# std::ranges::fold_right

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< cpp‎ | algorithm‎ | ranges

Defined in header `<algorithm>` |  |
Call signature |  |
| (1) |
template< std::bidirectional_iterator I, std::sentinel_for <I> S, class T, /* indirectly-binary-right-foldable */<T, I> F > constexpr auto fold_right( I first, S last, T init, F f ); |  | (since C++23) (until C++26)
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 fold_right( I first, S last, T init, F f ); |  | (since C++26)
| (2) |
template< ranges::bidirectional_range R, class T, /* indirectly-binary-right-foldable */ <T, ranges::iterator_t <R>> F > constexpr auto fold_right( R&& r, T init, F f ); |  | (since C++23) (until C++26)
template< ranges::bidirectional_range R, class T = ranges::range_value_t <R>, /* indirectly-binary-right-foldable */ <T, ranges::iterator_t <R>> F > constexpr auto fold_right( R&& r, T init, F f ); |  | (since C++26)
Helper concepts |  |
template< class F, class T, class I > concept /* indirectly-binary-left-foldable */ = /* see description */; | (3) | (exposition only*)
template< class F, class T, class I > concept /* indirectly-binary-right-foldable */ = /* see description */; | (4) | (exposition only*)

Right-folds the elements of given range, that is, returns the result of evaluation of the chain expression:
`f(x1, f(x2, ...f(xn, init)))`, where `x1`, `x2`, ..., `xn` 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> && std::invocable <F&, U, std::iter_reference_t <I>> && std::assignable_from <U&, std::invoke_result_t <F&, U, std::iter_reference_t <I>>>; | (3A) | (exposition only*)

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, 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>>>>;

(3B)

(exposition only*)

4) Equivalent to:

Helper concepts |  |
template< class F, class T, class I > concept /*indirectly-binary-right-foldable*/ = /*indirectly-binary-left-foldable*/</*flipped*/<F>, T, I>; | (4A) | (exposition only*)
Helper class templates |  |
template< class F > class /*flipped*/ { F f; // exposition only public: template< class T, class U > requires std::invocable <F&, U, T> std::invoke_result_t <F&, U, T> operator()( T&&, U&& ); }; | (4B) | (exposition only*)

The function-like entities described on this page are algorithm function objects (informally known as 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.

### 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 = std::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 from | Initial value | Return type
--- | --- | --- | ---
ranges::fold_left | left | init | U
ranges::fold_left_first | left | first element | std::optional <U>
ranges::fold_right | right | init | U
ranges::fold_right_last | right | last element | std::optional <U>
ranges::fold_left_with_iter | left | init | (1) ranges::in_value_result <I, U> (2) ranges::in_value_result <BR, U>, where BR is ranges::borrowed_iterator_t <R>
ranges::fold_left_first_with_iter | left | first element | (1) ranges::in_value_result <I, std::optional <U>> (2) ranges::in_value_result <BR, 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` | `202403L` | (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 14882:2024):

  - 27.6.18 Fold [alg.fold]

### See also

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

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