I'm learning sorting algorithms and as next step, I'm trying to get my implementation perform close to the std::sort(). I'm pretty far, so far.. :-)
I have 3 implementations of quicksort:
- standard quicksort (using temp arrays).
- quicksort with following optimizations:
- median3 used to select median
- tail-recursion
- quicksort applied only upto partition sizes < 16. For smaller partitions insertion sort is used.
- insertion sort applied to the whole array at once instead of applying to each partition, left unsorted by quicksort.
- quicksort with all optimizations listed above + in-place partitioning (no temp arrays).
I expected the performance to be best bottom up, but it's best top down!
What's wrong with my implementation? Given the drastic difference between the performance I assume there is something outrightly wrong.
Some numbers to give you a feel of how bad things are (N = number of elements in array, figures are time taken by each algo in microseconds):
Sorting vector<int> and each algo is given exactly the same sequence of numbers.
N quick mixed mixed_inplace
8 0 0 0
16 0 1 1
32 1 2 2
64 1 3 3
128 1 8 8
256 3 16 17
512 6 34 41
1,024 16 84 87
2,048 28.3 177.1 233.2
4,096 48.5 366.6 410.1
8,192 146.5 833.5 1,012.6
16,384 408.4 1,855.6 1,964.2
32,768 1,343.5 3,895.0 4,241.7
65,536 2,661.1 7,927.5 8,757.8
Using Visual Studio Express 2010.
CODE:
// ------------ QUICK SORT ------------------
template<typename T, typename key_compare>
void quicksort( T first, T last, const size_t pivot_index, key_compare comp ) {
T saved_first = first;
size_t N = last - first;
if (N > 1) {
// create a temp new array, which contains all items less than pivot
// on left and greater on right. With pivot value in between.
// vector<typename decltype(*T)> temp(N);
typename iterator_traits<T>::pointer temp = (typename iterator_traits<T>::pointer) malloc(sizeof(T)*N);
size_t left_index = 0, right_index = N - 1 ;
iterator_traits<T>::value_type pivot_val = *(first + pivot_index);
for(; first < saved_first + pivot_index; first++) {
if( !comp(*first, pivot_val) )
temp[right_index--] = *first;
else
temp[left_index++] = *first;
}
// skip the pivot value
// TODO: swap the pivot to end so we can have a single loop instead.
++first;
// do the rest
for(; first < last; first++) {
if( !comp(*first, pivot_val) )
temp[right_index--] = *first;
else
temp[left_index++] = *first;
}
if( right_index == left_index )
temp[left_index] = pivot_val;
else
temp[left_index+1] = pivot_val;
// recurse for left and right..
quicksort(temp, temp+left_index, left_index/2, comp);
quicksort(temp+left_index+1, temp+N, (N-right_index)/2, comp);
// return a concat'd array..
for(size_t i = 0; i < N; i++)
*saved_first++ = temp[i];
free(temp);
}
}
/*
** best, average, worst: n log n, n log n, n^2
** space: log n
*/
template<typename T, typename key_compare >
void quicksort( T first, T last, key_compare comp ) {
size_t pivot_index = (last - first) / 2;
quicksort( first, last, pivot_index, comp);
}
// ------------ QUICK with optimizations ------------------
/*
quicksort partition on range [first, last[ using predicate function as the comparator.
"mid" is in-out param, function uses mid as mid, and updates it before returning it with
current/new mid position after partitioning.
*/
template<typename T, typename key_compare >
void _partial_quicksort_partition( T first, T last, T& mid, key_compare comp ) {
T savedFirst = first;
typedef typename iterator_traits<T>::value_type _val_type;
size_t N = last - first;
_val_type *temp = (_val_type *) malloc((N*sizeof(_val_type)));
// move pivot to the end..
_val_type pivot_val = *mid;
std::swap(*mid, *(last - 1));
size_t left_index = 0, right_index = N - 1;
for( ; first != last - 1; first++ ) {
if( !comp(*first, pivot_val) )
temp[right_index--] = *first;
else
temp[left_index++] = *first;
}
assert( right_index == left_index );
temp[left_index] = pivot_val;
std::copy(temp, temp+N, savedFirst);
free(temp);
mid = savedFirst + left_index;
}
template<typename T, typename key_compare >
void _partial_quicksort( T first, T last, key_compare comp ) {
size_t s = last - first;
// sort only if the list is smaller than our limit.. else it's too small for
// us to bother.. caller would take care of it using some other stupid algo..
if( 16 > s ) {
// only one call to insertion_sort(), after whole array is partially sorted
// using quicksort().
