Insertion or Heap Sort (25分)【C语言】

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题目：

According to Wikipedia:
Insertion sort iterates, consuming one input element each repetition, and growing a sorted output list. Each iteration, insertion sort removes one element from the input data, finds the location it belongs within the sorted list, and inserts it there. It repeats until no input elements remain.
Heap sort divides its input into a sorted and an unsorted region, and it iteratively shrinks the unsorted region by extracting the largest element and moving that to the sorted region. it involves the use of a heap data structure rather than a linear-time search to find the maximum.
Now given the initial sequence of integers, together with a sequence which is a result of several iterations of some sorting method, can you tell which sorting method we are using?

输入格式

Each input file contains one test case. For each case, the first line gives a positive integer N (≤100). Then in the next line, N integers are given as the initial sequence. The last line contains the partially sorted sequence of the N numbers. It is assumed that the target sequence is always ascending. All the numbers in a line are separated by a space.

输出格式

For each test case, print in the first line either “Insertion Sort” or “Heap Sort” to indicate the method used to obtain the partial result. Then run this method for one more iteration and output in the second line the resulting sequence. It is guaranteed that the answer is unique for each test case. All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line.

输入样例

10
3 1 2 8 7 5 9 4 6 0
1 2 3 7 8 5 9 4 6 0

输出样例

Insertion Sort
1 2 3 5 7 8 9 4 6 0

输入样例

10
3 1 2 8 7 5 9 4 6 0
6 4 5 1 0 3 2 7 8 9

输出样例

Heap Sort
5 4 3 1 0 2 6 7 8 9

算法

问题分析

判断是否是插入排序
如何进行下一步堆排序

用原始数据，一次一次生成堆排序序列，和已经存在的队列对比。当发现符合时，再进行一步。

代码实现

typedef int ElementType;
int main()
{	int N;scanf("%d",&N);ElementType * A=(ElementType*)malloc(sizeof(ElementType)*N);ElementType * B=(ElementType*)malloc(sizeof(ElementType)*N);int i;for(i=0;i<N;i++){scanf("%d",&(A[i]));}for(i=0;i<N;i++){scanf("%d",&(B[i]));}int Is=IsInsertion(A,B,N);if(Is>1){printf("Insertion Sort\n");int Temp=B[Is];for(i=Is;i>0&&(B[i-1]>Temp);i--){B[i]=B[i-1];}B[i]=Temp;}else{printf("Heap Sort\n");int flag=0;int t=N;do{HeapSort(A,t);for(i=0;i<N;i++){if(A[i]!=B[i]){t--;break;}if(i==N-1){flag=1;}}}while(flag==0);HeapSort(A,t-1);for(i=0;i<N;i++){B[i]=A[i];}}for(i=0;i<N;i++){printf("%d",B[i]);if(i!=N-1){printf(" ");}}return 0;
}

HeapSort函数：一趟堆排序

void HeapSort(ElementType A[],int N)
{static flag=0;if(flag==0){BuildMaxHeap(A,N);flag=1; }ElementType T=A[0];A[0]=A[N-1];A[N-1]=T;PerDown(A,N-1,0);
}

PerDown、BuildMaxHeap函数：下滤和生成最大堆

void PerDown(ElementType A[],int N,int Add)
{//child=2*parent+1; ElementType T=A[Add];int parent=Add;int child;for(;parent*2+1<=N-1;parent=child){child=parent*2+1;if(child<N-1&&A[child+1]>A[child]){child+=1;}if(A[child]<=T){break;};A[parent]=A[child];}A[parent]=T;
}
void BuildMaxHeap(ElementType A[],int N)
{int i;for(i=N/2-1;i>-1;i--){PerDown(A,N,i);}
}

IsInsertion函数：判断是否是插入函数

int IsInsertion(ElementType A[],ElementType B[],int N)
{int i;int ret=0;for(i=1;i<N;i++){if(B[i]<B[i-1]){ret=i;break;}}for(i=ret;i<N;i++){if(A[i]!=B[i]){ret=0;}}return ret;
}