std::partition(3)

NAME
std::partition - std::partition

Synopsis
   Defined in header <algorithm>
   template< class BidirIt, class UnaryPredicate >
   BidirIt partition( BidirIt first, BidirIt last, UnaryPredicate (until C++11)
   p );
   template< class ForwardIt, class UnaryPredicate > (since C++11)
   ForwardIt partition( ForwardIt first, ForwardIt last, (until C++20)
   UnaryPredicate p );
   template< class ForwardIt, class UnaryPredicate >
   constexpr ForwardIt partition( ForwardIt first, ForwardIt (1) (since C++20)
   last, UnaryPredicate p );
   template< class ExecutionPolicy, class ForwardIt, class
   UnaryPredicate >
                        (2) (since C++17)
   ForwardIt partition( ExecutionPolicy&& policy,
   ForwardIt first, ForwardIt last, UnaryPredicate p );
   1) Reorders the elements in the range [first, last) in such a way that all elements
   for which the predicate p returns true precede the elements for which predicate p
   returns false. Relative order of the elements is not preserved.
   2) Same as (1), but executed according to policy. This overload does not participate
   in overload resolution unless
   std::is_execution_policy_v<std::decay_t<ExecutionPolicy>>
   (until C++20)
   std::is_execution_policy_v<std::remove_cvref_t<ExecutionPolicy>>
   (since C++20) is true.

Parameters
   first, last - the range of elements to reorder
   policy - the execution policy to use. See execution policy for details.
                  unary predicate which returns true if the element should be
                  ordered before other elements.
                  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
   -
   BidirIt must meet the requirements of LegacyBidirectionalIterator.
   -
   ForwardIt must meet the requirements of ValueSwappable and LegacyForwardIterator.
   However, the operation is more efficient if ForwardIt also satisfies the
   requirements of LegacyBidirectionalIterator
   -
   UnaryPredicate must meet the requirements of Predicate.

Return value
   Iterator to the first element of the second group.

Complexity
   Given N = std::distance(first,last),
   1) Exactly N applications of the predicate. At most N/2 swaps if ForwardIt meets the
   requirements of LegacyBidirectionalIterator, and at most N swaps otherwise.
   2) O(N log N) swaps and O(N) applications of the predicate.

Exceptions
   The overload with a template parameter named ExecutionPolicy reports 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
   template<class ForwardIt, class UnaryPredicate>
   ForwardIt partition(ForwardIt first, ForwardIt last, UnaryPredicate p)
   {
       first = std::find_if_not(first, last, p);
       if (first == last) return first;
       for (ForwardIt i = std::next(first); i != last; ++i) {
           if (p(*i)) {
               std::iter_swap(i, first);
               ++first;
           }
       }
       return first;
   }

Example
// Run this code
 #include <algorithm>
 #include <iostream>
 #include <iterator>
 #include <vector>
 #include <forward_list>
 template <class ForwardIt>
  void quicksort(ForwardIt first, ForwardIt last)
  {
     if(first == last) return;
     auto pivot = *std::next(first, std::distance(first,last)/2);
     ForwardIt middle1 = std::partition(first, last,
                        [pivot](const auto& em){ return em < pivot; });
     ForwardIt middle2 = std::partition(middle1, last,
                        [pivot](const auto& em){ return !(pivot < em); });
     quicksort(first, middle1);
     quicksort(middle2, last);
  }
 int main()
 {
     std::vector<int> v = {0,1,2,3,4,5,6,7,8,9};
     std::cout << "Original vector:\n ";
     for(int elem : v) std::cout << elem << ' ';
     auto it = std::partition(v.begin(), v.end(), [](int i){return i % 2 == 0;});
     std::cout << "\nPartitioned vector:\n ";
     std::copy(std::begin(v), it, std::ostream_iterator<int>(std::cout, " "));
     std::cout << " * " " ";
     std::copy(it, std::end(v), std::ostream_iterator<int>(std::cout, " "));
     std::forward_list<int> fl = {1, 30, -4, 3, 5, -4, 1, 6, -8, 2, -5, 64, 1, 92};
     std::cout << "\nUnsorted list:\n ";
     for(int n : fl) std::cout << n << ' ';
     std::cout << '\n';
     quicksort(std::begin(fl), std::end(fl));
     std::cout << "Sorted using quicksort:\n ";
     for(int fi : fl) std::cout << fi << ' ';
     std::cout << '\n';
 }

Possible output:
 Original vector:
     0 1 2 3 4 5 6 7 8 9
 Partitioned vector:
     0 8 2 6 4 * 5 3 7 1 9
 Unsorted list:
     1 30 -4 3 5 -4 1 6 -8 2 -5 64 1 92
 Sorted using quicksort:
     -8 -5 -4 -4 1 1 1 2 3 5 6 30 64 92

See also
   is_partitioned determines if the range is partitioned by the given predicate
   (C++11) (function template)
                     divides elements into two groups while preserving their relative
   stable_partition order
                     (function template)
   ranges::partition divides a range of elements into two groups
   (C++20) (niebloid)