排序算法之简单选择排序和堆排序

每一趟在n-i+1个记录中选取关键字最小的记录，并与当前序列中的第i个记录交换，作为有序序列中第i个记录

#include <stdio.h>
#include <stdlib.h>
#include <limits.h>
#define MAXSIZE 20
typedef int KeyType;
typedef int InfoType;

typedef struct
{
    KeyType key;
    InfoType otherinfo;
}RedType;

typedef struct
{
    RedType r[MAXSIZE+1];
    int length;
}SqList;
int LT(KeyType a,KeyType b);
void Swap(SqList *L,int low,int high);
void SelectSort(SqList *L);
int SelectMinKey(SqList *L,int i);
void HeapAdjust(SqList *L,int s,int m);
void HeapSort(SqList *L);

int main()
{
    SqList *L,*L1,*L2,*L3,*L4;
    L=(SqList *)malloc(sizeof(SqList));
    L1=(SqList *)malloc(sizeof(SqList));
    L2=(SqList *)malloc(sizeof(SqList));
    L3=(SqList *)malloc(sizeof(SqList));
    L4=(SqList *)malloc(sizeof(SqList));

    int i;
    printf("需排序的项数为：");
    scanf("%d",&L->length);

    for(i=0;i<L->length;i++)
    {
        printf("please input the number:");
        scanf("%d",&L->r[i+1].key);
    }
    *L1=*L2=*L3=*L4=*L;

    SelectSort(L1);
    HeapSort(L2);
    printf("选择排序的结果:");
    for(i=0;i<L1->length;i++)
    {
        printf("%d ",L1->r[i+1].key);
    }
    printf("\n");
    printf("堆排序的结果:");
    for(i=0;i<L2->length;i++)
    {
        printf("%d ",L2->r[i+1].key);
    }
    printf("\n");

    return 0;
}
int LT(KeyType a,KeyType b)
{
    return a<b;
}

void Swap(SqList *L,int low,int high)
{
    RedType *t;
    t=(RedType *)malloc(sizeof(RedType));
    *t=L->r[low];
    L->r[low]=L->r[high];
    L->r[high]=*t;
    free(t);
}
/*简单选择排序，时间复杂度为n^2*/
void SelectSort(SqList *L)
{
    int i,j;
    for(i=1;i<L->length;i++)
    {
        j=SelectMinKey(L,i);
        if(i!=j)
            Swap(L,i,j);
    }
}
int SelectMinKey(SqList *L,int i)
{
    int k,t=i;
    for(k=i+1;k<=L->length;k++)
        if(L->r[t].key>L->r[k].key)
            t=k;
    return t;
}
/*树形选择排序/锦标赛排序*/
/*时间复杂度为nlogn，但是所需辅助空间较多，因此提出另一种堆排序*/

/*堆排序：即使最坏情况下，时间复杂度为nlogn*/
/*筛选：即s至m序列中，除s外均满足堆定义，将s自顶向下调整，以满足堆定义*/
void HeapAdjust(SqList *L,int s,int m)
{
    int j;
    RedType rc;
    rc=L->r[s];
    for(j=2*s;j<=m;j*=2)
    {
        if(j<m && LT(L->r[j].key,L->r[j+1].key))
            j++;
        if(!LT(rc.key,L->r[j].key))
            break;
        L->r[s]=L->r[j];
        s=j;
    }
    L->r[s]=rc;
}

void HeapSort(SqList *L)
{
    int i;
    for(i=L->length/2;i>0;i--)
        HeapAdjust(L,i,L->length);
    for(i=L->length;i>1;i--)
    {
        Swap(L,1,i);
        HeapAdjust(L,1,i-1);
    }
}