Quicksort 3 way partition too slow - c++

Question

I am using quicksort 3 way partition, but it is turning out to be too slow as and when the vector size is greater than 10000.
What am I doing wrong? Please guide me! Any help will be appreciated
The answer should be computed in less than 2.2 sec.
#include <iostream>
#include <vector>
#include <cstdlib>
#include <algorithm>
using std::vector;
using std::swap;
void print(vector<int> v)
{
for(int i = 0; i < v.size(); i++) std::cout << v[i] << " ";
std::cout << std::endl;
}
void partition2(vector<int> &a, int l, int r, int &i, int &j) {
int k;
int middle=(l+r)/2;
/*Selecting pivot as median of low, high and middle*/
if(((a[l]<=a[middle]) && (a[middle]<=a[r])) || ((a[r]<=a[middle]) && (a[middle]<=a[l])))
k=middle;
else if(((a[middle]<=a[l]) && (a[l]<=a[r])) || ((a[r]<=a[l]) && (a[l]<=a[middle])))
k=l;
else if(((a[middle]<=a[r]) && (a[r]<=a[l])) || ((a[l]<=a[r]) && (a[r]<=a[middle])))
k=r;
swap(a[l], a[k]);
//print(a);
int low_value = a[l];
int index_low = l;
int index_high = l;
int counter=l;
for (int i = l + 1; i <= r; i++) {
if (a[i] < low_value) {
swap(a[i], a[index_low]);
counter++;
low_value=a[l];
}
else if(a[i]==low_value)
{
index_high++;
swap(a[i], a[index_high]);
}
//print(a);
}
i=counter;
j=index_high;
//swap(a[l], a[j]);
//return j;
}
void randomized_quick_sort(vector<int> &a, int l, int r) {
if (l >= r) {
return;
}
int i,j;
partition2(a, l, r, i, j);
randomized_quick_sort(a, l, i-1);
randomized_quick_sort(a, j+1, r);
}
int main() {
int n;
std::cin >> n;
//while(1){
//n=100+rand()%99999;
//std::cout<<n<<std::endl;
vector<int> a(n);
for (size_t i = 0; i < a.size(); ++i) {
std::cin >> a[i];
//a[i]=1+rand()%99999999;
}
randomized_quick_sort(a, 0, a.size() - 1);
for (size_t i = 0; i < a.size(); ++i) {
std::cout << a[i] << ' ';
}
//std::cout<<"Pass\n";
//}
return 0;
}

Answer 1

Everything at first glance is correct. However, there are probably just too many comparison operations. Try this option - it works on my computer for 1.6 seconds on average.
#include <stdlib.h>
#include <stdio.h>
#include <iostream>
#include <vector>
#include <ctime>
#include <random>
#include <chrono>
#include <iomanip>
using namespace std;
using namespace std::chrono;
//======= quick_sort =======//
template<typename T>
int partition(vector<T>& numbers, const int& left, const int& right)
{
swap(numbers[left], numbers[left + (right - left) / 2]);
T mid = numbers[left];
int i(left + 1), j(right);
while (i <= j)
{
while ( i <= j && numbers[i] <= mid ) i++;
while ( i <= j && numbers[j] > mid ) j--;
if ( i < j ) swap(numbers[i], numbers[j]);
}
swap(numbers[i - 1], numbers[left]);
return i - 1;
}
template<typename T>
void quick_sort_rec(vector<T>& numbers, const int& left, const int& right)
{
if (left >= right) return;
int p = partition(numbers, left, right);
quick_sort_rec(numbers, left , p - 1);
quick_sort_rec(numbers, p + 1 , right);
}
//=========================//
template<typename T>
T random_T(long min, long max)
{
return (T)min + static_cast<T>(rand()) / (static_cast<T>(RAND_MAX / ((T)(max - min))));
}
template<typename T>
float time_func(void (*f)(vector<T>&, const int&, const int&), vector<T>& a)
{
high_resolution_clock::time_point t1 = high_resolution_clock::now();
f(a, 0, a.size() - 1);
high_resolution_clock::time_point t2 = high_resolution_clock::now();
return 1000.0 * (duration_cast<microseconds>(t2 - t1).count()) / (float)(CLOCKS_PER_SEC); /// CLOCKS_PER_SEC;
}
int main()
{
srand((unsigned)(777));
vector<int> a;
for (int i = 0; i < 10000; i++)
{
a.push_back(random_T<int>(0, 1000));
}
cout << setprecision(10) << "quick sort rec = " << time_func(quick_sort_rec, a) << endl;
return 0;
}

Answer 2

I run the following code to test partition2
int main(){
vector<int> a = {2, 1, 1, 9, 5, 3, 4, 2, 7};
int i, j;
partition2(a, 0, a.size() - 1, i, j);
for (auto i : a)
cout << i << ' ';
cout << '\n';
return 0;
}
And the results are
1 1 5 9 2 3 4 2 7
If the partition2 selecting median of low, high and middle as pivot, then the pivot should be 5 and the results should be something like
2 1 1 3 4 2 5 9 7
Then I check the code
if (a[i] < low_value) {
swap(a[i], a[index_low]);
counter++;
low_value=a[l];
}
else if(a[i]==low_value)
{
index_high++;
swap(a[i], a[index_high]);
}
It seems to be that the code try to find the minimum value of array and then move them to beginning of array. It seems that it is doing selection sort instead of quicksort. It explains why it is slow when input size is large.