Function declaration

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

Effect

Process the [first, last] element so that the element satisfying p moves to the front of [first, last], the element not satisfying p moves to the back, and returns the iterator of the first element not satisfying p, and the last if all of them are satisfied

Possible implementation code

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;
}

Complexity

1. One cycle, so the time complexity is O(N)
2. In the worst case, O(N) times of swap will be performed (only the first one is unsatisfied)

Example

Use partition for general operation, and use partition to implement a fast scheduling

#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; });
    quicksort(first, middle1);
    quicksort(std::next(middle1, 1), 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';
}

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