Question

在我的编译器和mergesort的实现上比较我的quicksort实现和std :: sort时，我注意到大数据集上有一个奇怪的模式：当操作64位整数时，quicksort始终比mergesort快;但是，在较小的int大小上，quicksort变慢，mergesort变得更快。

以下是测试代码：

#include <iostream>
#include <vector>
#include <iterator>
#include <algorithm>
#include <utility>
#include <random>
#include <chrono>
#include <limits>
#include <functional>

#include <cstdint>


template <typename Iterator>
void insertion_sort(Iterator first, Iterator last)
{
    using namespace std;

    Iterator head = first;
    Iterator new_position;

    while(head != last)
    {
        new_position = head;
        while(new_position != first && *new_position < *prev(new_position))
        {
            swap(*new_position, *prev(new_position));
            --new_position;
        }
        ++head;
    }
}

template <typename Iterator>
void recursive_mergesort_impl(Iterator first, Iterator last, std::vector<typename Iterator::value_type>& temp)
{
    if(last - first > 32)
    {
        auto middle = first + (last-first)/2;
        recursive_mergesort_impl(first, middle, temp);
        recursive_mergesort_impl(middle, last, temp);
        auto last_merged = merge_move(first, middle, middle, last, temp.begin());
        std::move(temp.begin(), last_merged, first);
    }
    else
    {
        insertion_sort(first, last);
    }
}

template <typename Iterator>
void recursive_mergesort(Iterator first, Iterator last)
{
    std::vector<typename Iterator::value_type> temp(last-first);
    recursive_mergesort_impl(first, last, temp);
}

// Pick a pivot and move it to front of range
template <typename Iterator>
template <typename Iterator>
void quicksort_pivot_back(Iterator first, Iterator last)
{
    using namespace std;

    auto middle = first + (last-first)/2;
    auto last_elem = prev(last);
    Iterator pivot;

    if(*first < *middle)
    {
        if(*middle < *last_elem)
            pivot = middle;
        else if(*first < *last_elem)
            pivot = last_elem;
        else
            pivot = first;
    }
    else if(*first < *last_elem)
        pivot = first;
    else if(*middle < *last_elem)
        pivot = last_elem;
    else
        pivot = middle;

    swap(*last_elem, *pivot);
}

template <typename Iterator, typename Function>
std::pair<Iterator, Iterator> quicksort_partition(Iterator first, Iterator last, Function pivot_select)
{
    using namespace std;

    pivot_select(first, last);

    auto pivot = prev(last);
    auto bottom = first;
    auto top = pivot;

    while(bottom != top)
    {
        if(*bottom < *pivot) ++bottom;
        else swap(*bottom, *--top);
    }

    swap(*pivot, *top++);

    return make_pair(bottom, top);
}

template <typename Iterator>
void quicksort_loop(Iterator first, Iterator last)
{
    using namespace std;

    while(last - first > 32)
    {
        auto bounds = quicksort_partition(first, last, quicksort_pivot_back<Iterator>);

        quicksort_loop(bounds.second, last);
        last = bounds.first;
    }
}


template <typename Iterator>
void quicksort(Iterator first, Iterator last)
{
    quicksort_loop(first, last);
    insertion_sort(first, last);
}

template <typename IntType = uint64_t, typename Duration = std::chrono::microseconds, typename Timer = std::chrono::high_resolution_clock, typename Function, typename Generator>
void run_trial(Function sort_func, Generator gen, std::string name, std::size_t trial_size, std::size_t trial_count)
{
    using namespace std;
    using namespace chrono;

    vector<IntType> data(trial_size);

    Duration elapsed(0);

    cout << "Sorting with " << name << endl;

    for(unsigned int i = 0; i < trial_count; ++i)
    {
        generate(data.begin(), data.end(), gen);

        auto start = Timer::now();
        sort_func(data.begin(), data.end());
        auto finish = Timer::now();

        elapsed += duration_cast<Duration>(finish-start);
    }

    cout << "Done. Average elapsed time: " << elapsed.count() / trial_count << endl;
    cout << "Is correct: " << is_sorted(data.begin(), data.end()) << endl << endl;
}

int main()
{
    using namespace std;
    using namespace chrono;

    using int_type = uint64_t;
    const size_t trial_size = 12800000;
    const int trial_count = 15;

    vector<int_type> data(trial_size);
    uniform_int_distribution<int_type> distr;
    mt19937_64 rnd;

    run_trial<int_type>(recursive_mergesort<vector<int_type>::iterator>, bind(distr, rnd), "recursive mergesort", trial_size, trial_count);
    run_trial<int_type>(quicksort<vector<int_type>::iterator>, bind(distr, rnd), "quicksort", trial_size, trial_count);
    run_trial<int_type>(sort<vector<int_type>::iterator>, bind(distr, rnd), "std::sort", trial_size, trial_count);
}

以下是来自12个12800000元素的15次试验的时间：

uint64_t：

Sorting with recursive mergesort
Done. Average elapsed time: 1725431
Is correct: 1

Sorting with quicksort
Done. Average elapsed time: 1238070
Is correct: 1

Sorting with std::sort
Done. Average elapsed time: 1131464
Is correct: 1

uint16_t：

Sorting with recursive mergesort
Done. Average elapsed time: 1186467
Is correct: 1

Sorting with quicksort
Done. Average elapsed time: 2368535
Is correct: 1

Sorting with std::sort
Done. Average elapsed time: 888517
Is correct: 1

我有一种感觉，问题与未对齐的内存访问有关，但是这仍然让我想知道为什么其他算法在快速排序变慢的同时获得加速。

Answer 1

使用uint16_t，您将在如此庞大的数组中获得大量重复项：期望值为195，每次出现的次数为0到65535。如果没有three-way ("fat") partition，或者至少有一个返回子矩阵中重复出现的中间，则会导致快速排序变为二次方。（尝试在只有零的数组上执行简单快速排序的铅笔和纸张，以查看效果。）

手写编码的快速排序在较小的整数上较慢

1 个答案: