`<algorithm>`

```
adjacent_find
· binary_search
· copy
· copy_backward
· count
· count_if
· equal
· equal_range
· fill
· fill_n
· find
· find_end
· find_first_of
· find_if
· for_each
· generate
· generate_n
· includes
· inplace_merge
· iter_swap
· lexicographical_compare
· lower_bound
· make_heap
· max
· max_element
· merge
· min
· min_element
· mismatch
· next_permutation
· nth_element
· partial_sort
· partial_sort_copy
· partition
· pop_heap
· prev_permutation
· push_heap
· random_shuffle
· remove
· remove_copy
· remove_copy_if
· remove_if
· replace
· replace_copy
· replace_copy_if
· replace_if
· reverse
· reverse_copy
· rotate
· rotate_copy
· search
· search_n
· set_difference
· set_intersection
· set_symmetric_difference
· set_union
· sort
· sort_heap
· stable_partition
· stable_sort
· swap
· swap_ranges
· transform
· unique
· unique_copy
· upper_bound
```

Include the STL
standard header ** <algorithm>**
to define numerous template functions that perform
useful algorithms. The descriptions that follow
make extensive use of common template parameter names
(or prefixes) to indicate the least powerful category
of iterator permitted as an actual argument type:

-- to indicate an output iterator`OutIt`

-- to indicate an input iterator`InIt`

-- to indicate a forward iterator`FwdIt`

-- to indicate a bidirectional iterator`BidIt`

-- to indicate a random-access iterator`RanIt`

The descriptions of these templates employ a number of conventions common to all algorithms.

namespace std { template<class InIt, class Fn1> Fn1for_each(InIt first, InIt last, Fn1 func); template<class InIt, class Ty> InItfind(InIt first, InIt last, const Ty& val); template<class InIt, class Pr> InItfind_if(InIt first, InIt last, Pr pred); template<class FwdIt1, class FwdIt2> FwdIt1find_end(FwdIt1 first1, FwdIt1 last1, FwdIt2 first2, FwdIt2 last2); template<class FwdIt1, class FwdIt2, class Pr> FwdIt1find_end(FwdIt1 first1, FwdIt1 last1, FwdIt2 first2, FwdIt2 last2, Pr pred); template<class FwdIt1, class FwdIt2> FwdIt1find_first_of(FwdIt1 first1, FwdIt1 last1, FwdIt2 first2, FwdIt2 last2); template<class FwdIt1, class FwdIt2, class Pr> FwdIt1find_first_of(FwdIt1 first1, FwdIt1 last1, FwdIt2 first2, FwdIt2 last2, Pr pred); template<class FwdIt> FwdItadjacent_find(FwdIt first, FwdIt last); template<class FwdIt, class Pr> FwdItadjacent_find(FwdIt first, FwdIt last, Pr pred); template<class InIt, class Ty, class Dist> typename iterator_traits<InIt>::difference_typecount(InIt first, InIt last, const Ty& val); template<class InIt, class Pr, class Dist> typename iterator_traits<InIt>::difference_typecount_if(InIt first, InIt last, Pr pred); template<class InIt1, class InIt2> pair<InIt1, InIt2>mismatch(InIt1 first1, InIt1 last1, InIt2 first2); template<class InIt1, class InIt2, class Pr> pair<InIt1, InIt2>mismatch(InIt1 first1, InIt1 last1, InIt2 first2, Pr pred); template<class InIt1, class InIt2> boolequal(InIt1 first1, InIt1 last1, InIt2 first2); template<class InIt1, class InIt2, class Pr> boolequal(InIt1 first1, InIt1 last1, InIt2 first2, Pr pred); template<class FwdIt1, class FwdIt2> FwdIt1search(FwdIt1 first1, FwdIt1 last1, FwdIt2 first2, FwdIt2 last2); template<class FwdIt1, class FwdIt2, class Pr> FwdIt1search(FwdIt1 first1, FwdIt1 last1, FwdIt2 first2, FwdIt2 last2, Pr pred); template<class FwdIt1, class Diff2, class Ty> FwdIt1search_n(FwdIt1 first1, FwdIt1 last1, Diff2 count, const Ty& val); template<class FwdIt1, class Diff2, class Ty, class Pr> FwdIt1search_n(FwdIt1 first1, FwdIt1 last1, Diff2 count, const Ty& val, Pr pred); template<class InIt, class OutIt> OutItcopy(InIt first, InIt last, OutIt dest); template<class BidIt1, class BidIt2> BidIt2copy_backward(BidIt1 first, BidIt1 last, BidIt2 dest); template<class Ty> voidswap(Ty& left, Ty& right); template<class FwdIt1, class FwdIt2> FwdIt2swap_ranges(FwdIt1 first1, FwdIt1 last1, FwdIt2 last2); template<class FwdIt1, class FwdIt2> voiditer_swap(FwdIt1 left, FwdIt2 right); template<class InIt, class OutIt, class Fn1> OutIttransform(InIt first, InIt last, OutIt dest, Fn1 func); template<class InIt1, class InIt2, class OutIt, class Fn2> OutIttransform(InIt1 first1, InIt1 last1, InIt2 first2, OutIt dest, Fn2 func);

template<class FwdIt, class Ty> voidreplace(FwdIt first, FwdIt last, const Ty& oldval, const Ty& newval); template<class FwdIt, class Pr, class Ty> voidreplace_if(FwdIt first, FwdIt last, Pr pred, const Ty& val); template<class InIt, class OutIt, class Ty> OutItreplace_copy(InIt first, InIt last, OutIt dest, const Ty& oldval, const Ty& newval); template<class InIt, class OutIt, class Pr, class Ty> OutItreplace_copy_if(InIt first, InIt last, OutIt dest, Pr pred, const Ty& val); template<class FwdIt, class Ty> voidfill(FwdIt first, FwdIt last, const Ty& val); template<class OutIt, class Diff, class Ty> voidfill_n(OutIt first, Diff count, const Ty& val); template<class FwdIt, class Fn0> voidgenerate(FwdIt first, FwdIt last, Fn0 func); template<class OutIt, class Diff, class Fn0> voidgenerate_n(OutIt first, Diff count, Fn0 func); template<class FwdIt, class Ty> FwdItremove(FwdIt first, FwdIt last, const Ty& val); template<class FwdIt, class Pr> FwdItremove_if(FwdIt first, FwdIt last, Pr pred); template<class InIt, class OutIt, class Ty> OutItremove_copy(InIt first, InIt last, OutIt dest, const Ty& val); template<class InIt, class OutIt, class Pr> OutItremove_copy_if(InIt first, InIt last, OutIt dest, Pr pred); template<class FwdIt> FwdItunique(FwdIt first, FwdIt last); template<class FwdIt, class Pr> FwdItunique(FwdIt first, FwdIt last, Pr pred); template<class InIt, class OutIt> OutItunique_copy(InIt first, InIt last, OutIt dest); template<class InIt, class OutIt, class Pr> OutItunique_copy(InIt first, InIt last, OutIt dest, Pr pred); template<class BidIt> voidreverse(BidIt first, BidIt last); template<class BidIt, class OutIt> OutItreverse_copy(BidIt first, BidIt last, OutIt dest); template<class FwdIt> voidrotate(FwdIt first, FwdIt mid, FwdIt last); template<class FwdIt, class OutIt> OutItrotate_copy(FwdIt first, FwdIt mid, FwdIt last, OutIt dest); template<class RanIt> voidrandom_shuffle(RanIt first, RanIt last); template<class RanIt, class Fn1> voidrandom_shuffle(RanIt first, RanIt last, Fn1& func); template<class BidIt, class Pr> BidItpartition(BidIt first, BidIt last, Pr pred); template<class BidIt, class Pr> BidItstable_partition(BidIt first, BidIt last, Pr pred); template<class RanIt> voidsort(RanIt first, RanIt last); template<class RanIt, class Pr> voidsort(RanIt first, RanIt last, Pr pred); template<class BidIt> voidstable_sort(BidIt first, BidIt last); template<class BidIt, class Pr> voidstable_sort(BidIt first, BidIt last, Pr pred); template<class RanIt> voidpartial_sort(RanIt first, RanIt mid, RanIt last); template<class RanIt, class Pr> voidpartial_sort(RanIt first, RanIt mid, RanIt last, Pr pred); template<class InIt, class RanIt> RanItpartial_sort_copy(InIt first1, InIt last1, RanIt first2, RanIt last2); template<class InIt, class RanIt, class Pr> RanItpartial_sort_copy(InIt first1, InIt last1, RanIt first2, RanIt last2, Pr pred);

