PAT_A1098#Insertion or Heap Sort

Source:

PAT_A1098 Insertion or Heap Sort (25 分)

Description:

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

keys:

• 插入排序（Insertion Sort）；
• 堆排序（Heap Sort）；

Attention:

• 初始状态与中间状态相同时为插入排序；
• 初始状态与中间状态相同时，下一个前插的元素应该是A【k】< A【k-1】的元素，而非直接把第二个元素前插（初始状态 != 中间状态）；

Code:

/*
Data 2019-06-21 17:11:02
Problem: PAT_A1098#Insertion or Heap Sort
AC: 41:05

题目大意：
给定初始序列和经过若干阶段排序的中间序列，判断是插入排序还是堆排序
设最终序列递增有序
输出：
插入排序或堆排序，并给出下一阶段的排序结果

基本思路：
根据插入排序的特点来判断，
前半部分递增，后半部分与初始序列相同，则为插入排序
注意：初始序列与中间序列相同，为插入排序
*/
#include<cstdio>
#include<algorithm>
using namespace std;
const int M=110;
int n, init[M], sorted[M];

void DownAdjust(int low, int high)
{
    int i=low, j=i*2;
    while(j<=high)
    {
        if(j+1<=high && sorted[j+1]>sorted[j])
            j++;
        if(sorted[i] < sorted[j])
        {
            swap(sorted[i], sorted[j]);
            i=j;
            j=i*2;
        }
        else
            break;
    }
}

int main()
{
#ifdef  ONLINE_JUDGE
#else
    freopen("Test.txt", "r", stdin);
#endif // ONLINE_JUDGE

    scanf("%d", &n);
    for(int i=1; i<=n; i++)
        scanf("%d", &init[i]);
    for(int i=1; i<=n; i++)
        scanf("%d", &sorted[i]);
    int pos=n;
    while(pos>=2 && init[pos]==sorted[pos])
        pos--;
    int pt=pos;
    while(pos>=2 && sorted[pos-1]<=sorted[pos])
        pos--;
    if(pos==1)
    {
        printf("Insertion Sort\n");
        if(pt==1)
            while(pt<=n && sorted[pt]<=sorted[pt+1])
                pt++;
        sort(sorted+1,sorted+pt+2);
    }
    else
    {
        printf("Heap Sort\n");
        pt=n;
        while(pt>=1 && sorted[1]<=sorted[pt])
            pt--;
        swap(sorted[1], sorted[pt]);
        DownAdjust(1,pt-1);
    }
    for(int i=1; i<=n; i++)
        printf("%d%c", sorted[i], i==n?'\n':' ');


    return 0;
}