std::ranges::fold_right(3)

NAME
std::ranges::fold_right - std::ranges::fold_right

Synopsis
   Defined in header <algorithm>
   Call signature
   template< std::bidirectional_iterator I,
   std::sentinel_for<I> S, class T,
                        (since
             /* indirectly-binary-right-foldable */<T, C++23)
   I> F > (until
                        C++26)
   constexpr auto fold_right( I first, S last, T init, F
   f );
   template< std::bidirectional_iterator I,
   std::sentinel_for<I> S,
             class T = std::iter_value_t<I>, (since
             /* indirectly-binary-right-foldable */<T, C++26)
   I> F >
   constexpr auto fold_right( I first, S last, T init, F
   f );
   template< ranges::bidirectional_range R, class T,
                        (1)
             /* indirectly-binary-right-foldable */ (since C++23)
                 <T, ranges::iterator_t<R>> F > (until C++26)
   constexpr auto fold_right( R&& r, T init, F f );
   template< ranges::bidirectional_range R, class T =
   ranges::range_value_t<R>,
             /* indirectly-binary-right-foldable */ (2) (since C++26)
                 <T, ranges::iterator_t<R>> F >
   constexpr auto fold_right( R&& r, T init, F f );
   Helper concepts
   template< class F, class T, class I > (exposition
   concept /* indirectly-binary-left-foldable */ = /* (3) only*)
   see description */;
   template< class F, class T, class I > (exposition
   concept /* indirectly-binary-right-foldable */ = /* (4) only*)
   see description */;
   Right-folds the elements of given range, that is, returns the result of evaluation
   of the chain expression:
   f(x[1], f(x[2], ...f(x[n], init))), where x[1], x[2], ..., x[n] are elements of the
   range.
   Informally, ranges::fold_right behaves like std::fold_left(ranges::reverse(r), init,
   /* flipped */(f)).
   The behavior is undefined if [first, last) is not a valid range.
   1) The range is [first, last).
   2) Same as (1), except that uses r as the range, as if by using ranges::begin(r) as
   first and ranges::end(r) as last.
   3) Equivalent to:
   Helper concepts
   template< class F, class T, class I, class U >
   concept /*indirectly-binary-left-foldable-impl*/ =
       std::movable<T> &&
       std::movable<U> &&
       std::convertible_to<T, U> && (3A) (exposition only*)
       std::invocable<F&, U, std::iter_reference_t<I>> &&
       std::assignable_from<U&,
           std::invoke_result_t<F&, U,
   std::iter_reference_t<I>>>;
   template< class F, class T, class I >
   concept /*indirectly-binary-left-foldable*/ =
       std::copy_constructible<F> &&
       std::indirectly_readable<I> &&
       std::invocable<F&, T, std::iter_reference_t<I>> &&
       std::convertible_to<std::invoke_result_t<F&, T, (3B) (exposition only*)
   std::iter_reference_t<I>>,
           std::decay_t<std::invoke_result_t<F&, T,
   std::iter_reference_t<I>>>> &&
       /*indirectly-binary-left-foldable-impl*/<F, T, I,
           std::decay_t<std::invoke_result_t<F&, T,
   std::iter_reference_t<I>>>>;
   4) Equivalent to:
   Helper concepts
   template< class F, class T, class I >
                        (exposition
   concept /*indirectly-binary-right-foldable*/ = (4A) only*)
       /*indirectly-binary-left-foldable*/</*flipped*/<F>, T, I>;
   Helper class templates
   template< class F >
   class /*flipped*/
   {
       F f; // exposition only (exposition
   public: (4B) only*)
       template< class T, class U >
           requires std::invocable<F&, U, T>
       std::invoke_result_t<F&, U, T> operator()( T&&, U&& );
   };
   The function-like entities described on this page are niebloids, that is:
     * Explicit template argument lists cannot be specified when calling any of them.
     * None of them are visible to argument-dependent lookup.
     * When any of them are found by normal unqualified lookup as the name to the left
       of the function-call operator, argument-dependent lookup is inhibited.
   In practice, they may be implemented as function objects, or with special compiler
   extensions.

Parameters
   first, last - the range of elements to fold
   r - the range of elements to fold
   init - the initial value of the fold
   f - the binary function object

Return value
   An object of type U that contains the result of right-fold of the given range over
   f, where U is equivalent to std::decay_t<std::invoke_result_t<F&,
   std::iter_reference_t<I>, T>>;.
   If the range is empty, U(std::move(init)) is returned.