template<class RanIt> voidnth_element(RanIt first, RanIt nth, RanIt last); template<class RanIt, class Pr> voidnth_element(RanIt first, RanIt nth, RanIt last, Pr pred); template<class FwdIt, class Ty> FwdItlower_bound(FwdIt first, FwdIt last, const Ty& val); template<class FwdIt, class Ty, class Pr> FwdItlower_bound(FwdIt first, FwdIt last, const Ty& val, Pr pred); template<class FwdIt, class Ty> FwdItupper_bound(FwdIt first, FwdIt last, const Ty& val); template<class FwdIt, class Ty, class Pr> FwdItupper_bound(FwdIt first, FwdIt last, const Ty& val, Pr pred); template<class FwdIt, class Ty> pair<FwdIt, FwdIt>equal_range(FwdIt first, FwdIt last, const Ty& val); template<class FwdIt, class Ty, class Pr> pair<FwdIt, FwdIt>equal_range(FwdIt first, FwdIt last, const Ty& val, Pr pred); template<class FwdIt, class Ty> boolbinary_search(FwdIt first, FwdIt last, const Ty& val); template<class FwdIt, class Ty, class Pr> boolbinary_search(FwdIt first, FwdIt last, const Ty& val, Pr pred); template<class InIt1, class InIt2, class OutIt> OutItmerge(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest); template<class InIt1, class InIt2, class OutIt, class Pr> OutItmerge(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest, Pr pred); template<class BidIt> voidinplace_merge(BidIt first, BidIt mid, BidIt last); template<class BidIt, class Pr> voidinplace_merge(BidIt first, BidIt mid, BidIt last, Pr pred); template<class InIt1, class InIt2> boolincludes(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2); template<class InIt1, class InIt2, class Pr> boolincludes(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, Pr pred); template<class InIt1, class InIt2, class OutIt> OutItset_union(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest); template<class InIt1, class InIt2, class OutIt, class Pr> OutItset_union(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest, Pr pred); template<class InIt1, class InIt2, class OutIt> OutItset_intersection(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest); template<class InIt1, class InIt2, class OutIt, class Pr> OutItset_intersection(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest, Pr pred); template<class InIt1, class InIt2, class OutIt> OutItset_difference(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest); template<class InIt1, class InIt2, class OutIt, class Pr> OutItset_difference(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest, Pr pred); template<class InIt1, class InIt2, class OutIt> OutItset_symmetric_difference(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest); template<class InIt1, class InIt2, class OutIt, class Pr> OutItset_symmetric_difference(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest, Pr pred); template<class RanIt> voidpush_heap(RanIt first, RanIt last); template<class RanIt, class Pr> voidpush_heap(RanIt first, RanIt last, Pr pred); template<class RanIt> voidpop_heap(RanIt first, RanIt last); template<class RanIt, class Pr> voidpop_heap(RanIt first, RanIt last, Pr pred); template<class RanIt> voidmake_heap(RanIt first, RanIt last); template<class RanIt, class Pr> voidmake_heap(RanIt first, RanIt last, Pr pred); template<class RanIt> voidsort_heap(RanIt first, RanIt last); template<class RanIt, class Pr> voidsort_heap(RanIt first, RanIt last, Pr pred); template<class Ty> const Ty&max(const Ty& left, const Ty& right); template<class Ty, class Pr> const Ty&max(const Ty& left, const Ty& right, Pr pred); template<class Ty> const Ty&min(const Ty& left, const Ty& right); template<class Ty, class Pr> const Ty&min(const Ty& left, const Ty& right, Pr pred); template<class FwdIt> FwdItmax_element(FwdIt first, FwdIt last); template<class FwdIt, class Pr> FwdItmax_element(FwdIt first, FwdIt last, Pr pred); template<class FwdIt> FwdItmin_element(FwdIt first, FwdIt last); template<class FwdIt, class Pr> FwdItmin_element(FwdIt first, FwdIt last, Pr pred); template<class InIt1, class InIt2> boollexicographical_compare(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2); template<class InIt1, class InIt2, class Pr> boollexicographical_compare(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, Pr pred); template<class BidIt> boolnext_permutation(BidIt first, BidIt last); template<class BidIt, class Pr> boolnext_permutation(BidIt first, BidIt last, Pr pred); template<class BidIt> boolprev_permutation(BidIt first, BidIt last); template<class BidIt, class Pr> boolprev_permutation(BidIt first, BidIt last, Pr pred); } // namespace std

`adjacent_find`

template<class FwdIt> FwdItadjacent_find(FwdIt first, FwdIt last); template<class FwdIt, class Pr> FwdItadjacent_find(FwdIt first, FwdIt last, Pr pred);

The first template function determines the lowest `N`

in the range `[0, last - first)`

for which
`N + 1 < last - first`

and the predicate
`*(first + N) == *(first + N + 1)`

is true.
Here, `operator==`

must perform a
pairwise comparison
between its operands.
It then returns `first + N`

.
If no such value exists, the function returns `last`

.
If the sequence contains fewer than two elements, the function
never evaluates the predicate. Otherwise, if it returns
`last`

, it evaluates the predicate exactly
`last - first - 1`

times. Otherwise,
it evaluates the predicate exactly `N + 1`

times.

The second template function behaves the same, except that
the predicate is `pred(*(first + N), *(first + N + 1))`

.

`binary_search`

template<class FwdIt, class Ty> boolbinary_search(FwdIt first, FwdIt last, const Ty& val); template<class FwdIt, class Ty, class Pr> boolbinary_search(FwdIt first, FwdIt last, const Ty& val, Pr pred);

The first template function determines whether
a value of `N`

exists
in the range `[0, last - first)`

for which
`*(first + N)`

has
equivalent ordering
to `val`

, where the elements designated by iterators
in the range `[first, last)`

form a sequence
ordered by `operator<`

.
If so, the function returns true.
If no such value exists, it returns false.

Yhe function evaluates the ordering predicate `X < Y`

at most
`ceil(log(last - first)) + 2`

times.

The second template function behaves the same, except that
it replaces `operator<(X, Y)`

with
`pred(X, Y)`

.

