PAT-1098(Insertion Or Heap Sort)

　　题目链接见这里

　　分析:考察的是插入排序和堆排序两种基本的数据结构,注意利用两种排序的基本特征----插入排序不影响全局,而堆排序影响全局

#include <stdio.h>
#define SWAP(a,b) a = b-a+(b=a) 
#define N 105 
 
void Input(int *unSorted, int partialSorted[], int *n){
    int i;
    scanf("%d",n);
    for(i=1;i<=*n;i++) scanf("%d",&unSorted[i]);
    for(i=1;i<=*n;i++) scanf("%d",&partialSorted[i]);
}
 
void AdjustDown(int *partialSorted, int k, int n){
    //将元素k向下进行调整
    int i;
    partialSorted[0] = partialSorted[k]; //partialSorted[0]暂存
    for(i=2*k;i<=n;i*=2){ //沿key较大的子结点向下筛选
        if(i<n && partialSorted[i]<partialSorted[i+1]) 
            i ++; //取key值较大的子结点的下标
        if(partialSorted[0]>=partialSorted[i]) break; //筛选结束
        else{
            partialSorted[k] = partialSorted[i]; //将partialSorted[i]调整到双亲结点上
            k = i; //修改k值,以便继续向下筛选
        } 
    } 
    partialSorted[k] = partialSorted[0]; //被筛选结点的值放入最终的位置 
} 
 
void BuildMaxHeap(int *partialSorted, int n){
    int i = n/2;
    for(;i>0;i--) //从i=[n/2]~1,反复调整堆
        AdjustDown(partialSorted,i,n); 
}
 
int HeapSort(int *unSorted, int *partialSorted, int n){  
    int index = n;
    for(;index>1 && partialSorted[index-1]<=partialSorted[index];index--);
    //进入下一次迭代 
    BuildMaxHeap(partialSorted,index); //asending:大顶堆
    SWAP(partialSorted[index],partialSorted[1]); //输出堆顶元素(和堆底元素交换) 
    AdjustDown(partialSorted,1,index-1); //整理,把剩余的index-2个元素整理成堆
    printf("Heap Sort\n"); 
}
 
int InsertionSort(int unSorted[], int partialSorted[], int n){
    int i,j,index,low,high,mid;
    for(i=1;i<n && partialSorted[i]<=partialSorted[i+1];i++);
    index = ++i;
    for(;i<=n && unSorted[i]==partialSorted[i];i++);
    if(i>n){
        //折半插入(稳定) 
        partialSorted[0] = partialSorted[index]; //暂存partialSorted[index] 
        low = 1, high = index-1;
        while(low<=high){
            mid = (low+high)/2; //取中间点 
            if(partialSorted[mid]>partialSorted[0]) high = mid-1; //查找左半子表 
            else low = mid+1; //查找右半子表 
        }
        for(j=index-1;j>=high+1;j--)
            partialSorted[j+1] = partialSorted[j]; //统一后移元素,空出插入位置
        partialSorted[high+1] = partialSorted[0];
        printf("Insertion Sort\n");
        return 1;
    }   
    return 0;
}
 
void Show(int partialSorted[], int n){
    int i;
    for(i=1;i<=n;i++){
        printf("%d",partialSorted[i]);
        if(i==n) printf("\n");
        else printf(" ");
    }
}
 
int main(){
    int unSorted[N],partialSorted[N];
    int n;
//  freopen("Data.txt","r",stdin); //段错误 
    Input(unSorted,partialSorted,&n);
    //模拟来判断unSorted和partialSorted相等是非常愚蠢的行为 
    //运用一下堆排序和插入排序的特征,处理问题更快捷 
    //先做插入排序的判断,然后进行堆排序
    //插入排序不影响全局,而堆排序影响全局(亦即无法根据特征性质判断是否为堆排序)
    if(InsertionSort(unSorted,partialSorted,n));
    else HeapSort(unSorted,partialSorted,n);
    Show(partialSorted,n);
    return 0;
}