Possible implementations
   struct fold_right_fn
   {
       template<std::bidirectional_iterator I, std::sentinel_for<I> S,
                class T = std::iter_value_t<I>,
                /* indirectly-binary-right-foldable */<T, I> F>
       constexpr auto operator()(I first, S last, T init, F f) const
       {
           using U = std::decay_t<std::invoke_result_t<F&, std::iter_reference_t<I>, T>>;
           if (first == last)
               return U(std::move(init));
           I tail = ranges::next(first, last);
           U accum = std::invoke(f, *--tail, std::move(init));
           while (first != tail)
               accum = invoke(f, *--tail, std::move(accum));
           return accum;
       }
       template<ranges::bidirectional_range R, class T = ranges::range_value_t<R>,
                /* indirectly-binary-right-foldable */<T, ranges::iterator_t<R>> F>
       constexpr auto operator()(R&& r, T init, F f) const
       {
           return (*this)(ranges::begin(r), ranges::end(r), std::move(init), std::ref(f));
       }
   };
   inline constexpr fold_right_fn fold_right;

Complexity
   Exactly ranges::distance(first, last) applications of the function object f.

Notes
   The following table compares all constrained folding algorithms:
        Fold function template Starts Initial Return type
                        from value
   ranges::fold_left left init U
   ranges::fold_left_first left first std::optional<U>
                        element
   ranges::fold_right right init U
   ranges::fold_right_last right last std::optional<U>
                        element
                        (1) ranges::in_value_result<I, U>
   ranges::fold_left_with_iter left init (2) ranges::in_value_result<BR, U>,
                        where BR is
                        ranges::borrowed_iterator_t<R>
                        (1) ranges::in_value_result<I,
                        std::optional<U>>
   ranges::fold_left_first_with_iter left first (2) ranges::in_value_result<BR,
                        element std::optional<U>>
                        where BR is
                        ranges::borrowed_iterator_t<R>
             Feature-test macro Value Std Feature
   __cpp_lib_ranges_fold 202207L (C++23) std::ranges fold algorithms
   __cpp_lib_algorithm_default_value_type 202403 (C++26) List-initialization for
                        algorithms (1,2)

Example
// Run this code
 #include <algorithm>
 #include <complex>
 #include <functional>
 #include <iostream>
 #include <ranges>
 #include <string>
 #include <utility>
 #include <vector>
 using namespace std::literals;
 namespace ranges = std::ranges;
 int main()
 {
     auto v = {1, 2, 3, 4, 5, 6, 7, 8};
     std::vector<std::string> vs{"A", "B", "C", "D"};
     auto r1 = ranges::fold_right(v.begin(), v.end(), 6, std::plus<>()); // (1)
     std::cout << "r1: " << r1 << '\n';
     auto r2 = ranges::fold_right(vs, "!"s, std::plus<>()); // (2)
     std::cout << "r2: " << r2 << '\n';
     // Use a program defined function object (lambda-expression):
     std::string r3 = ranges::fold_right
     (
         v, "A", [](int x, std::string s) { return s + ':' + std::to_string(x); }
     );
     std::cout << "r3: " << r3 << '\n';
     // Get the product of the std::pair::second of all pairs in the vector:
     std::vector<std::pair<char, float>> data{{'A', 2.f}, {'B', 3.f}, {'C', 3.5f}};
     float r4 = ranges::fold_right
     (
         data | ranges::views::values, 2.0f, std::multiplies<>()
     );
     std::cout << "r4: " << r4 << '\n';
     using CD = std::complex<double>;
     std::vector<CD> nums{{1, 1}, {2, 0}, {3, 0}};
     #ifdef __cpp_lib_algorithm_default_value_type
         auto r5 = ranges::fold_right(nums, {7, 0}, std::multiplies{});
     #else
         auto r5 = ranges::fold_right(nums, CD{7, 0}, std::multiplies{});
     #endif
     std::cout << "r5: " << r5 << '\n';
 }

Output:
 r1: 42
 r2: ABCD!
 r3: A:8:7:6:5:4:3:2:1
 r4: 42
 r5: (42,42)

References
     * C++23 standard (ISO/IEC 14882:2023):
     * 27.6.18 Fold [alg.fold]

See also
   ranges::fold_right_last right-folds a range of elements using the last
   (C++23) element as an initial value
                        (niebloid)
   ranges::fold_left left-folds a range of elements
   (C++23) (niebloid)
   ranges::fold_left_first left-folds a range of elements using the first
   (C++23) element as an initial value
                        (niebloid)
   ranges::fold_left_with_iter left-folds a range of elements, and returns a pair
   (C++23) (iterator, value)
                        (niebloid)
                        left-folds a range of elements using the first
   ranges::fold_left_first_with_iter element as an initial value, and returns a pair
   (C++23) (iterator, optional)
                        (niebloid)
   accumulate sums up or folds a range of elements
                        (function template)
   reduce similar to std::accumulate, except out of order
   (C++17) (function template)