Simple quicksort implementation

A simple C++ quicksort implementation. This version is not in place and therefore requires O(n) extra space...

#include "math.h"
#include <vector>
#include <iostream>

using namespace std;

template<class value_type>
void quick_sort(vector<value_type> &values,size_t start,size_t end,size_t pivot) {

  vector<value_type> less;
  vector<value_type> greater;

  for(size_t n=start;n<end;n++) {
    if(n != pivot)
    if(values[n] < values[pivot]) {
      less.push_back(values[n]);
    } else {
      greater.push_back(values[n]);
    }
  }

  value_type pivot_temp = values[pivot];
  for(size_t n=0;n<less.size();n++) {
    values[n+start] = less[n];
  }

  values[start+less.size()] = pivot_temp;

  for(size_t n=0;n<greater.size();n++) {
    values[n+start+less.size()+1] = greater[n];
  }

  if(less.size()    > 1) { quick_sort(values,start      ,start+less.size(),start+(less.size()/2)); }
  if(greater.size() > 1) { quick_sort(values,less.size(),end              ,less.size()+(end/2)  ); }
}

int main() {

  vector<size_t> values;

  for(size_t n=0;n<10;n++) {
    values.push_back(rand());
  }

  cout << "start values..." << endl;
  for(size_t n=0;n<values.size();n++) {
    cout << "val[" << n << "]: " << values[n] << endl;
  }

  quick_sort(values,0,values.size(),5);
  cout << "sorted values..." << endl;
  for(size_t n=0;n<values.size();n++) {
    cout << values[n] << endl;
  }
}