// my_insertion_sort::insertion_sort(first, last, pred);
return ;
}
// select pivot.. use median 3
T mid = my_mixed_inplace_quicksort::median3(first, last - 1, s, comp);
// partition
_partial_quicksort_partition(first, last, mid, comp);
// recurse..
_partial_quicksort(first, mid, comp);
// tail recurse..
// TODO: tail recurse on longer partition..
_partial_quicksort(mid+1, last, comp);
}
template<typename T, typename key_compare >
void mixed_quicksort( T first, T last, key_compare pred ) {
_partial_quicksort(first, last, pred );
my_insertion_sort::insertion_sort(first, last, pred);
}
// ------------ "in place" QUICK with optimizations ------------------
/*
in place quicksort partition on range [first, last[ using predicate function as the comparator.
"mid" is in-out param, function uses mid as mid, and updates it before returning it with
current/new mid position after partitioning.
*/
template<typename T, typename key_compare >
void _partial_inplace_quicksort_partition( T first, T last, T& mid, key_compare comp ) {
typename iterator_traits<T>::value_type midVal = *mid;
// move pivot to end..
std::swap(*mid, *(last - 1));
mid = first;
// in-place quick sort:
for( ; first < last - 1; first++ ) {
if( comp(*first, midVal) ) {
std::swap(*first, *mid);
mid++;
}
}
// bring pivot to the mid..
std::swap(*mid, *(last - 1));
}
// brings best median to middle and returns it..
// works on array as [first, last] NOT [first, last[
template<typename T, typename key_compare >
T median3(T first, T last, size_t size, key_compare comp ) {
T mid = first + size/2;
if (comp(*mid, *first)) {
std::swap(*mid, *first);
}
if (comp(*last, *mid)) {
std::swap(*last, *mid);
}
if (comp(*mid, *first)) {
std::swap(*mid, *first);
}
return mid;
}
template<typename T, typename key_compare >
void _partial_inplace_quicksort( T first, T last, key_compare comp ) {
size_t s = last - first;
// sort only if the list is smaller than our limit.. else it's too small for
// us to bother.. caller would take care of it using some other stupid algo..
if( 16 > s ) {
// only one call to insertion_sort(), after whole array is partially sorted
// using quicksort().
// my_insertion_sort::insertion_sort(first, last, pred);
return ;
}
// select pivot.. use median 3
T mid = median3(first, last - 1, s, comp);
// partition
_partial_inplace_quicksort_partition(first, last, mid, comp);
// recurse..
_partial_inplace_quicksort(first, mid, comp);
// tail recurse..
_partial_inplace_quicksort(mid+1, last, comp);
// print_array(first, last, "_partial_inplace_quicksort(exit2)" );
}
// in-place quick sort
// tail recurse
// median
// final insertion sort..
template<typename T, typename key_compare >
void mixedsort_inplace( T first, T last, key_compare pred ) {
_partial_inplace_quicksort(first, last, pred );
my_insertion_sort::insertion_sort(first, last, pred);
}
// ---------------- INSERTION SORT used above ----------------
namespace my_insertion_sort {
template<typename T, typename key_compare>
void insertion_sort( T first, T last, key_compare comp ) {
// for each element in the array [first+1, last[
for( T j = first+1; j < last; j++) {
iterator_traits<T>::value_type curr = *j;
T hole = j;
// keep moving all the elements comp(hole.e. > or <) hole to right
while( hole > first && comp(curr, *(hole-1)) ) {
*hole = *(hole-1);
--hole;
}
// insert curr at the correct position.
*hole = curr;
}
}
}
Code used for testing:
#include <ctime>
#ifdef _WIN32
#include <Windows.h>
#include <WinBase.h>
#endif // _WIN32
template<typename T, typename key_compare = std::less<T>> class MySortAlgoTester;
template <typename T>
void print_array( T begin, T end, string prefix = "" ) {
cout << prefix.c_str();
for_each(begin, end, []( typename std::iterator_traits<T>::reference it) { cout << it << ','; } );
cout << endl;
}
int main () {
srand(123456789L);
size_t numElements = 4;
vector<char*> algoNames;
map<double, vector<double>> results;
int numTests = 0;
while( (numElements *= 2) <= 4096*16 ) {
MySortAlgoTester<int> tester(numElements);
results[numElements] = vector<double>();
algoNames.push_back("mixedsort_inplace");
results[numElements].push_back(tester.test(my_mixed_inplace_quicksort::mixedsort_inplace, "mixedsort_inplace"));
tester.reset();
algoNames.push_back("quick");
results[numElements].push_back(tester.test(my_quicksort::quicksort, "quicksort"));
tester.reset();
algoNames.push_back("mixed_quicksort");
results[numElements].push_back(tester.test(my_mixed_quicksort::mixed_quicksort, "mixed_quicksort"));
}
// --- print the results...
