std::partition_point(3)

NAME
std::partition_point - std::partition_point

Synopsis
   Defined in header <algorithm>
   template< class ForwardIt, class UnaryPred > (since C++11)
   ForwardIt partition_point( ForwardIt first, ForwardIt last, (constexpr since C++20)
   UnaryPred p );
   Examines the partitioned 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.
   If the elements elem of [first, last) are not partitioned with respect to the
   expression bool(p(elem)), the behavior is undefined.

Parameters
   first, last - the partitioned range of elements to examine
                 unary predicate which returns true for the elements found in the
                 beginning of the range.
                 The expression p(v) must be convertible to bool for every argument v
   p - of type (possibly const) VT, where VT is the value type of ForwardIt,
                 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 must meet the requirements of LegacyForwardIterator.
   -
   UnaryPred must meet the requirements of Predicate.

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

Complexity
   Given \(\scriptsize N\)N as std::distance(first, last), performs \(\scriptsize
   O(log(N))\)O(log(N)) applications of the predicate p.

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 [&](const auto& e) { return e <
   value; });.

Possible implementation
   template<class ForwardIt, class UnaryPred>
   constexpr //< since C++20
   ForwardIt partition_point(ForwardIt first, ForwardIt last, UnaryPred 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;
   }

Example
// Run this code
 #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());
 }

Possible 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

See also
   find
   find_if finds the first element satisfying specific criteria
   find_if_not (function template)
   (C++11)
   is_sorted checks whether a range is sorted into ascending order
   (C++11) (function template)
                        returns an iterator to the first element not less than the
   lower_bound given value
                        (function template)
   ranges::partition_point locates the partition point of a partitioned range
   (C++20) (niebloid)