std::ranges::is_partitioned(3)

NAME
std::ranges::is_partitioned - std::ranges::is_partitioned

Synopsis
   Defined in header <algorithm>
   Call signature
   template< std::input_iterator I, std::sentinel_for<I> S,
             class Proj = std::identity,
             std::indirect_unary_predicate<std::projected<I, Proj>> (1) (since C++20)
   Pred >
   constexpr bool
       is_partitioned( I first, S last, Pred pred, Proj proj = {} );
   template< ranges::input_range R, class Proj = std::identity,
             std::indirect_unary_predicate<
                 std::projected<ranges::iterator_t<R>, Proj>> Pred > (2) (since C++20)
   constexpr bool
       is_partitioned( R&& r, Pred pred, Proj proj = {} );
   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.
   2) Same as (1), but uses r as the source range, as if using ranges::begin(r) as
   first and ranges::end(r) as last.
   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 - iterator-sentinel pair denoting the range of elements to examine
   r - the range of elements to examine
   pred - predicate to apply to the projected elements
   proj - projection to apply to the elements

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

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

Possible implementation
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();

Example
// Run this code
 #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

See also
   ranges::partition divides a range of elements into two groups
   (C++20) (niebloid)
   ranges::partition_point locates the partition point of a partitioned range
   (C++20) (niebloid)
   is_partitioned determines if the range is partitioned by the given
   (C++11) predicate
                        (function template)