PAT (Advanced Level) Practise 1098 Insertion or Heap Sort (25)

1098. Insertion or Heap Sort (25)

时间限制

100 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

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

题意：给你一个原始序列和一个经过一些步骤后的序列，问这个序列是原始序列通过插入排序还是堆排序形成的，并输出下一步形成的序列

解题思路：插入排序前面部分是有序的，后面是和原序列一样的，堆排序是后面部分是有序的，序列的第一个是前面部分最大的，插入排序下一步可以通过sort直接完成，堆排序需要将前面部分的第一个和最后一个交换，然后调整

#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <cmath>

using namespace std;

#define LL long long
const int INF = 0x3f3f3f3f;

int n,a[105],b[105];

int main()
{
    while(~scanf("%d",&n))
    {
        for(int i=1; i<=n; i++) scanf("%d",&a[i]);
        for(int i=1; i<=n; i++) scanf("%d",&b[i]);
        int k;
        for(int i=1; i<n; i++)
            if(b[i]>b[i+1]) {k=i;break;}
        int flag=1;
        for(int i=k+1; i<=n; i++)
            if(a[i]!=b[i]) {flag=0;break;}
        if(flag)
        {
            printf("Insertion Sort\n");
            sort(a+1,a+2+k);
            printf("%d",a[1]);
            for(int i=2; i<=n; i++) printf(" %d",a[i]);
            printf("\n");
            continue;
        }
        printf("Heap Sort\n");
        sort(a+1,a+1+n);
        for(int i=n; i>=1; i--)
            if(a[i]!=b[i]) {k=i;break;}
        swap(b[1],b[k]);
        k--;
        int p=1,pp=p*2;
        while(pp<=k)
        {
            if(pp+1<=k&&b[pp]<b[pp+1]) pp++;
            if(b[p]<b[pp])
            {
                swap(b[p],b[pp]);
                p=pp;pp=p*2;
            }
            else break;
        }
        printf("%d",b[1]);
        for(int i=2; i<=n; i++) printf(" %d",b[i]);
        printf("\n");
    }
    return 0;
}