std::partition_point() algorithm

since C++20

template< class ForwardIt, class UnaryPredicate >
constexpr ForwardIt partition_point( ForwardIt first, ForwardIt last, UnaryPredicate p );

since C++11

// (1)
template< class ForwardIt, class UnaryPredicate >
ForwardIt partition_point( ForwardIt first, ForwardIt last, UnaryPredicate p );

Examines the partitioned (as if by std::partition) range [first; last) and locates the end of the first partition, that is, the first element that does not satisfy p or last if all elements satisfy p.

Parameters

first last	The partitioned range of elements to examine
policy	The execution policy to use. See execution policy for details.
p	Unary predicate which returns true for the required element. The expression p(v) must be convertible to bool for every argument v of type (possibly const) VT, where VT is the value type of InputIt, regardless of value category, and must not modify v. Thus, a parameter type of VT& is not allowed , nor is VT unless for VT a move is equivalent to a copy. (since C++11).

Type requirements

ForwardIt	LegacyForwardIterator
UnaryPredicate	Predicate

Return value

The iterator past the end of the first partition within [first; last) or last if all elements satisfy p.

Complexity

Given N as std::distance(first, last):

Performs O(log(N)) applications of the predicate p.

However, for non-LegacyRandomAccessIterators, the number of iterator increments is O(N).

Exceptions

The overloads with a template parameter named ExecutionPolicy report errors as follows:

• If execution of a function invoked as part of the algorithm throws an exception and ExecutionPolicy is one of the standard policies, std::terminate is called. For any other ExecutionPolicy, the behavior is implementation-defined.
• If the algorithm fails to allocate memory, std::bad_alloc is thrown.

Possible implementation

partition_point (1)

template<class ForwardIt, class UnaryPredicate>
constexpr //< since C++20
ForwardIt partition_point(ForwardIt first, ForwardIt last, UnaryPredicate p)
{
    for (auto length = std::distance(first, last); 0 < length; )
    {
        auto half = length / 2;
        auto middle = std::next(first, half);
        if (p(*middle))
        {
            first = std::next(middle);
            length -= (half + 1);
        }
        else
            length = half;
    }

    return first;
}

Notes

This algorithm is a more general form of std::lower_bound, which can be expressed in terms of std::partition_point with the predicate [&](auto const& e) { return e < value; });.

Examples

Main.cpp

#include <algorithm>
#include <array>
#include <iostream>
#include <iterator>

auto print_seq = [](auto rem, auto first, auto last)
{
    for (std::cout << rem; first != last; std::cout << *first++ << ' ') {}
    std::cout << '\n';
};

int main()
{
    std::array v {1, 2, 3, 4, 5, 6, 7, 8, 9};

    auto is_even = [](int i) { return i % 2 == 0; };

    std::partition(v.begin(), v.end(), is_even);
    print_seq("After partitioning, v: ", v.cbegin(), v.cend());

    const auto pp = std::partition_point(v.cbegin(), v.cend(), is_even);
    const auto i = std::distance(v.cbegin(), pp);
    std::cout << "Partition point is at " << i << "; v[" << i << "] = " << *pp << '\n';

    print_seq("First partition (all even elements): ", v.cbegin(), pp);
    print_seq("Second partition (all odd elements): ", pp, v.cend());
}

Output

After partitioning, v: 8 2 6 4 5 3 7 1 9
Partition point is at 4; v[4] = 5
First partition (all even elements): 8 2 6 4
Second partition (all odd elements): 5 3 7 1 9