/*
 ******************************************************************************
 * file name  : cb_sort.h
 * author     : Hung Q. Ngo
 * description: implementations of template versions of randomized quick sort
 *              and insertion sort with a comparison callback
 ******************************************************************************
 */

#include <vector>
#include <cstdlib>  // for rand() and srand()
#include <ctime>    // for time()

/**
 * -----------------------------------------------------------------------------
 * -1 if a < b, 0 if a==b, 1 if a>b
 * -----------------------------------------------------------------------------
 */
template <typename Item_Type>
int default_cmp(Item_Type a, Item_Type b) {
    return a < b? -1 : a == b ? 0 : 1;
}

/**
 * -----------------------------------------------------------------------------
 * Template Insertion Sort
 * for each i from 1 to n-1, insert vec[i] to the right place in the prefix
 * -----------------------------------------------------------------------------
 */
template <typename Item_Type>
void insertion_sort(std::vector<Item_Type> &vec, 
                    int (*cmp)(Item_Type, Item_Type) = default_cmp)
{
    Item_Type temp; 
    int j;
    for (int i=1; i<vec.size(); i++) {
        temp = vec[i];
        j = i-1;
        // uses 'cmp' to compare instead of '>'
        while (j >= 0 && cmp(vec[j],temp) > 0) {
            vec[j+1] = vec[j];
            j--;
        }
        vec[j+1] = temp;
    }
}

/**
 * -----------------------------------------------------------------------------
 * The Randomized Quick Sort algorithm
 * - pick a random pivot, that's all
 * -----------------------------------------------------------------------------
 */
template <typename Item_Type>
void rqs_with_range(std::vector<Item_Type> &vec, int p, int q,
                    int (*cmp)(Item_Type, Item_Type))
{
    if (p >= q) return;

    // pick a random pivot
    int m = std::rand() % (q-p+1);
    std::swap(vec[q], vec[p+m]); 

    // partition
    int r=p-1;
    for (int j=p; j<q; j++) {
        if (rand() % 2 == 0) {
            if (cmp(vec[j],vec[q])<0)
                std::swap(vec[++r], vec[j]);
        } else {
            if (cmp(vec[j],vec[q])<=0)
                std::swap(vec[++r], vec[j]);
        }
    }
    std::swap(vec[++r], vec[q]);

    // sort the left & the right parts
    rqs_with_range(vec, p, r-1, cmp);
    rqs_with_range(vec, r+1, q, cmp);
}

/**
 * -----------------------------------------------------------------------------
 * Wrapper to the randomized quick sort algorithm
 * -----------------------------------------------------------------------------
 */
template <typename Item_Type>
void randomized_quick_sort(std::vector<Item_Type> &vec,
                    int (*cmp)(Item_Type, Item_Type) = default_cmp) 
{
    std::srand(static_cast<unsigned int>(std::time(0)));
    rqs_with_range(vec, 0, vec.size()-1, cmp);
}