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<Head>
<Title>next_permutation</Title>
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<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>
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<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 are
ordered by <tt><A href="lexicographical_compare.html">lexicographical_compare</A></tt>, there is an unambiguous
definition of which permutation is lexicographically next. If such
a 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 is
lexicographically 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 define
whether one element is less than another. The first version
compares objects using <tt>operator<</tt>, and the second compares objects
using 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 nonstandard
backward-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 known
deterministic 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 each
other, then there are exactly <tt>N!</tt> permutations. If some elements are
the same as each other, though, then there are fewer. There are, for
example, 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, by
definition, 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>
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