`copy`

template<class InIt, class OutIt> OutItcopy(InIt first, InIt last, OutIt dest);

The template function evaluates `*(dest + N) = *(first + N))`

once for each `N`

in the range `[0, last - first)`

,
for strictly increasing values of `N`

beginning with
the lowest value. It then returns `dest + N`

.
If `dest`

and `first`

designate regions of storage,
`dest`

must not be in the range `[first, last)`

.

`copy_backward`

template<class BidIt1, class BidIt2> BidIt2copy_backward(BidIt1 first, BidIt1 last, BidIt2 dest);

The template function evaluates
`*(dest - N - 1) = *(last - N - 1))`

once for
each `N`

in the range `[0, last - first)`

,
for strictly increasing values of `N`

beginning with
the lowest value. It then returns `dest - (last - first)`

.
If `dest`

and `first`

designate regions of storage,
`dest`

must not be in the range `[first, last)`

.

`count`

template<class InIt, class Ty> typename iterator_traits<InIt>::difference_typecount(InIt first, InIt last, const Ty& val);

The template function sets a count `count`

to zero. It then
executes `++count`

for
each `N`

in the range `[0, last - first)`

for which the predicate `*(first + N) == val`

is true.
Here, `operator==`

must perform a
pairwise comparison
between its operands.
The function returns `count`

.
It evaluates the predicate exactly `last - first`

times.

`count_if`

template<class InIt, class Pr, class Dist> typename iterator_traits<InIt>::difference_typecount_if(InIt first, InIt last, Pr pred);

The template function sets a count `count`

to zero. It then
executes `++count`

for
each `N`

in the range `[0, last - first)`

for which the predicate `pred(*(first + N))`

is true.
The function returns `count`

.
It evaluates the predicate exactly `last - first`

times.

`equal`

template<class InIt1, class InIt2> boolequal(InIt1 first1, InIt1 last1, InIt2 first2); template<class InIt1, class InIt2, class Pr> boolequal(InIt1 first1, InIt1 last1, InIt2 first2, Pr pred);

The first template function returns true only if, for
each `N`

in the range `[0, last1 - first1)`

,
the predicate `*(first1 + N) == *(first2 + N)`

is true.
Here, `operator==`

must perform a
pairwise comparison
between its operands.
The function evaluates the predicate at most once
for each `N`

.

The second template function behaves the same, except that
the predicate is `pred(*(first1 + N), *(first2 + N))`

.

`equal_range`

template<class FwdIt, class Ty> pair<FwdIt, FwdIt>equal_range(FwdIt first, FwdIt last, const Ty& val); template<class FwdIt, class Ty, class Pr> pair<FwdIt, FwdIt>equal_range(FwdIt first, FwdIt last, const Ty& val, Pr pred);

The first template function effectively returns
```
pair(
lower_bound(first, last, val),
upper_bound(first, last, val))
```

,
where the elements designated by iterators
in the range `[first, last)`

form a sequence
ordered by `operator<`

.
Thus, the function determines the largest range of positions
over which `val`

can be inserted in the sequence
and still preserve its ordering.

The function evaluates the ordering predicate `X < Y`

at most
`ceil(2 * log(last - first)) + 2`

.

The second template function behaves the same, except that
it replaces `operator<(X, Y)`

with
`pred(X, Y)`

.

`fill`

template<class FwdIt, class Ty> voidfill(FwdIt first, FwdIt last, const Ty& val);

The template function evaluates `*(first + N) = val`

once for
each `N`

in the range `[0, last - first)`

.

`fill_n`

template<class OutIt, class Diff, class Ty> voidfill_n(OutIt first, Diff count, const Ty& val);

The template function evaluates `*(first + N) = val`

once for
each `N`

in the range `[0, count)`

.

`find`

template<class InIt, class Ty> InItfind(InIt first, InIt last, const Ty& val);

The template function determines the lowest value of `N`

in the range `[0, last - first)`

for which the predicate
`*(first + N) == val`

is true.
Here, `operator==`

must perform a
pairwise comparison
between its operands.
It then returns `first + N`

.
If no such value exists, the function returns `last`

.
It evaluates the predicate at most once
for each `N`

.

`find_end`

template<class FwdIt1, class FwdIt2> FwdIt1find_end(FwdIt1 first1, FwdIt1 last1, FwdIt2 first2, FwdIt2 last2); template<class FwdIt1, class FwdIt2, class Pr> FwdIt1find_end(FwdIt1 first1, FwdIt1 last1, FwdIt2 first2, FwdIt2 last2, Pr pred);

The first template function determines the highest value of
`N`

in the range ```
[0,
last1 - first1 - (last2 - first2))
```

such that for each `M`

in the range
`[0, last2 - first2)`

,
the predicate `*(first1 + N + M) == *(first2 + N + M)`

is true.
Here, `operator==`

must perform a
pairwise comparison
between its operands.
It then returns `first1 + N`

.
If no such value exists, the function returns `last1`

.
It evaluates the predicate at most ```
(last2 - first2) *
(last1 - first1 - (last2 - first2) + 1)
```

times.

The second template function behaves the same, except that
the predicate is `pred(*(first1 + N + M), *(first2 + N + M))`

.

`find_first_of`

template<class FwdIt1, class FwdIt2> FwdIt1find_first_of(FwdIt1 first1, FwdIt1 last1, FwdIt2 first2, FwdIt2 last2); template<class FwdIt1, class FwdIt2, class Pr> FwdIt1find_first_of(FwdIt1 first1, FwdIt1 last1, FwdIt2 first2, FwdIt2 last2, Pr pred);

The first template function determines the lowest value of
`N`

in the range `[0, last1 - first1)`

such that
for some `M`

in the range `[0, last2 - first2)`

,
the predicate `*(first1 + N) == *(first2 + M)`

is true.
Here, `operator==`

must perform a
pairwise comparison
between its operands.
It then returns `first1 + N`

.
If no such value exists, the function returns `last1`

.
It evaluates the predicate at most
`(last1 - first1) * (last2 - first2)`

times.

The second template function behaves the same, except that
the predicate is `pred(*(first1 + N), *(first2 + M))`

.

`find_if`

template<class InIt, class Pr> InItfind_if(InIt first, InIt last, Pr pred);

The template function determines the lowest value of `N`

in the range `[0, last - first)`

for which the predicate
`pred(*(first + N))`

is true.
It then returns `first + N`

.
If no such value exists, the function returns `last`

.
It evaluates the predicate at most once
for each `N`

.

`for_each`

template<class InIt, class Fn1> Fn1for_each(InIt first, InIt last, Fn1 func);

The template function evaluates `func(*(first + N))`

once for
each `N`

in the range `[0, last - first)`

.
It then returns `func`

.

`generate`

template<class FwdIt, class Fn0> voidgenerate(FwdIt first, FwdIt last, Fn0 func);

The template function evaluates `*(first + N) = func()`

once for
each `N`

in the range `[0, last - first)`

.

`generate_n`

template<class OutIt, class Pr, class Fn0> voidgenerate_n(OutIt first, Diff count, Fn0 func);

The template function evaluates `*(first + N) = func()`

once for
each `N`

in the range `[0, count)`

.

