, helvetica, sans-serif; font-size: 8pt;}A.home {font-family: Arial, helvetica, sans-serif;}--></STYLE><P><A CLASS="home" HREF="index.html">STL Home</A><P><TABLE WIDTH="600" CELLPADDING="0" CELLPADDING="0" BORDER="0"> <TR> <TD ALIGN="RIGHT" CLASS="footer"><A HREF="/company_info/terms.html" TARGET="_top">terms of use</A> | <A HREF="/company_info/privacy.html" TARGET="_top">privacy policy</A></TD> <TD ALIGN="CENTER" CLASS="footer"> | </TD> <TD ALIGN="LEFT" CLASS="footer"><A HREF="/cgi-bin/feedback/" TARGET="_top">contact us</A></TD> </TR><TR> <TD ALIGN="RIGHT" CLASS="footer">Copyright © 1993-2003 Silicon Graphics, Inc. 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