1098. Insertion or Heap Sort (25)

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 resuling 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

---

与89题类似，判断第二个序列是由第一个序列经过插入排序得到的还是经过堆排序得到的（还没有完全排好序），并进行下一步的排序。插入排序的特点是后面还没排序的部分和原序列的那部分是一样的，符合这个特点的是插入排序，不符合的是堆排序。为了偷懒，直接用stl的函数进行下一步的排序。如果是插入排序，计算当前已排序的个数，用sort函数排序多一个。如果是堆排序，因为堆的根节点（序列第一个数）是最大的，后面比它大的数看作已经pop出去了，所以忽略掉后面比根节点大的数，对子序列进行一次pop_heap操作。最后输出序列即可。

代码：

#include <iostream>
#include <cstring>
#include <cstdio>
#include <cstdlib>
#include <vector>
#include <algorithm>
using namespace std;

void printvec(vector<int>vec)
{
	printf("%d",vec[0]);
	for(int i=1;i<vec.size();i++)
	{
		printf(" %d",vec[i]);
	}
	printf("\n");
}

int main()
{
	int n,i;
	cin>>n;
	vector<int>a(n);
	vector<int>b(n);
	for(i=0;i<n;i++) 
	{
		cin>>a[i];
	}
	for(i=0;i<n;i++) 
	{
		cin>>b[i];
	}

	int idx=1;
	while(b[idx]>=b[idx-1]) idx++;
	i=idx;
	while(b[i]==a[i]&&i<n) i++;
	if(i==n)
	{
		printf("Insertion Sort\n");
		sort(b.begin(),b.begin()+idx+1);
		printvec(b);
	}
	else 
	{
		printf("Heap Sort\n");
		for(i=n-1;i>=0;i--)
		{
			if(b[i]<b[0]) break; 
		}
		pop_heap(b.begin(),b.begin()+i+1);
		printvec(b);
	}
}