`includes`

template<class InIt1, class InIt2> boolincludes(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2); template<class InIt1, class InIt2, class Pr> boolincludes(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, Pr pred);

The first template function determines whether
a value of `N`

exists
in the range `[0, last2 - first2)`

such that,
for each `M`

in the range `[0, last1 - first1)`

,
`*(first1 + M)`

and `*(first2 + N)`

do not have
equivalent ordering,
where the elements designated by iterators
in the ranges `[first1, last1)`

and `[first2, last2)`

each form a sequence
ordered by `operator<`

.
If so, the function returns false.
If no such value exists, it returns true.
Thus, the function determines whether the ordered sequence
designated by iterators in the range
`[first2, last2)`

all have equivalent ordering with some
element designated by iterators in the range
`[first1, last1)`

.

The function evaluates the predicate at most
`2 * ((last1 - first1) + (last2 - first2)) - 1`

times.

The second template function behaves the same, except that
it replaces `operator<(X, Y)`

with
`pred(X, Y)`

.

`inplace_merge`

template<class BidIt> voidinplace_merge(BidIt first, BidIt mid, BidIt last); template<class BidIt, class Pr> voidinplace_merge(BidIt first, BidIt mid, BidIt last, Pr pred);

The first template function reorders the
sequences designated by iterators in the ranges `[first, mid)`

and `[mid, last)`

, each
ordered by `operator<`

,
to form a merged sequence of length `last - first`

beginning at `first`

also ordered by `operator<`

.
The merge occurs without altering the relative order of
elements within either original sequence. Moreover, for any two elements
from different original sequences that have
equivalent ordering,
the element from the ordered range `[first, mid)`

precedes the other.

The function evaluates the ordering predicate
`X < Y`

at most
`ceil((last - first) * log(last - first))`

times.
(Given enough temporary storage, it can evaluate the predicate at most
`(last - first) - 1`

times.)

`operator<(X, Y)`

with
`pred(X, Y)`

.

`iter_swap`

template<class FwdIt1, class FwdIt2> voiditer_swap(FwdIt1 left, FwdIt2 right);

The template function leaves the value originally stored in
`*right`

subsequently stored in `*left`

,
and the value originally stored in `*left`

subsequently stored in `*right`

.

`lexicographical_compare`

template<class InIt1, class InIt2> boollexicographical_compare(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2); template<class InIt1, class InIt2, class Pr> boollexicographical_compare(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, Pr pred);

The first template function determines `K`

,
the number of elements to compare as the smaller of
`last1 - first1`

and `last2 - first2`

.
It then determines the lowest value of `N`

in the range `[0, K)`

for which
`*(first1 + N)`

and `*(first2 + N)`

do not have
equivalent ordering.
If no such value exists, the function returns true only if
`K < (last2 - first2)`

. Otherwise, it returns
true only if `*(first1 + N) < *(first2 + N)`

.
Thus, the function returns true only if the sequence designated
by iterators in the range `[first1, last1)`

is
lexicographically less than the other sequence.

The function evaluates the ordering predicate
`X < Y`

at most `2 * K`

times.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`lower_bound`

template<class FwdIt, class Ty> FwdItlower_bound(FwdIt first, FwdIt last, const Ty& val); template<class FwdIt, class Ty, class Pr> FwdItlower_bound(FwdIt first, FwdIt last, const Ty& val, Pr pred);

The first template function determines the highest value of `N`

in the range `(0, last - first]`

such that,
for each `M`

in the range `[0, N)`

the predicate `*(first + M) < val`

is true,
where the elements designated by iterators
in the range `[first, last)`

form a sequence
ordered by `operator<`

.
It then returns `first + N`

.
Thus, the function determines the lowest position
before which `val`

can be inserted in the sequence
and still preserve its ordering.

The function evaluates the ordering predicate `X < Y`

at most
`ceil(log(last - first)) + 1`

times.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`make_heap`

template<class RanIt> voidmake_heap(RanIt first, RanIt last); template<class RanIt, class Pr> voidmake_heap(RanIt first, RanIt last, Pr pred);

The first template function reorders the sequence
designated by iterators in the
range `[first, last)`

to form a heap
ordered by `operator<`

.

The function evaluates the ordering predicate
`X < Y`

at most
`3 * (last - first)`

times.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`max`

template<class Ty> const Ty&max(const Ty& left, const Ty& right); template<class Ty, class Pr> const Ty&max(const Ty& left, const Ty& right, Pr pred);

The first template function returns `right`

if
`left < right`

. Otherwise it returns `left`

.
`Ty`

need supply only a single-argument constructor and a
destructor.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`max_element`

template<class FwdIt> FwdItmax_element(FwdIt first, FwdIt last); template<class FwdIt, class Pr> FwdItmax_element(FwdIt first, FwdIt last, Pr pred);

The first template function determines the lowest value of `N`

in the range `[0, last - first)`

such that,
for each `M`

in the range `[0, last - first)`

the predicate `*(first + N) < *(first + M)`

is false.
It then returns `first + N`

.
Thus, the function determines the lowest position
that contains the largest value in the sequence.

The function evaluates the ordering predicate
`X < Y`

exactly
`max((last - first) - 1, 0)`

times.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`merge`

template<class InIt1, class InIt2, class OutIt> OutItmerge(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest); template<class InIt1, class InIt2, class OutIt, class Pr> OutItmerge(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest, Pr pred);

