排序算法-归并排序

1.归并排序

归并排序是将一组数据分成若干个数组进行排序，排序后的若干数组合并成一个有序的数组。

两路归并算法的基本思路：设两个有序的数组放在同一向量中的相邻的位置上，A[low...mid],A[m+1...hight],先将他们合并到一个局部的暂存向量Temp中，将合并后存储在临时变量复制回A[low,hight]中。

a.分解：将当前区间一分为二，

b.求解：递归地对两个子区间A[low...mid]和A[mid+1...hight]进行归并排序。

c.组合：将已排序的两个子区间合并为一个区间

d.递归结束的条件：子区间的长度为1

代码实现

//归并排序

void merge(int *arr, int low, int mid, int hight)

{
int *temp = (int *)malloc(sizeof(int)*(hight - low + 1));
int left_low = low;
int left_end = mid ;
int hight_low = mid+1;
int hight_end = hight;
int i = 0;
int len = hight - low + 1;
while (left_low <= left_end && hight_low<=hight_end)
{
if (arr[left_low] <= arr[hight_low])
{
temp[i++] = arr[left_low++];
}
else
{
temp[i++] = arr[hight_low++];
}
}
while (left_low <= left_end)
{
temp[i++] = arr[left_low++];
}
while (hight_low <= hight_end)
{
temp[i++] = arr[hight_low++];
}
for (int k = 0; k < len; k++)
{
arr[k+low] = temp[k];
}

}

void merge_sort(int *arr, int low, int hight)

{
if (low < hight)
{
int mid = (low + hight) / 2;
merge_sort(arr, low, mid);
merge_sort(arr, mid+1, hight);
merge(arr, low, mid, hight);
}
return;

}

//打印数组

void print_sort(int *arr, int len)

{
for (int i = 0; i < len; i++)
{
printf("%d  ", arr[i]);
}
printf("\n");

}

void main()

{
int arr[] = { 3, 2, 9, 7, 11, 4, 5, 0 };
int len = sizeof(arr)/sizeof(arr[0]);
printf("len is %d\n", len);
merge_sort(arr, 0, len - 1);
print_sort(arr, len);
system("pause");

}