All of the algorithms
are separated from the particular implementations of data structures and
are parameterized by iterator types.

Because of this, they can work with program-defined data structures,
as long as these data structures have iterator types
satisfying the assumptions on the algorithms.

The entities defined in the std::ranges namespace in this Clause
are not found by argument-dependent name lookup ([basic.lookup.argdep]).

When found by unqualified ([basic.lookup.unqual]) name lookup
for the *postfix-expression* in a function call ([expr.call]),
they inhibit argument-dependent name lookup.

[ Example

: *end example*

]void foo() { using namespace std::ranges; std::vector<int> vec{1,2,3}; find(begin(vec), end(vec), 2); // #1 }

The function call expression at #1 invokes std::ranges::find,
not std::find, despite that
(a) the iterator type returned from begin(vec) and end(vec)
may be associated with namespace std and
(b) std::find is more specialized ([temp.func.order]) than
std::ranges::find since the former requires
its first two parameters to have the same type.

— For purposes of determining the existence of data races,
algorithms shall not modify objects referenced through an iterator argument
unless the specification requires such modification.

Throughout this Clause, where the template parameters are not constrained,
the names of template parameters are used to express type requirements.

- If an algorithm's template parameter is named InputIterator, InputIterator1, or InputIterator2, the template argument shall satisfy the Cpp17InputIterator requirements ([input.iterators]).
- If an algorithm's template parameter is named OutputIterator, OutputIterator1, or OutputIterator2, the template argument shall satisfy the Cpp17OutputIterator requirements ([output.iterators]).
- If an algorithm's template parameter is named ForwardIterator, ForwardIterator1, or ForwardIterator2, the template argument shall satisfy the Cpp17ForwardIterator requirements ([forward.iterators]).
- If an algorithm's template parameter is named BidirectionalIterator, BidirectionalIterator1, or BidirectionalIterator2, the template argument shall satisfy the Cpp17BidirectionalIterator requirements ([bidirectional.iterators]).
- If an algorithm's template parameter is named RandomAccessIterator, RandomAccessIterator1, or RandomAccessIterator2, the template argument shall satisfy the Cpp17RandomAccessIterator requirements ([random.access.iterators]).

If an algorithm's Effects: element specifies
that a value pointed to by any iterator passed as an argument is modified,
then that algorithm has an additional type requirement:
The type of that argument shall satisfy
the requirements of a mutable iterator ([iterator.requirements]).

When not otherwise constrained, the Predicate parameter is used
whenever an algorithm expects a function object ([function.objects]) that,
when applied to the result of dereferencing the corresponding iterator,
returns a value testable as true.

In other words,
if an algorithm takes Predicate pred as its argument and
first as its iterator argument with value type T,
it should work correctly in the construct
pred(*first) contextually converted to bool ([conv]).

The function object pred shall not apply any non-constant function
through the dereferenced iterator.

Given a glvalue u of type (possibly const) T
that designates the same object as *first,
pred(u) shall be a valid expression
that is equal to pred(*first).

When not otherwise constrained, the BinaryPredicate parameter is used
whenever an algorithm expects a function object that when applied
to the result of dereferencing two corresponding iterators or
to dereferencing an iterator and type T
when T is part of the signature
returns a value testable as true.

In other words,
if an algorithm takes BinaryPredicate binary_pred as its argument and
first1 and first2 as its iterator arguments
with respective value types T1 and T2,
it should work correctly in the construct
binary_pred(*first1, *first2) contextually converted to bool ([conv]).

Unless otherwise specified,
BinaryPredicate always takes the first iterator's value_type
as its first argument, that is, in those cases when T value
is part of the signature, it should work correctly in the construct
binary_pred(*first1, value) contextually converted to bool ([conv]).

binary_pred shall not apply any non-constant function
through the dereferenced iterators.

Given a glvalue u of type (possibly const) T1
that designates the same object as *first1, and
a glvalue v of type (possibly const) T2
that designates the same object as *first2,
binary_pred(u, *first2),
binary_pred(*first1, v), and
binary_pred(u, v)
shall each be a valid expression that is equal to
binary_pred(*first1, *first2), and
binary_pred(u, value)
shall be a valid expression that is equal to
binary_pred(*first1, value).

The parameters
UnaryOperation,
BinaryOperation,
BinaryOperation1,
and BinaryOperation2
are used
whenever an algorithm expects a function object ([function.objects]).

[ Note

: *end note*

]Unless otherwise specified, algorithms that take function objects as arguments
are permitted to copy those function objects freely.

Programmers for whom object identity is important should consider
using a wrapper class that points to a noncopied implementation object
such as reference_wrapper<T> ([refwrap]), or some equivalent solution.

— When the description of an algorithm gives an expression such as
*first == value for a condition, the expression
shall evaluate to either true or false in boolean contexts.

In the description of the algorithms, operator +
is used for some of the iterator categories
for which it does not have to be defined.

In these cases the semantics of a + n are the same as those of

auto tmp = a; for (; n < 0; ++n) --tmp; for (; n > 0; --n) ++tmp; return tmp;

Similarly, operator - is used
for some combinations of iterators and sentinel types
for which it does not have to be defined.

If [a, b) denotes a range,
the semantics of b - a in these cases are the same as those of

iter_difference_t<remove_reference_t<decltype(a)>> n = 0; for (auto tmp = a; tmp != b; ++tmp) ++n; return n;and if [b, a) denotes a range, the same as those of

iter_difference_t<remove_reference_t<decltype(b)>> n = 0; for (auto tmp = b; tmp != a; ++tmp) --n; return n;

In the description of algorithm return values,
a sentinel value s denoting the end of a range [i, s)
is sometimes returned where an iterator is expected.

In these cases,
the semantics are as if the sentinel is converted into an iterator using
ranges::next(i, s).

Overloads of algorithms that take Range arguments ([range.range])
behave as if they are implemented by calling ranges::begin and
ranges::end on the Range(s) and
dispatching to the overload in namespace ranges
that takes separate iterator and sentinel arguments.

The number and order of deducible template parameters for algorithm declarations
are unspecified, except where explicitly stated otherwise.

The class templates
binary_transform_result,
for_each_result,
minmax_result,
mismatch_result,
copy_result, and
partition_copy_result
have the template parameters, data members, and special members specified above.

They have no base classes or members other than those specified.

The decision whether to include a copying version was
usually based on complexity considerations.

When the cost of doing the operation dominates the cost of copy,
the copying version is not included.

For example, sort_copy is not included
because the cost of sorting is much more significant,
and users might as well do copy followed by sort.