The first template function determines `K`

,
the number of elements to copy as ```
(last1 - first1) +
(last2 - first2)
```

. It then alternately
copies two sequences, designated by iterators
in the ranges `[first1, last1)`

and `[first2, last2)`

and each
ordered by `operator<`

,
to form a merged sequence of length `K`

beginning
at `dest`

, also ordered by `operator<`

.
The function then returns `dest + K`

.

The merge occurs without altering the relative order of
elements within either sequence. Moreover, for any two elements
from different sequences that have
equivalent ordering,
the element from the ordered range `[first1, last1)`

precedes the other. Thus, the function merges two ordered
sequences to form another ordered sequence.

If `dest`

and `first1`

designate regions of storage,
the range `[dest, dest + K)`

must not
overlap the range `[first1, last1)`

.
If `dest`

and `first2`

designate regions of storage,
the range `[dest, dest + K)`

must not
overlap the range `[first2, last2)`

.
The function evaluates the ordering predicate `X < Y`

at most
`K - 1`

times.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`min`

template<class Ty> const Ty&min(const Ty& left, const Ty& right); template<class Ty, class Pr> const Ty&min(const Ty& left, const Ty& right, Pr pred);

The first template function returns `right`

if
`right < left`

. Otherwise it returns `left`

.
`Ty`

need supply only a single-argument constructor and a
destructor.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`min_element`

template<class FwdIt> FwdItmin_element(FwdIt first, FwdIt last); template<class FwdIt, class Pr> FwdItmin_element(FwdIt first, FwdIt last, Pr pred);

The first template function determines the lowest value of `N`

in the range `[0, last - first)`

such that,
for each `M`

in the range `[0, last - first)`

the predicate `*(first + M) < *(first + N)`

is false.
It then returns `first + N`

.
Thus, the function determines the lowest position
that contains the smallest value in the sequence.

The function evaluates the ordering predicate
`X < Y`

exactly
`max((last - first) - 1, 0)`

times.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`mismatch`

template<class InIt1, class InIt2> pair<InIt1, InIt2>mismatch(InIt1 first1, InIt1 last1, InIt2 first2); template<class InIt1, class InIt2, class Pr> pair<InIt1, InIt2>mismatch(InIt1 first1, InIt1 last1, InIt2 first2, Pr pred);

The first template function determines the lowest value of
`N`

in the range `[0, last1 - first1)`

for which the predicate
`!(*(first1 + N) == *(first2 + N))`

is true.
Here, `operator==`

must perform a
pairwise comparison
between its operands.
It then returns
`pair(first1 + N, first2 + N)`

.
If no such value exists, N has the value `last1 - first1`

.
The function evaluates the predicate at most once
for each `N`

.

The second template function behaves the same, except that
the predicate is `pred(*(first1 + N), *(first2 + N))`

.

`next_permutation`

template<class BidIt> boolnext_permutation(BidIt first, BidIt last); template<class BidIt, class Pr> boolnext_permutation(BidIt first, BidIt last, Pr pred);

The first template function determines a repeating
sequence of permutations, whose initial permutation occurs when
the sequence designated by iterators
in the range `[first, last)`

is
ordered by `operator<`

.
(The elements are sorted in *ascending* order.)
It then reorders the elements in the sequence, by evaluating
`swap(X, Y)`

for the elements
`X`

and `Y`

zero or more times,
to form the next permutation. The function returns true only if the resulting
sequence is not the initial permutation. Otherwise, the resultant
sequence is the one next larger lexicographically than the original
sequence.

The function evaluates `swap(X, Y)`

at most `(last - first) / 2`

.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`nth_element`

template<class RanIt> voidnth_element(RanIt first, RanIt nth, RanIt last); template<class RanIt, class Pr> voidnth_element(RanIt first, RanIt nth, RanIt last, Pr pred);

The first template function reorders the sequence
designated by iterators in the
range `[first, last)`

such that for each `N`

in the range `[0, nth - first)`

and for each `M`

in the range `[nth - first, last - first)`

the predicate
`!(*(first + M) < *(first + N))`

is true. Moreover, for `N`

equal to
`nth - first`

and for each `M`

in the range `(nth - first, last - first)`

the predicate
`!(*(first + M) < *(first + N))`

is true. Thus, if `nth != last`

the element `*nth`

is in its proper position if elements of the entire sequence
were sorted in *ascending* order,
ordered by `operator<`

.
Any elements before this one belong before it in the sort sequence,
and any elements after it belong after it.

The function evaluates the ordering predicate `X < Y`

a number of times proportional to
`last - first`

, on average.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`partial_sort`

template<class RanIt> voidpartial_sort(RanIt first, RanIt mid, RanIt last); template<class RanIt, class Pr> voidpartial_sort(RanIt first, RanIt mid, RanIt last, Pr pred);

The first template function reorders the sequence
designated by iterators in the
range `[first, last)`

such that for each `N`

in the range `[0, mid - first)`

and for each `M`

in the range `(N, last - first)`

the predicate
`!(*(first + M) < *(first + N))`

is true. Thus, the smallest `mid - first`

elements of the entire sequence are sorted in *ascending* order,
ordered by `operator<`

.
The order of the remaining elements is otherwise unspecified.

The function evaluates
the ordering predicate `X < Y`

a number of times proportional to at most
`ceil((last - first) * log(mid - first))`

.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`partial_sort_copy`

template<class InIt, class RanIt> RanItpartial_sort_copy(InIt first1, InIt last1, RanIt first2, RanIt last2); template<class InIt, class RanIt, class Pr> RanItpartial_sort_copy(InIt first1, InIt last1, RanIt first2, RanIt last2, Pr pred);

The first template function determines `K`

,
the number of elements to copy as the smaller of
`last1 - first1`

and `last2 - first2`

. It then
copies and reorders `K`

elements of the sequence
designated by iterators in the
range `[first1, last1)`

such that
the `K`

elements copied to `first2`

are
ordered by `operator<`

.
Moreover, for each `N`

in the range `[0, K)`

and for each `M`

in the range `(0, last1 - first1)`

corresponding
to an uncopied element, the predicate
`!(*(first2 + M) < *(first1 + N))`

is true. Thus, the smallest `K`

elements of the entire sequence designated by iterators
in the range `[first1, last1)`

are copied and sorted in *ascending* order to the range
`[first2, first2 + K)`

.

The function evaluates
the ordering predicate `X < Y`

a number of times proportional to at most
`ceil((last - first) * log(K))`

.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`partition`

template<class BidIt, class Pr> BidItpartition(BidIt first, BidIt last, Pr pred);

The template function reorders the sequence designated by iterators in the
range `[first, last)`

and determines the value
`K`

such that for each `N`

in the range
`[0, K)`

the predicate `pred(*(first + N))`

is true, and for each `N`

in the range
`[K, last - first)`

the predicate `pred(*(first + N))`

is false. The function then returns `first + K`

.

The predicate must not alter its operand.
The function evaluates `pred(*(first + N))`

exactly
`last - first`

times, and swaps at most
`(last - first) / 2`

pairs of elements.

`pop_heap`

template<class RanIt> voidpop_heap(RanIt first, RanIt last); template<class RanIt, class Pr> voidpop_heap(RanIt first, RanIt last, Pr pred);

The first template function reorders the sequence
designated by iterators in the
range `[first, last)`

to form a new heap,
ordered by `operator<`

and
designated by iterators in the range
`[first, last - 1)`

, leaving the original
element at `*first`

subsequently at `*(last - 1)`

.
The original sequence must designate an existing heap,
also ordered by `operator<`

. Thus, ```
first !=
last
```

must be true and `*(last - 1)`

is the
element to remove from (pop off) the heap.

The function evaluates the ordering predicate
`X < Y`

at most
`ceil(2 * log(last - first))`

times.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`prev_permutation`

template<class BidIt> boolprev_permutation(BidIt first, BidIt last); template<class BidIt, class Pr> boolprev_permutation(BidIt first, BidIt last, Pr pred);

The first template function determines a repeating
sequence of permutations, whose initial permutation occurs when
the sequence designated by iterators
in the range `[first, last)`

is the *reverse* of one
ordered by `operator<`

.
(The elements are sorted in *descending* order.)
It then reorders the elements in the sequence, by evaluating
`swap(X, Y)`

for the elements
`X`

and `Y`

zero or more times,
to form the previous permutation.
The function returns true only if the resulting
sequence is not the initial permutation. Otherwise, the resultant
sequence is the one next smaller lexicographically than the original
sequence.

The function evaluates `swap(X, Y)`

at most `(last - first) / 2`

.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`push_heap`

template<class RanIt> voidpush_heap(RanIt first, RanIt last); template<class RanIt, class Pr> voidpush_heap(RanIt first, RanIt last, Pr pred);

The first template function reorders the sequence
designated by iterators in the
range `[first, last)`

to form a new heap
ordered by `operator<`

.
Iterators in the range
`[first, last - 1)`

must designate an existing heap,
also ordered by `operator<`

. Thus, ```
first !=
last
```

must be true and `*(last - 1)`

is the
element to add to (push on) the heap.

The function evaluates the ordering predicate
`X < Y`

at most
`ceil(log(last - first))`

times.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`random_shuffle`

template<class RanIt> voidrandom_shuffle(RanIt first, RanIt last); template<class RanIt, class Fn1> voidrandom_shuffle(RanIt first, RanIt last, Fn1& func);

The first template function evaluates
`swap(*(first + N), *(first + M))`

once for
each `N`

in the range `[1, last - first)`

,
where `M`

is a value from some uniform random distribution
over the range `[0, N]`

.
Thus, the function randomly shuffles
the order of elements in the sequence.

The function evaluates `M`

and calls `swap`

exactly `last - first - 1`

times.

The second template function behaves the same, except that
`M`

is `(Diff)func((Diff)N)`

, where
`Diff`

is the type
```
iterator_traits<RanIt>::
difference_type
```

.

`remove`

template<class FwdIt, class Ty> FwdItremove(FwdIt first, FwdIt last, const Ty& val);

The template function effectively assigns `first`

to
`X`

, then executes the statement:

if (!(*(first + N) == val)) *X++ = *(first + N);

once for each `N`

in the range
`[0, last - first)`

.
Here, `operator==`

must perform a
pairwise comparison
between its operands.
It then returns `X`

.
Thus, the function removes from the resulting sequence all elements for
which the predicate `*(first + N) == val`

is true,
without altering the relative order of remaining elements,
and returns the iterator value that designates the end of the
resulting sequence.

`remove_copy`

template<class InIt, class OutIt, class Ty> OutItremove_copy(InIt first, InIt last, OutIt dest, const Ty& val);

The template function effectively executes the statement:

if (!(*(first + N) == val)) *dest++ = *(first + N);

once for each `N`

in the range
`[0, last - first)`

.
Here, `operator==`

must perform a
pairwise comparison
between its operands.
It then returns `dest`

.
Thus, the function removes from the resulting sequence all elements for
which the predicate `*(first + N) == val`

is true,
without altering the relative order of remaining elements,
and returns the iterator value that designates the end of the
resulting sequence.

If `dest`

and `first`

designate regions of storage,
the range `[dest, dest + (last - first))`

must not
overlap the range `[first, last)`

.

`remove_copy_if`

template<class InIt, class OutIt, class Pr> OutItremove_copy_if(InIt first, InIt last, OutIt dest, Pr pred);

The template function effectively executes the statement:

if (!pred(*(first + N))) *dest++ = *(first + N);

once for each `N`

in the range
`[0, last - first)`

. It then returns `dest`

.
Thus, the function removes from the resulting sequence all elements for
which the predicate `pred(*(first + N))`

is true,
without altering the relative order of remaining elements,
and returns the iterator value that designates the end of the
resulting sequence.

If `dest`

and `first`

designate regions of storage,
the range `[dest, dest + (last - first))`

must not
overlap the range `[first, last)`

.

`remove_if`

template<class FwdIt, class Pr> FwdItremove_if(FwdIt first, FwdIt last, Pr pred);

The template function effectively assigns `first`

to
`X`

, then executes the statement:

if (!pred(*(first + N))) *X++ = *(first + N);

once for each `N`

in the range
`[0, last - first)`

. It then returns `X`

.
Thus, the function removes from the resulting sequence all elements for
which the predicate `pred(*(first + N))`

is true,
without altering the relative order of remaining elements,
and returns the iterator value that designates the end of the
resulting sequence.

`replace`

template<class FwdIt, class Ty> voidreplace(FwdIt first, FwdIt last, const Ty& oldval, const Ty& newval);

The template function executes the statement:

if (*(first + N) == oldval) *(first + N) = newval;

once for each `N`

in the range
`[0, last - first)`

.
Here, `operator==`

must perform a
pairwise comparison
between its operands.

`replace_copy`

template<class InIt, class OutIt, class Ty> OutItreplace_copy(InIt first, InIt last, OutIt dest, const Ty& oldval, const Ty& newval);

The template function executes the statement:

if (*(first + N) == oldval) *(dest + N) = newval; else *(dest + N) = *(first + N)

once for each `N`

in the range
`[0, last - first)`

.
Here, `operator==`

must perform a
pairwise comparison
between its operands. The function returns the iterator value that
designates the end of the resulting sequence.

If `dest`

and `first`

designate regions of storage,
the range `[dest, dest + (last - first))`

must not
overlap the range `[first, last)`

.

`replace_copy_if`

template<class InIt, class OutIt, class Pr, class Ty> OutItreplace_copy_if(InIt first, InIt last, OutIt dest, Pr pred, const Ty& val);

The template function executes the statement:

if (pred(*(first + N))) *(dest + N) = val; else *(dest + N) = *(first + N)

once for each `N`

in the range
`[0, last - first)`

.

If `dest`

and `first`

designate regions of storage,
the range `[dest, dest + (last - first))`

must not
overlap the range `[first, last)`

. The function returns the iterator
value that designates the end of the resulting sequence.

`replace_if`

template<class FwdIt, class Pr, class Ty> voidreplace_if(FwdIt first, FwdIt last, Pr pred, const Ty& val);

The template function executes the statement:

if (pred(*(first + N))) *(first + N) = val;

once for each `N`

in the range
`[0, last - first)`

.

`reverse`

template<class BidIt> voidreverse(BidIt first, BidIt last);

The template function evaluates
`swap(*(first + N), *(last - 1 - N)`

once for
each `N`

in the range `[0, (last - first) / 2)`

.
Thus, the function reverses the order of elements in the sequence.

`reverse_copy`

template<class BidIt, class OutIt> OutItreverse_copy(BidIt first, BidIt last, OutIt dest);

The template function evaluates
`*(dest + N) = *(last - 1 - N)`

once for
each `N`

in the range `[0, last - first)`

.
It then returns `dest + (last - first)`

.
Thus, the function reverses the order of elements in the sequence
that it copies.

`dest`

and `first`

designate regions of storage,
the range `[dest, dest + (last - first))`

must not
overlap the range `[first, last)`

.

`rotate`

template<class FwdIt> voidrotate(FwdIt first, FwdIt mid, FwdIt last);

The template function leaves the value originally stored in
`*(first + (N + (mid - first)) % (last - first))`

subsequently stored in `*(first + N)`

for
each `N`

in the range `[0, last - first)`

.
Thus, if a ``left'' shift by one element leaves the element
originally stored in `*(first + (N + 1) % (last - first))`

subsequently stored in `*(first + N)`

, then the function
can be said to rotate the sequence either left by
`mid - first`

elements or right by `last - mid`

elements. Both `[first, mid)`

and `[mid, last)`

must be valid ranges. The function swaps at most `last - first`

pairs of elements.

`rotate_copy`

template<class FwdIt, class OutIt> OutItrotate_copy(FwdIt first, FwdIt mid, FwdIt last, OutIt dest);

The template function evaluates
`*(dest + N) = *(first + (N + (mid - first)) % (last - first))`

once for each `N`

in the range `[0, last - first)`

.
Thus, if a ``left'' shift by one element leaves the element
originally stored in `*(first + (N + 1) % (last - first))`

subsequently stored in `*(first + N)`

, then the function
can be said to rotate the sequence either left by
`mid - first`

elements or right by `last - mid`

elements as it copies.
Both `[first, mid)`

and `[mid, last)`

must be valid ranges. The function returns the iterator value
that designates the end of the resulting sequence.

`dest`

and `first`

designate regions of storage,
the range `[dest, dest + (last - first))`

must not
overlap the range `[first, last)`

.

`search`

template<class FwdIt1, class FwdIt2> FwdIt1search(FwdIt1 first1, FwdIt1 last1, FwdIt2 first2, FwdIt2 last2); template<class FwdIt1, class FwdIt2, class Pr> FwdIt1search(FwdIt1 first1, FwdIt1 last1, FwdIt2 first2, FwdIt2 last2, Pr pred);

The first template function determines the lowest value of
`N`

in the range ```
[0,
(last1 - first1) - (last2 - first2))
```

such that
for each `M`

in the range `[0, last2 - first2)`

,
the predicate `*(first1 + N + M) == *(first2 + M)`

is true.
Here, `operator==`

must perform a
pairwise comparison
between its operands.
It then returns `first1 + N`

