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Showing content from https://en.cppreference.com/w/cpp/algorithm/../symbol_index/../algorithm/ranges/is_partitioned.html below:

std::ranges::is_partitioned - cppreference.com

Call signature

1) Returns true if all elements in the range [first, last) that satisfy the predicate pred after projection appear before all elements that don't. Also returns true if [first, last) is empty.

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.

true if the range [first, last) is empty or is partitioned by pred, false otherwise.

At most ranges::distance(first, last) applications of pred and proj.

struct is_partitioned_fn
{
    template<std::input_iterator I, std::sentinel_for<I> S, class Proj = std::identity,
             std::indirect_unary_predicate<std::projected<I, Proj>> Pred>
    constexpr bool operator()(I first, S last, Pred pred, Proj proj = {}) const
    {
        for (; first != last; ++first)
            if (!std::invoke(pred, std::invoke(proj, *first)))
                break;
 
        for (; first != last; ++first)
            if (std::invoke(pred, std::invoke(proj, *first)))
                return false;
 
        return true;
    }
 
    template<ranges::input_range R, class Proj = std::identity,
             std::indirect_unary_predicate<std::projected<ranges::iterator_t<R>, Proj>> Pred>
    constexpr bool operator()(R&& r, Pred pred, Proj proj = {}) const
    {
        return (*this)(ranges::begin(r), ranges::end(r), std::ref(pred), std::ref(proj));
    }
};
 
inline constexpr auto is_partitioned = is_partitioned_fn();

#include <algorithm>
#include <array>
#include <iostream>
#include <numeric>
#include <utility>
 
int main()
{
    std::array<int, 9> v;
 
    auto print = [&v](bool o)
    {
        for (int x : v)
            std::cout << x << ' ';
        std::cout << (o ? "=> " : "=> not ") << "partitioned\n";
    };
 
    auto is_even = [](int i) { return i % 2 == 0; };
 
    std::iota(v.begin(), v.end(), 1); // or std::ranges::iota(v, 1);
    print(std::ranges::is_partitioned(v, is_even));
 
    std::ranges::partition(v, is_even);
    print(std::ranges::is_partitioned(std::as_const(v), is_even));
 
    std::ranges::reverse(v);
    print(std::ranges::is_partitioned(v.cbegin(), v.cend(), is_even));
    print(std::ranges::is_partitioned(v.crbegin(), v.crend(), is_even));
}

Output:

1 2 3 4 5 6 7 8 9 => not partitioned
2 4 6 8 5 3 7 1 9 => partitioned
9 1 7 3 5 8 6 4 2 => not partitioned
9 1 7 3 5 8 6 4 2 => partitioned

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