cout << std::setprecision(2) << std::fixed << endl << "N";
for_each(algoNames.begin(), algoNames.begin()+(algoNames.size()/numTests), [](char* s){cout << ',' << s ;} );
typedef std::pair<double,vector<double>> result_iter;
BOOST_FOREACH(result_iter it, results) {
cout << endl << it.first << ',';
BOOST_FOREACH( double d, it.second ) {
cout << d << ',' ;
}
}
template<typename T, typename key_compare = std::less<T>>
class MySortAlgoTester {
key_compare comp;
vector<T> vec;
typedef typename vector<T>::iterator vecIter;
vector<T> vec_copy;
size_t m_numElements;
bool is_sorted(vecIter first, vecIter last) {
vecIter sFirst = first;
for(vecIter next = first+1; next != last;)
// '>' associativity: left to right
// ++ has precedence over >
if( !comp(*(first++), *(next++)) ) {
if(*(next-1) == *(first-1))
continue;
print_array(sFirst, last, "is_sorted() returning false: ");
cout << "comp(" << *(first-1) << ", " << *(next-1) << ") = false && "
<< *(next-1) << " != " << *(first-1) << endl ;
return false;
}
return true;
}
public:
MySortAlgoTester(size_t numElements) : m_numElements(numElements) {
srand(123456789L);
vec.resize(m_numElements);
vec_copy.resize(m_numElements);
// std::generate(vec.begin(), vec.end(), rand);
for(size_t i = 0; i < vec.size(); i++) {
vec[i] = rand() % (m_numElements * 2);
vec_copy[i] = vec[i];
}
}
~MySortAlgoTester() {
}
void reset() {
// copy the data back so next algo can be tested with same array.
std::copy(vec_copy.begin(), vec_copy.end(), vec.begin());
for(size_t i = 0; i < vec_copy.size(); i++) {
vec[i] = vec_copy[i];
}
// std::copy(vec_copy.begin(), vec_copy.end(), vec);
}
double m___start_time_asdfsa = 0;
double getTimeInMicroSecs() {
#ifdef _WIN32
LARGE_INTEGER li;
if(!QueryPerformanceFrequency(&li))
cout << "getTimeInMicroSecs(): QueryPerformanceFrequency() failed!" << endl;
QueryPerformanceCounter(&li);
return double(li.QuadPart)/1000.0;
#else // _WIN32
struct timeval tv;
gettimeofday(&tv, NULL);
return tv.tv_usec + 10e6 * tv.tv_sec;
}
#endif // _WIN32
inline void printClock( const char* msg ) {
cout << msg << (long)(getTimeInMicroSecs() - m___start_time_asdfsa) << " micro seconds" << endl;
}
inline double getClock() {
return (getTimeInMicroSecs() - m___start_time_asdfsa);
}
inline void startClock() {
m___start_time_asdfsa = getTimeInMicroSecs();
}
double test( void (*sort_func)(typename vector<T>::iterator first, typename vector<T>::iterator last, typename key_compare pred), const char* name ) {
cout << "START Testing: " << name << ". With --- " << m_numElements << " elements." << endl;
startClock();
sort_func(vec.begin(), vec.end(), comp);
double ms = getClock();
if(!MySortAlgoTester::is_sorted(vec.begin(), vec.end())) {
cout << name << " did not sort the array." << endl;
// throw string(name) + " did not sort the array.";
}
cout << "DONE Testing: " << name << ". Time taken (ms): " << ms << endl;
return ms;
}
double test( void (*sort_func)(typename vector<T>::iterator first, typename vector<T>::iterator last), const char* name ) {
cout << "START Testing: " << name << ". With --- " << m_numElements << " elements." << endl;
startClock();
sort_func(vec.begin(), vec.end());
double ms = getClock();
if(!MySortAlgoTester::is_sorted(vec.begin(), vec.end())) {
cout << name << " did not sort the array." << endl;
// throw string(name) + " did not sort the array.";
}
cout << "DONE Testing: " << name << ". Time taken (ms): " << ms << endl;
return ms;
}
};