.
If no such value exists, the function returns `last1`

.
It evaluates the predicate at most ```
(last2 - first2) *
(last1 - first1)
```

times.

The second template function behaves the same, except that
the predicate is `pred(*(first1 + N + M), *(first2 + M))`

.

`search_n`

template<class FwdIt1, class Diff2, class Ty> FwdIt1search_n(FwdIt1 first1, FwdIt1 last1, Diff2 count, const Ty& val); template<class FwdIt1, class Diff2, class Ty, class Pr> FwdIt1search_n(FwdIt1 first1, FwdIt1 last1, Diff2 count, const Ty& val, Pr pred);

The first template function determines the lowest value of
`N`

in the range ```
[0,
(last - first) - count)
```

such that
for each `M`

in the range `[0, count)`

,
the predicate `*(first + N + M) == val`

is true.
Here, `operator==`

must perform a
pairwise comparison
between its operands.
It then returns `first + N`

.
If no such value exists, the function returns `last`

.
It evaluates the predicate at most `count * (last - first)`

times.

The second template function behaves the same, except that
the predicate is `pred(*(first + N + M), val)`

.

`set_difference`

template<class InIt1, class InIt2, class OutIt> OutItset_difference(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest); template<class InIt1, class InIt2, class OutIt, class Pr> OutItset_difference(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest, Pr pred);

The first template function alternately
copies values from two sequences designated by iterators in the ranges
`[first1, last1)`

and `[first2, last2)`

, both
ordered by `operator<`

,
to form a merged sequence of length `K`

beginning
at `dest`

, also ordered by `operator<`

.
The function then returns `dest + K`

.

The merge occurs without altering the relative order of
elements within either sequence. Moreover, for two elements
from different sequences that have
equivalent ordering
that would otherwise be copied to adjacent elements,
the function copies only
the element from the ordered range `[first1, last1)`

and skips the other. An element from one sequence that has
equivalent ordering with no element from the other sequence
is copied from the ordered range `[first1, last1)`

and skipped from the other.
Thus, the function merges two ordered
sequences to form another ordered sequence that is effectively
the difference of two sets.

If `dest`

and `first1`

designate regions of storage,
the range `[dest, dest + K)`

must not
overlap the range `[first1, last1)`

.
If `dest`

and `first2`

designate regions of storage,
the range `[dest, dest + K)`

must not
overlap the range `[first2, last2)`

.
The function evaluates the ordering predicate `X < Y`

at most
`2 * ((last1 - first1) + (last2 - first2)) - 1`

times.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`set_intersection`

template<class InIt1, class InIt2, class OutIt> OutItset_intersection(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest); template<class InIt1, class InIt2, class OutIt, class Pr> OutItset_intersection(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest, Pr pred);

The first template function alternately
copies values from two sequences designated by iterators in the ranges
`[first1, last1)`

and `[first2, last2)`

, both
ordered by `operator<`

,
to form a merged sequence of length `K`

beginning
at `dest`

, also ordered by `operator<`

.
The function then returns `dest + K`

.

The merge occurs without altering the relative order of
elements within either sequence. Moreover, for two elements
from different sequences that have
equivalent ordering
that would otherwise be copied to adjacent elements,
the function copies only
the element from the ordered range `[first1, last1)`

and skips the other. An element from one sequence that has
equivalent ordering with no element from the other sequence
is also skipped.
Thus, the function merges two ordered
sequences to form another ordered sequence that is effectively
the intersection of two sets.

If `dest`

and `first1`

designate regions of storage,
the range `[dest, dest + K)`

must not
overlap the range `[first1, last1)`

.
If `dest`

and `first2`

designate regions of storage,
the range `[dest, dest + K)`

must not
overlap the range `[first2, last2)`

.
The function evaluates the ordering predicate `X < Y`

at most
`2 * ((last1 - first1) + (last2 - first2)) - 1`

times.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`set_symmetric_difference`

template<class InIt1, class InIt2, class OutIt> OutItset_symmetric_difference(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest); template<class InIt1, class InIt2, class OutIt, class Pr> OutItset_symmetric_difference(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest, Pr pred);

The first template function alternately
copies values from two sequences designated by iterators in the ranges
`[first1, last1)`

and `[first2, last2)`

, both
ordered by `operator<`

,
to form a merged sequence of length `K`

beginning
at `dest`

, also ordered by `operator<`

.
The function then returns `dest + K`

.

The merge occurs without altering the relative order of elements within either sequence. Moreover, for two elements from different sequences that have equivalent ordering that would otherwise be copied to adjacent elements, the function copies neither element. An element from one sequence that has equivalent ordering with no element from the other sequence is copied. Thus, the function merges two ordered sequences to form another ordered sequence that is effectively the symmetric difference of two sets.

If `dest`

and `first1`

designate regions of storage,
the range `[dest, dest + K)`

must not
overlap the range `[first1, last1)`

.
If `dest`

and `first2`

designate regions of storage,
the range `[dest, dest + K)`

must not
overlap the range `[first2, last2)`

.
The function evaluates the ordering predicate `X < Y`

at most
`2 * ((last1 - first1) + (last2 - first2)) - 1`

times.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`set_union`

template<class InIt1, class InIt2, class OutIt> OutItset_union(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest); template<class InIt1, class InIt2, class OutIt, class Pr> OutItset_union(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest, Pr pred);

`[first1, last1)`

and `[first2, last2)`

, both
ordered by `operator<`

,
to form a merged sequence of length `K`

beginning
at `dest`

, also ordered by `operator<`

.
The function then returns `dest + K`

.

The merge occurs without altering the relative order of
elements within either sequence. Moreover, for two elements
from different sequences that have
equivalent ordering
that would otherwise be copied to adjacent elements,
the function copies only
the element from the ordered range `[first1, last1)`

and skips the other.
Thus, the function merges two ordered
sequences to form another ordered sequence that is effectively
the union of two sets.

`dest`

and `first1`

designate regions of storage,
the range `[dest, dest + K)`

must not
overlap the range `[first1, last1)`

.
If `dest`

and `first2`

designate regions of storage,
the range `[dest, dest + K)`

must not
overlap the range `[first2, last2)`

.
The function evaluates the ordering predicate `X < Y`

at most
`2 * ((last1 - first1) + (last2 - first2)) - 1`

times.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`sort`

template<class RanIt> voidsort(RanIt first, RanIt last); template<class RanIt, class Pr> voidsort(RanIt first, RanIt last, Pr pred);

The first template function reorders the sequence
designated by iterators in the
range `[first, last)`

to form a sequence
ordered by `operator<`

.
Thus, the elements are sorted in *ascending* order.

