快速排序与合并排序性能分析

合并排序的最坏情况复杂度为O(logN),而快速排序的最坏情况复杂度为O(N^2),因此理论上,合并排序应该比快速排序性能更好。但我听说,由于一些复制开销,大多数情况下,快速排序优于合并排序。 See the reference .

然后我决定实现和测试,下面是我用C语言编写的完整源代码,

#include <stdio.h>
#include <time.h>

#define SZ 10000000
#define MOD 10000007
#define i64 long long int

i64 nums[SZ];

i64 L[SZ], R[SZ];

i64 seed = 0xff;
i64 srand(){
    seed = (seed + 17 * seed) % MOD;
    return seed;
}

void make(){
    for (register int i = 0; i < SZ; i++)
        nums[i] = srand() % MOD;
}

void swap(i64 *a, i64 *b){
    i64 t = *a;
    *a = *b;
    *b = t;
}

int pivote(int s, int e){

    //int p = s + srand() % (e - s + 1);
    int p = s + (e - s) / 2;
    //int p = s;
    //int p = e;

    i64 v = nums[p];
    int c = s;
    swap(nums + p, nums + e);
    for (register int i = s; i < e; i++){
        if (nums[i] < v){
            swap(nums + i, nums + c);
            c++;
        }
    }
    swap(nums + c, nums + e);
    return c;
}

void qsort(int s, int e){

    if (s < e){
        int p = pivote(s, e);
        qsort(s, p - 1);
        qsort(p + 1, e);
    }
}

void merge(i64 arr[], int l, int m, int r){
    int i, j, k;
    int n1 = m - l + 1;
    int n2 = r - m;

    for (i = 0; i < n1; i++)
        L[i] = arr[l + i];
    for (j = 0; j < n2; j++)
        R[j] = arr[m + 1 + j];

    i = 0;
    j = 0;
    k = l;
    while (i < n1 && j < n2)
    {
        if (L[i] <= R[j])
        {
            arr[k] = L[i];
            i++;
        }
        else
        {
            arr[k] = R[j];
            j++;
        }
        k++;
    }

    while (i < n1)
    {
        arr[k] = L[i];
        i++;
        k++;
    }

    while (j < n2)
    {
        arr[k] = R[j];
        j++;
        k++;
    }
}

void mergeSort(i64 arr[], int l, int r){
    if (l < r){
        int m = l + (r - l) / 2;

        mergeSort(arr, l, m);
        mergeSort(arr, m + 1, r);
        merge(arr, l, m, r);
    }
}


void testQsort(){
    double s, e;

    make();

    s = clock();
    qsort(0, SZ - 1);
    e = clock();
    printf("qsort random: %Lf ms\n", (e - s) / 1);

    s = clock();
    qsort(0, SZ - 1);
    e = clock();
    printf("qsort sorted: %Lf ms\n", (e - s) / 1);

}

void testMsort(){
    double s, e;

    make();

    s = clock();
    mergeSort(nums, 0, SZ - 1);
    e = clock();
    printf("msort random: %Lf ms\n", (e - s) / 1);

    s = clock();
    mergeSort(nums, 0, SZ - 1);
    e = clock();
    printf("msort sorted: %Lf ms\n", (e - s) / 1);
}

int main(){

    testMsort();
    testQsort();

    return 0;
}

1000万个元素的结果:

msort random: 4596.000000 ms
msort sorted: 3354.000000 ms
qsort random: 7637.000000 ms
qsort sorted: 5074.000000 ms

• 在第一个位置旋转
• 在最后一个位置旋转
• 中间位置转动

没有一个版本的快速排序似乎优于合并排序。 有人能告诉我为什么提到快速排序优于合并排序吗?

void qsort3(int s, int e){
    if (s < e){
        i64 p = nums[(s + e) / 2];
        int i = s - 1;
        int j = e + 1;
        while (true){
            while (nums[++i] < p);
            while (nums[--j] > p);
            if (i >= j) break;
            swap(nums + i, nums + j);
        }
        qsort3(s, j);
        qsort3(j + 1, e);
    }
}