nth_element

Algorithm

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Rearranges a collection so that all elements lower in sorted order than the nth element come before it and all elements higher in sorter order than the nth element come after it.

None

#include <algorithm>
template <class RandomAccessIterator>
 void nth_element (RandomAccessIterator first,
                   RandomAccessIterator nth,
                   RandomAccessIterator last);

template <class RandomAccessIterator, class Compare>
 void nth_element (RandomAccessIterator first,
                   RandomAccessIterator nth,
                   RandomAccessIterator last,
                   Compare comp);

The nth_element algorithm rearranges a collection according to either the default comparison operator (>) or a comparison operator given by the user. After the algorithm is applied, three things are true:

• The element that would be in the nth position if the collection were completely sorted is in the nth position

• All elements prior to the nth position would also precede that position in an ordered collection

• All elements following the nth position would also follow that position in an ordered collection

That is, for any iterator i in the range [first, nth) and any iterator j in the range [nth, last), it holds that !(*i > *j) or comp(*i, *j) == false.

Note that the elements that precede or follow the nth position are not necessarily sorted relative to each other. The nth_element algorithm does not sort the entire collection.

The algorithm is linear, on average, where N is the size of the range [first, last).

//
// nthelem.cpp
//
 #include <algorithm>
 #include <vector>
 #include <iostream>
 using namespace std;

 template<class RandomAccessIterator>
 void quik_sort(RandomAccessIterator start, 
                RandomAccessIterator end)
 {
   size_t dist = 0;
   distance(start, end, dist);

   //Stop condition for recursion
   if(dist > 2)
   {
     //Use nth_element to do all the work for quik_sort
     nth_element(start, start+(dist/2), end);

     //Recursive calls to each remaining unsorted portion
     quik_sort(start, start+(dist/2-1));
     quik_sort(start+(dist/2+1), end);
   }

   if(dist == 2 && *end < *start)
     swap(start, end);
 }

 int main()
 {
   //Initialize a vector using an array of ints
   int arr[10] = {37, 12, 2, -5, 14, 1, 0, -1, 14, 32};
   vector<int> v(arr, arr+10);

   //Print the initial vector
   cout << "The unsorted values are: " << endl << "     ";
   vector<int>::iterator i; 
   for(i = v.begin(); i != v.end(); i++)
     cout << *i << ", ";
   cout << endl << endl;

   //Use the new sort algorithm
   quik_sort(v.begin(), v.end());

   //Output the sorted vector
   cout << "The sorted values are: " << endl << "     ";
   for(i = v.begin(); i != v.end(); i++)
     cout << *i << ", ";
   cout << endl << endl;

   return 0;
 }

Program Output

The unsorted values are:
     37, 12, 2, -5, 14, 1, 0, -1, 14, 32,
The sorted values are:
     -5, -1, 0, 1, 2, 12, 14, 14, 32, 37,

If your compiler does not support default template parameters, then you always need to supply the Allocator template argument. For instance, you need to write:

vector<int, allocator<int> >

instead of:

vector<int>

If your compiler does not support namespaces, then you do not need the using declaration for std.

Algorithms