快速排序

　　快速排序是一种时间复杂度不太稳定的排序算法，是一种分治思想的排序算法。

　　这篇就谈一下随机化版本的快速排序的问题，所以快排就给个代码，表示学过了：

/**
 *    快速排序(QuickSort)
 */
#include <stdio.h>

static int SortByParts(int* nums, int prev, int rear)
{
    int i, j;
    int temp;
    int x = nums[rear];

    j = prev - 1;
    for(i = prev; i < rear; i++)
    {
        if(nums[i] < x)
        {
            temp = nums[i];
            nums[i] = nums[++j];
            nums[j] = temp;
        }
    }
    temp = nums[rear];
    nums[rear] = nums[j + 1];
    nums[j + 1] = temp;

    return j + 1;
}

void QuickSort(int* nums, int prev, int rear)
{
    int n;

    if(prev < rear)
    {
        n = SortByParts(nums, prev, rear);
        QuickSort(nums, prev, n - 1);
        QuickSort(nums, n + 1, rear);
    }
}

int main()
{
    int arr[] = {2,8,7,1,3,5,6,4}, *nums = arr;
    int i;

    QuickSort(nums, 0, sizeof(arr)/sizeof(int) - 1);
    for(i = 0; i < sizeof(arr)/sizeof(int); i++)
        printf("%d ", arr[i]);
    printf("
");

    return 0;
}

 　　随机化版本的快速排序，我比较迷惑的是产生随机数代码的地方，先看看代码（注释的部分）：

#include <cstdio>
#include <cstdlib>
#include <ctime>

static int Random();
static int RandomizedControl();
static int ArrayByParts();
void QuickSort();

static int Random(int prev, int rear)
{
    return prev + rand()%(rear + 1 - prev);        // 为什么不能是 rand()%(rear + 1 - prev) or rand()%(rear + 1)?
}

static int RandomizedControl(int* nums, int prev, int rear)
{
    int i = Random(prev, rear);
    int temp;

    temp = nums[i];
    nums[i] = nums[rear];
    nums[rear] = temp;

    return ArrayByParts(nums, prev, rear);
}

static int ArrayByParts(int* nums, int prev, int rear)
{
    int x = nums[rear];
    int temp;
    int i, j;

    j = prev - 1;
    for(i = prev; i < rear; i++)
    {
        if(nums[i] < x)
        {
            temp = nums[i];
            nums[i] = nums[++j];
            nums[j] = temp;
        }
    }
    temp = nums[rear];
    nums[rear] = nums[j + 1];
    nums[j + 1] = temp;

    return j + 1;
}

void QuickSort(int * nums, int start, int end)
{
    int mid;

    if(start < end)
    {
        mid = RandomizedControl(nums, start, end);
        QuickSort(nums, start, mid - 1);
        QuickSort(nums, mid + 1, end);
    }
}

int main(void)
{
    int arr[] = {13,-3,-25,20,-16,-23,18,-7,12,-5,-22,15,-4,7}, * nums = arr;
    int i;

    srand(time(NULL));

    QuickSort(nums, 0, sizeof(arr)/sizeof(int) - 1);

    for(i = 0; i < sizeof(arr)/sizeof(int); i++)
        printf("%d ", arr[i]);
    printf("
");

    return 0;
}

　　简版：

#include<bits/stdc++.h>
using namespace std;
#define ll long long
const int N = 100010;
void quicksort(int num[], int s, int e)
{
    if (s < e)
    {
        srand(time(NULL));
        int t = s + rand()%(e + 1 - s);
        swap(num[t], num[e]);
        int j = s - 1, x = num[e];
        for (int i = s; i < e; i++)
            if (num[i] < x)
                swap(num[i], num[++j]);
        swap(num[j + 1], num[e]);
        quicksort(num, s, j);
        quicksort(num, j + 2, e);
    }
}
int main()
{
    int num[N], n;
    cin >> n;
    for (int i = 0; i < n; i++)
        cin >> num[i];
    quicksort(num, 0, n - 1);
    for (int i = 0; i < n; i++)
        cout << num[i] << ' ';
    return 0;
}

　　尾递归版：

#include<bits/stdc++.h>
using namespace std;
#define ll long long
const int N = 100010;
void quicksort(int num[], int s, int e)
{
    while (s < e)
    {
        srand(time(NULL));
        int t = s + rand()%(e + 1 - s);
        swap(num[t], num[e]);
        int j = s - 1, x = num[e];
        for (int i = s; i < e; i++)
            if (num[i] < x)
                swap(num[i], num[++j]);
        swap(num[j + 1], num[e]);
        quicksort(num, s, j);
        s = j + 1;
    }
}
int main()
{
    int num[N], n;
    cin >> n;
    for (int i = 0; i < n; i++)
        cin >> num[i];
    quicksort(num, 0, n - 1);
    for (int i = 0; i < n; i++)
        cout << num[i] << ' ';
    return 0;
}