插入，选择，归并，快速排序

插入排序：

插入排序在最坏情况和平均情况下时间复杂度是Θ(n²)

#include <stdio.h>
#define LEN 5

int a[LEN] = {10, 5, 2, 4, 7};

void print(void)
{
    for (int i = 0; i < LEN; i++)
        printf(" %d", a[i]);
    printf("
");
}

void insertion_sort(void) //该算法要求背诵
{
    int j, key;
    for (int i = 1; i < LEN; i++)
    {
        print();
        key = a[i];
        
        for (j = i - 1; j >= 0 && a[j] > key; j--)
            a[j + 1] = a[j];

        a[j + 1] = key;
    }
    print();
}

int main(void)
{
    insertion_sort();
    return 0;
}

选择排序：

#include <stdio.h>
#define LEN 5

int a[LEN] = {10, 5, 2, 4, 7};

void print(void)
{
    for (int i = 0; i < LEN; i++)
        printf(" %d", a[i]);
    printf("
");
}

void selection_sort(void) //该算法要求背诵
{
    int min, low;
    for (int i = 0; i < LEN - 1; i++)
    {
        print();
        min = a[i];
        low = i;
        for (int j = i + 1; j < LEN; j++)
        {
            if (a[j] < min)
            {
                min = a[j];
                low = j;
            }
        }
        a[low] = a[i];
        a[i] = min;
    }
    print();
}

int main(void)
{
    selection_sort();
    return 0;
}

归并排序：

 1 #include <stdio.h>
 2 #define LEN 8
 3 int a[LEN] = {5, 2, 4, 7, 1, 3, 2, 6};
 4 
 5 void merge(int start, int mid, int end)
 6 {
 7     int n1 = mid - start + 1; // mid - start + 1
 8     int n2 = end - mid;          // end - (mid+1) + 1
 9     int left[n1], right[n2];
10 
11     //分别将a数组的左半部分和右半部分，拷贝到left和right数组
12     for (int i = 0; i < n1; i++) /* left holds a[start..mid] */
13         left[i] = a[start + i];
14     for (int j = 0; j < n2; j++) /* right holds a[mid+1..end] */
15         right[j] = a[mid + 1 + j];
16 
17     //归并操作，将排序完毕的left和right中较小的切片拷贝到a数组
18     int i = 0, j = 0, k = start;
19     while (i < n1 && j < n2)
20     {
21         if (left[i] < right[j])
22         {
23             a[k] = left[i];
24             k++, i++; //这两条语句等价于a[k++] = left[i++];
25         }
26         else
27         {
28             a[k] = right[j];
29             k++, j++; //这两条语句等价于a[k++] = right[j++];
30         }
31     }
32 
33     //经过上一步的归并，将left或者right中剩余的部分拷贝至a数组
34     while (i < n1)            /* left[] is not exhausted */
35         a[k++] = left[i++];   /* 循环体的展开形式同上 */
36     while (j < n2)            /* right[] is not exhausted */
37         a[k++] = right[j++];
38 }
39 
40 void print(void)
41 {
42     for (int i = 0; i < LEN; i++)
43         printf(" %d", a[i]);
44     printf("
");
45 }
46 
47 void sort(int start, int end)
48 {
49     int mid;
50     if (start < end)
51     {
52         mid = (start + end) / 2;
53         printf("sort (%d-%d, %d-%d)", start, mid, mid + 1, end);
54         print();
55 
56         sort(start, mid);
57         sort(mid + 1, end);
58         merge(start, mid, end);
59 
60         printf("merge (%d-%d, %d-%d)", start, mid, mid + 1, end);
61         print();
62     }
63 }
64 
65 int main(int argc, char const *argv[])
66 {
67     sort(0, LEN - 1);
68     return 0;
69 }

快速排序：

 1 #include <stdio.h>
 2 #define LENGTH 8
 3 
 4 int a[LENGTH] = {5, 2, 4, 7, 1, 3, 8, 6};
 5 
 6 int partition(int, int);
 7 void quicksort(int, int);
 8 
 9 void quicksort(int start, int end)
10 {
11 
12     if (start < end)
13     {
14         int mid = partition(start, end);
15         quicksort(start, mid - 1);
16         quicksort(mid + 1, end);
17     }
18 }
19 
20 int partition(int start, int end)
21 {
22     int pivot = a[end];
23 
24     while (start < end)
25     {
26         while (start < end && a[start] <= pivot)
27             start++;
28         a[end] = a[start];
29 
30         while (start < end && a[end] >= pivot)
31             end--;
32         a[start] = a[end];
33     }
34 
35     a[start] = pivot;
36     return start;
37 }
38 
39 int main(int argc, char const *argv[])
40 {
41     for (int i = 0; i < LENGTH; i++)
42         printf(" %d", a[i]);
43     printf("
");
44 
45     quicksort(0, LENGTH - 1);
46 
47     for (int i = 0; i < LENGTH; i++)
48         printf(" %d", a[i]);
49     printf("
");
50 
51     return 0;
52 }