The function evaluates
the ordering predicate `X < Y`

a number of times proportional to at most
`ceil((last - first) * log(last - first))`

.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`sort_heap`

template<class RanIt> voidsort_heap(RanIt first, RanIt last); template<class RanIt, class Pr> voidsort_heap(RanIt first, RanIt last, Pr pred);

The first template function reorders the sequence
designated by iterators in the
range `[first, last)`

to form a sequence
that is
ordered by `operator<`

.
The original sequence must designate a heap, also
ordered by `operator<`

.
Thus, the elements are sorted in *ascending* order.

The function evaluates the ordering predicate
`X < Y`

at most
`ceil((last - first) * log(last - first))`

times.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`stable_partition`

template<class BidIt, class Pr> BidItstable_partition(BidIt first, BidIt last, Pr pred);

The template function reorders the sequence designated by iterators in the
range `[first, last)`

and determines the value
`K`

such that for each `N`

in the range
`[0, K)`

the predicate `pred(*(first + N))`

is true, and for each `N`

in the range
`[K, last - first)`

the predicate `pred(*(first + N))`

is false. It does so without altering the relative order of either
the elements designated by indexes
in the range `[0, K)`

or
the elements designated by indexes
in the range `[K, last - first)`

.
The function then returns `first + K`

.

The predicate must not alter its operand.
The function evaluates `pred(*(first + N))`

exactly
`last - first`

times, and swaps at most
`ceil((last - first) * log(last - first))`

pairs of elements. (Given enough temporary storage, it can
replace the swaps with at most
`2 * (last - first)`

assignments.)

`stable_sort`

template<class BidIt> voidstable_sort(BidIt first, BidIt last); template<class BidIt, class Pr> voidstable_sort(BidIt first, BidIt last, Pr pred);

The first template function reorders the sequence
designated by iterators in the
range `[first, last)`

to form a sequence
ordered by `operator<`

.
It does so without altering the relative order of
elements that have
equivalent ordering.
Thus, the elements are sorted in *ascending* order.

The function evaluates
the ordering predicate `X < Y`

a number of times proportional to at most
`ceil((last - first) * (log(last - first))^2)`

.
(Given enough temporary storage, it can evaluate the predicate
a number of times proportional to at most
`ceil((last - first) * log(last - first))`

.

`operator<(X, Y)`

with
`pred(X, Y)`

.

`swap`

template<class Ty> voidswap(Ty& left, Ty& right);

The template function leaves the value originally stored in
`right`

subsequently stored in `left`

,
and the value originally stored in `left`

subsequently stored in `right`

.

`swap_ranges`

template<class FwdIt1, class FwdIt2> FwdIt2swap_ranges(FwdIt1 first1, FwdIt1 last1, FwdIt2 first2);

The template function evaluates
`swap(*(first1 + N), *(first2 + N))`

once for
each `N`

in the range `[0, last1 - first1)`

.
It then returns `first2 + (last1 - first1)`

.
If `first2`

and `first1`

designate regions of storage,
the range `[first2, first2 + (last1 - first1))`

must not
overlap the range `[first1, last1)`

.

`transform`

template<class InIt, class OutIt, class Fn1> OutIttransform(InIt first, InIt last, OutIt dest, Fn1 func); template<class InIt1, class InIt2, class OutIt, class Fn2> OutIttransform(InIt1 first1, InIt1 last1, InIt2 first2, OutIt dest, Fn2 func);

The first template function evaluates
`*(dest + N) = func(*(first + N))`

once for each `N`

in the range `[0, last - first)`

.
It then returns `dest + (last - first)`

. The call
`func(*(first + N))`

must not alter
`*(first + N)`

.

The second template function evaluates
`*(dest + N) = func(*(first1 + N), *(first2 + N))`

once for each `N`

in the range `[0, last1 - first1)`

.
It then returns `dest + (last1 - first1)`

. The call
`func(*(first1 + N), *(first2 + N))`

must not alter
either `*(first1 + N)`

or `*(first2 + N)`

.

`unique`

template<class FwdIt> FwdItunique(FwdIt first, FwdIt last); template<class FwdIt, class Pr> FwdItunique(FwdIt first, FwdIt last, Pr pred);

The first template function effectively assigns `first`

to
`X`

, then executes the statement:

if (!(*X == *(first + N + 1))) *++X = *(first + N + 1);

once for each `N`

in the range
`[1, last - first)`

. It then returns `X`

.
Thus, the function repeatedly removes from the resulting sequence
the second of a pair of elements for
which the predicate `*(first + N) == *(first + N + 1)`

is true,
until only the first of a sequence of elements survives
that satisfies the comparison.
Here, `operator==`

must perform a
pairwise comparison
between its operands.
It does so without altering the relative order of remaining elements,
and returns the iterator value that designates the end of the
resulting sequence. For a non-empty sequence,
the function evaluates the predicate
`last - first - 1`

times.

The second template function behaves the same, except that it executes the statement:

if (!pred(*(first + N), *(first + N + 1))) *++X = *(first + N + 1);

Note that for a sequence designated by the range `[first, last)`

and ordered by `pred`

,
you can remove all but the first of a sequence of elements that have
equivalent ordering by calling
```
unique(first, last,
not2(pred))
```

.

`unique_copy`

template<class InIt, class OutIt> OutItunique_copy(InIt first, InIt last, OutIt dest); template<class InIt, class OutIt, class Pr> OutItunique_copy(InIt first, InIt last, OutIt dest, Pr pred);

The first template function effectively executes the statement:

if (N == 0 || !(*(first + N - 1) == *(first + N))) *dest++ = *(first + N);

once for each `N`

in the range
`[0, last - first)`

. It then returns `dest`

.
Thus, the function repeatedly removes from the resulting sequence
the second of a pair of elements for
which the predicate `*(first + N) == *(first + N - 1)`

is true,
until only the first of a sequence of equal elements survives.
Here, `operator==`

must perform a
pairwise comparison
between its operands.
It does so without altering the relative order of remaining elements,
and returns the iterator value that designates the end of the
copied sequence. For a non-empty sequence,
the function evaluates the predicate
`last - first - 1`

times.

`dest`

and `first`

designate regions of storage,
the range `[dest, dest + (last - first))`

must not
overlap the range `[first, last)`

.

The second template function behaves the same, except that it executes the statement:

if (N == 0 || !pred(*(first + N - 1), *(first + N))) *dest++ = *(first + N);

`upper_bound`

template<class FwdIt, class Ty> FwdItupper_bound(FwdIt first, FwdIt last, const Ty& val); template<class FwdIt, class Ty, class Pr> FwdItupper_bound(FwdIt first, FwdIt last, const Ty& val, Pr pred);

The first template function determines the highest value of `N`

in the range `(0, last - first]`

such that,
for each `M`

in the range `[0, N)`

the predicate `!(val < *(first + M))`

is true,
where the elements designated by iterators
in the range `[first, last)`

form a sequence
ordered by `operator<`

.
It then returns `first + N`

.
Thus, the function determines the highest position
before which `val`

can be inserted in the sequence
and still preserve its ordering.

The function evaluates the ordering predicate `X < Y`

at most
`ceil(log(last - first)) + 1`

times.

`operator<(X, Y)`

with
`pred(X, Y)`

.

See also the
**Table of Contents** and the
**Index**.

*
Copyright © 1992-2006
by P.J. Plauger. Portions derived from work
copyright © 1994
by Hewlett-Packard Company. All rights reserved.*

Last modified: 2013-12-21