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std::ranges::fold_right

Defined in header `<algorithm>`
Call signature
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 );	(1)	(since C++23)
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 );	(2)	(since C++23)
Helper concepts
template< class F, class T, class I > concept __indirectly_binary_left_foldable = // exposition only /* see description */;	(3)	(since C++23)
template< class F, class T, class I > concept __indirectly_binary_right_foldable = // exposition only /* see description */;	(4)	(since C++23)

Right-folds the elements of given range, that is, returns the result of evaluation of the chain expression:
f(x₁, f(x₂, ...f(x_n, init))), where x₁, x₂, ..., 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:

template< class F, class T, class I, class U >
    concept __indirectly_binary_left_foldable_impl =  // exposition only
        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>>>;
 
template< class F, class T, class I >
    concept __indirectly_binary_left_foldable =      // exposition only
        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>>>>;

4) Equivalent to:

template< class F, class T, class I >
    concept __indirectly_binary_right_foldable =      // exposition only
            __indirectly_binary_left_foldable<__flipped<F>, T, I>;

The helper class template flipped is equivalent to:

template< class F >
class __flipped       // exposition only
{
    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&& );
};

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,
             __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,
             __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) `std::in_value_result<I, U>` (2) `std::in_value_result<BR, U>`, where `BR` is `ranges::borrowed_iterator_t<R>`
`ranges::fold_left_first_with_iter`	left	first element	(1) `std::in_value_result<I, std::optional<U>>` (2) `std::in_value_result<BR, std::optional<U>>` where `BR` is `ranges::borrowed_iterator_t<R>`

Feature-test macro	Value	Std	Comment
`__cpp_lib_ranges_fold`	202207L	(C++23)	`std::ranges` fold algorithms

Example

#include <algorithm>
#include <functional>
#include <iostream>
#include <ranges>
#include <string>
#include <utility>
#include <vector>
using namespace std::literals;
 
int main()
{
    auto v = {1, 2, 3, 4, 5, 6, 7, 8};
    std::vector<std::string> vs {"A", "B", "C", "D"};
 
    auto r1 = std::ranges::fold_right(v.begin(), v.end(), 6, std::plus<>()); // (1)
    std::cout << "r1: " << r1 << '\n';
 
    auto r2 = std::ranges::fold_right(vs, "!"s, std::plus<>()); // (2)
    std::cout << "r2: " << r2 << '\n';
 
    // Use a program defined function object (lambda-expression):
    std::string r3 = std::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 = std::ranges::fold_right
    (
        data | std::ranges::views::values, 2.0f, std::multiplies<>()
    );
    std::cout << "r4: " << r4 << '\n';
}

Output:

r1: 42
r2: ABCD!
r3: A:8:7:6:5:4:3:2:1
r4: 42

References

C++23 standard (ISO/IEC 14882:2023):

27.6.18 Fold [alg.fold]

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