1098 Insertion or Heap Sort （25 point(s))

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?

Input Specification:

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.

Output Specification:

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.

Sample Input 1:

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

Sample Output 1:

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

Sample Input 2:

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

Sample Output 2:

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

题目大意：给一个原始序列，给一个目的序列，问你目的序列是由原始序列的插入排序还是堆排序得到的，输出排序方法并给出此方法对应的下一趟排序序列。

分析：就是让你模拟插入排序和堆排序的过程，每一趟排序得到序列与目的序列作比较即可

八大排序：戳这里

几个注意点：

（1）初始序列不参与比较,不然会有一个测试点过不了

（2）由于对第 i 位进行插入排序时，前 i-1 位已经有序，因此可以调用sort函数对前i位进行排序，减少代码量

（3）判断不是插入排序后记得还原数组，然后进行堆排序处理，因此原始数据要备份，这里开三个数组，分别存初始序列、中间序列、目的序列。

AC代码：

#include<bits/stdc++.h>
using namespace std;
const int N=1010;
int ori[N],temp[N],fin[N];
int n;
bool same(){
	for(int i=1;i<=n;i++){
		if(temp[i]!=fin[i])
		   return false;
	}
	return true;
}

void print(){
	int cnt=0;
	for(int i=1;i<=n;i++){
		cout<<temp[i];
		cnt++;
		if(cnt<n) cout<<" ";
		else cout<<endl;
	}
}

bool insert(){
	bool flag=false;
	for(int i=2;i<=n;i++){
		if(i!=2 && same()){ 
		    flag=true;
			cout<<"Insertion Sort\n";
			sort(temp,temp+i+1);
			print();		
		}
		sort(temp,temp+i+1);
	}
	if(flag) return true;
	else return false;
}
//向下调整 
void AdjustDown(int k,int len){
	temp[0]=temp[k];//缓存一下；
	for(int i=k*2;i<=len;i*=2){
		if(i<len && temp[i]<temp[i+1])
		   i++; //左右子树中选大 
		if(temp[0]>temp[i]) break;
		else{
			temp[k]=temp[i];
			k=i; //i向下调整 
		} 
	}
	temp[k]=temp[0]; 
}

//大根堆 堆排序
void HeadSort(){
	for(int i=n/2;i>=1;i--){
		AdjustDown(i,n);//建堆完成 
	}
	for(int i=n;i>=1;i--){
		if(i!=n && same()){ //初始序列不参与判断 
			cout<<"Heap Sort\n";
			swap(temp[i],temp[1]);
		    AdjustDown(1,i-1);
			print();
		} 
		swap(temp[i],temp[1]);
		AdjustDown(1,i-1);  //根节点向下调整 
	}
}

int main(){
	cin>>n;
	for(int i=1;i<=n;i++){
		cin>>ori[i];
		temp[i]=ori[i]; 
	}
	for(int i=1;i<=n;i++) cin>>fin[i]; 
	insert();
    //还原数组 
    for(int i=1;i<=n;i++) temp[i]=ori[i]; 
	HeadSort();
	return 0;
}