how to implement quick sort algorithm in C++

Question 1

Your consideration is wrong. The value of r does not change, since it is given as value to the Quicksort function(not a reference). You handle the ranges with p,q such that p is the first index in the range and q the first index not in the range.

Thus, your calls were wrong:

r=partition(A, p,q);
quickSort(A,p,r); //range is from A[p] to A[r-1] 
quickSort(A,(r+1),q); //range is from A[r+1] to A[q-1]

Here is the complete example. I used std::swap to change elements and ans std::vector instead of an array.

#include <iostream>
#include <vector>

using namespace std;

void quickSort(vector<int>&,int,int);

int partition(vector<int>&, int,int);

int main()
{
    vector<int> A = {6,10,13,5,8,3,2,25,4,11};
    int p=0;
    int q=10;

    cout<<"======Original======="<<endl;
    for(auto e: A)
        cout<< e <<" ";
    cout<< endl;    

    quickSort(A,p,q);

    cout<<"======Sorted======="<<endl;
    for(auto e: A)
        cout<< e <<" ";
    cout<< endl;   
}


void quickSort(vector<int>& A, int p,int q)
{
    int r;
    if(p<q)
    {
        r=partition(A, p,q);
        quickSort(A,p,r);  
        quickSort(A,r+1,q);
    }
}


int partition(vector<int>& A, int p,int q)
{
    int x= A[p];
    int i=p;
    int j;

    for(j=p+1; j<q; j++)
    {
        if(A[j]<=x)
        {
            i=i+1;
            swap(A[i],A[j]);
        }

    }

    swap(A[i],A[p]);
    return i;
}

Live example: ideone

Question 2

This is a template based solution. However, it works only for arrays of elements for now. If anyone has an improvement to make it generic for both arrays and STL containers, please do so.

template<typename T, typename compare = std::less<T>>
void q_sort(T input[], int l_idx, int r_idx, compare comp = compare()) {

    if (l_idx >= r_idx)
        return;

    // The below is the partition block (can be made a sub function)

    int left = l_idx;
    int right = r_idx;
    {
        int pivot_idx = l_idx;
        T pivot = input[pivot_idx];

        while (left < right) {
            while (comp(input[left], pivot))
                left++;
            while (comp(pivot, input[right]))
                right--;
            swap(input[left], input[right]);
        }

        swap(pivot, input[left]);
    }

    q_sort(input, l_idx, left, comp);
    q_sort(input, left+1, r_idx, comp);

}

template<typename T, typename compare = std::less<T>>
void quick_sort(T array[], int N, compare comp = compare()) {
    // This is an improvisation on the merge sort algorithm
    // is in-place and works on the divide-and-conquer methodology
    // Choose a pivot and find its appropriate place, such that
    // All elements less than the pivot are on its left and all elements
    // greater are on its right. Once found, split the porlblem into subsets
    // of elements less than and greater than the pivot and recursively
    // follow the process.
    q_sort(array, 0, N-1, comp);

}

int main()
{

    int input[] = {11, 6, 3, 21, 9, 12};
    std::cout << "Before : ";
    for (int i=0; i < 6; i++)
        std::cout << input[i] << " ";
    std::cout << std::endl;

    quick_sort(input, 6);
    // or 
    //quick_sort(input, 6, std::greater<int>());

    std::cout << "After : ";
    for (int i=0; i < 6; i++)
        std::cout << input[i] << " ";
    std::cout << std::endl;

}

Question 3

A much easier and clean implementation, also gives you number of minimum SWAPS in for QuickSort:

int quickSort(int[], int, int);

int partition(int[], int, int, int&);

int main()
{
    int array[] = {4, 2, 5};
    int size = sizeof(array)/sizeof(array[0]);

    /*
     first and last indices are passed
     idea is to move lower elements to the left of the list/pivot
     */

    int swaps = quickSort(array, 0, size-1);

    std::cout << "Minimum Swaps are: " << swaps << std::endl;

    for(int i = 0; i < size; i++)
    {
        std::cout << array[i] << " ";
    }
}

int quickSort(int array[], int start, int end)
{
    int swaps = 0;
    if(start < end)
    {
        int pIndex = partition(array, start, end, swaps);
        //after each call one number(the PIVOT) will be at its final position
        swaps += quickSort(array, start, pIndex-1);
        swaps += quickSort(array, pIndex+1, end);
    }
    return swaps;
}

int partition(int array[], int start, int end, int& swaps)
{
    int pivot = array[end];
    int pIndex = start;

    for(int i = start; i < end; i++)
    {
        if(array[i] <= pivot)
        {

            if(pIndex != i)
            {
                std::swap(array[i], array[pIndex]);
                swaps++;
            }
            pIndex++;
        }
    }
    if(pIndex != end)
    {
        std::swap(array[pIndex], array[end]);
        swaps++;
    }
    return pIndex;
}

Question 4

Since I see various answers, you could try this:

#include <iostream>

void quickSort(int a[], int first, int last);
int pivot(int a[], int first, int last);
void swap(int& a, int& b);
void swapNoTemp(int& a, int& b);
void print(int array[], const int& N);

using namespace std;

int main()
{
    int test[] = { 7, -13, 1, 3, 10, 5, 2, 4 };
    int N = sizeof(test)/sizeof(int);

    cout << "Size of test array :"  << N << endl;

    cout << "Before sorting : " << endl;
    print(test, N);

    quickSort(test, 0, N-1);

    cout << endl << endl << "After sorting : " << endl;
    print(test, N);

    return 0;
}

/**
 * Quicksort.
 * @param a - The array to be sorted.
 * @param first - The start of the sequence to be sorted.
 * @param last - The end of the sequence to be sorted.
*/
void quickSort( int a[], int first, int last ) 
{
    int pivotElement;

    if(first < last)
    {
        pivotElement = pivot(a, first, last);
        quickSort(a, first, pivotElement-1);
        quickSort(a, pivotElement+1, last);
    }
}

/**
 * Find and return the index of pivot element.
 * @param a - The array.
 * @param first - The start of the sequence.
 * @param last - The end of the sequence.
 * @return - the pivot element
*/
int pivot(int a[], int first, int last) 
{
    int  p = first;
    int pivotElement = a[first];

    for(int i = first+1 ; i <= last ; i++)
    {
        /* If you want to sort the list in the other order, change "<=" to ">" */
        if(a[i] <= pivotElement)
        {
            p++;
            swap(a[i], a[p]);
        }
    }

    swap(a[p], a[first]);

    return p;
}

I have it in Quicksort (C++).