PAT A1098 Insertion or Heap Sort (25 分)

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

思路：
就是判断初始序列排成目的序列是通过插入排序实现还是通过堆排来实现的，并且给出目的序列的下一轮序列，只需要实现一下堆排和插排即可，当然也可以简便采用sort函数来实现，本处采用最基础实现排序方式去做。
注意点：堆是一棵完全二叉树，所以采用数组下标来存的时候尽量从下标1开始，所以初始序列都从1开始存。

AC代码：

#include <iostream>
#include <vector>
using namespace std;
const int N=110;
vector<int> q1,q2,ans,temp;
bool tag;
int n;

bool insertSort() {
	tag=false;
	for(int i=2; i<temp.size(); i++) {
		int pos=i-1,val=temp[i];
		while(pos>0) {
			if(temp[i]<temp[pos]) pos--;
			else break;
		}
		pos++;
		for(int j=i-1; j>=pos; j--)
			temp[j+1]=temp[j];
		temp[pos]=val;
		if(tag) {
			ans=temp;
			return true;
		}
		if(temp==q2) tag=true;
	}
	return false;
}

void downCast(int up,int down) {
	int i=up,j=i*2;
	while(j<=down) {
		if(j+1<=down&&q1[j+1]>q1[j]) j=j+1;
		if(q1[j]>q1[i]) {
			swap(q1[i],q1[j]);
			i=j;
			j=j*2;
		} else break;
	}
}

void buildHeap() {//建立初始大根堆
	for(int i=n/2; i>0; i--) {
		downCast(i,n);
	}
}

void heapSort() {
	tag=false;
	buildHeap();
	for(int i=n; i>1; i--) {
		swap(q1[i],q1[1]);
		downCast(1,i-1);
		if(tag) {
			ans=q1;
			return;
		}
		if(q1==q2) tag=true;
	}
}

void Print() {
	for(int i=1; i<ans.size(); i++) {
		printf("%d",ans[i]);
		if(i<ans.size()-1) printf(" ");
		else printf("\n");
	}
}

int main() {
	cin>>n;
	q1.resize(n+1);
	q2.resize(n+1);
	for(int i=1; i<=n; i++) scanf("%d",&q1[i]);
	for(int i=1; i<=n; i++) scanf("%d",&q2[i]);
	temp=q1;
	if(insertSort()) printf("Insertion Sort\n");
	else {
		heapSort();
		printf("Heap Sort\n");
	}
	Print();
	return 0;
}