夯实基础——归并排序

逻辑结构：递归栈

物理结构：数组

归并排序分析：

最优时间复杂度：O(n)

最坏时间复杂度：O(nlog2n) 

平均时间复杂度：O(nlog2n)

最差空间复杂度：O(n) 

稳定性：稳定

归并排序主要有两个函数：

1 一次归并排序 int MergeArray(int *list1,int list1_size,int *list2,int list2_size);

2  递归归并排序 int MergeSort(int *list,int list_size);

3 非递归归并排序 int MergeSort(int *list,int list_size);

//一次归并排序int MergeArray(int *list1,int list1_size,int *list2,int list2_size){    int i,j,k,a;    i=j=k=0;    int *list=(int *)malloc(sizeof(int)*(list1_size+list2_size));    while(i<list1_size && j<list2_size)    {        if(*(list1+i) <= *(list2+j))        {            *(list+k) = *(list1+i);            i++;            k++;        }        else        {            *(list+k) = *(list2+j);            j++;            k++;        }    }    while(i < list1_size)    {        *(list+k) = *(list1+i);        i++;        k++;    }    while(j < list2_size)    {        *(list+k) = *(list2+j);        j++;        k++;    }    for(a=0;a<(list1_size+list2_size);a++)        *(list1+a)=*(list+a);    free(list);}

//递归归并排序int MergeSort(int *list,int list_size){    if(list_size>1)    {        int *list1=list;        int list1_size=list_size/2;        int *list2=list+list_size/2;        int list2_size=list_size-list1_size;        MergeSort(list1,list1_size);        MergeSort(list2,list2_size);        MergeArray(list1,list1_size,list2,list2_size);    }}

//非递归归并排序int NonMergeSort(int *list,int list_size){    int i,l_min,l_max,r_min,r_max,cursor;    int *aux = (int *)malloc(sizeof(int)*list_size);    for( i = 1 ;i < list_size; i *= 2)    {        for(l_min = 0; l_min < list_size - i; l_min = r_max)        {                r_min = l_max = l_min + i ;                r_max = l_max + i;                if(r_max > list_size)                    r_max = list_size;                cursor = 0;                while(l_min < l_max && r_min < r_max)                {                    if(list[l_min] <= list[r_min])                    {                        aux[cursor++] = list[l_min++];                    }                    else                    {                        aux[cursor++] = list[r_min++];                    }                }                while(l_min < l_max)                    aux[cursor++] = list[l_min++];                while(r_min < r_max)                    aux[cursor++] = list[r_min++];                while( cursor > 0 )                    list[--r_min] = aux [--cursor];        }    }    free(aux);}

//非递归归并排序int NonMergeSort1(int *list , int length){    int i, left_min, left_max, right_min, right_max, next;    int *tmp = (int*)malloc(sizeof(int) * length);    if (tmp == NULL)    {        fputs("Error: out of memory\n", stderr);        abort();    }    for (i = 1; i < length; i *= 2)    {        for (left_min = 0; left_min < length - i; left_min = right_max)        {            right_min = left_max = left_min + i;            right_max = left_max + i;            if (right_max > length)                right_max = length;            next = 0;            while (left_min < left_max && right_min < right_max)                tmp[next++] = list[left_min] > list[right_min] ? list[right_min++] : list[left_min++];            while (left_min < left_max)                list[--right_min] = list[--left_max];            while (next > 0)                list[--right_min] = tmp[--next];        }    }    free(tmp);}