PAT_A1098#Insertion or Heap Sort

Posted 2021-11-28 blue-lin

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:

 1 /*
 2 Data 2019-05-09 22:06:13
 3 Problem: PAT_A1098#Insertion or Heap Sort
 4 AC: 38:44
 5 */
 6 
 7 #include<cstdio>
 8 #include<algorithm>
 9 using namespace std;
10 const int M=110;
11 int n, init[M], sorted[M];
12 
13 void DownAdjust(int low, int high)
14 {
15     int i=low, j=i*2;
16     while(j<=high)
17     {
18         if(j+1<=high && sorted[j+1]>sorted[j])
19             j++;
20         if(sorted[i] < sorted[j])
21         {
22             swap(sorted[i], sorted[j]);
23             i=j;
24             j=i*2;
25         }
26         else
27             break;
28     }
29 }
30 
31 int main()
32 {
33 #ifdef  ONLINE_JUDGE
34 #else
35     freopen("Test.txt", "r", stdin);
36 #endif // ONLINE_JUDGE
37 
38     scanf("%d", &n);
39     for(int i=1; i<=n; i++)
40         scanf("%d", &init[i]);
41     for(int i=1; i<=n; i++)
42         scanf("%d", &sorted[i]);
43     int pos=n;
44     while(pos>=2 && init[pos]==sorted[pos])
45         pos--;
46     int pt=pos;
47     while(pos>=2 && sorted[pos-1]<=sorted[pos])
48         pos--;
49     if(pos==1)
50     {
51         printf("Insertion Sort\\n");
52         if(pt==1)
53             while(pt<=n && sorted[pt]<=sorted[pt+1])
54                 pt++;
55         for(int i=pt+1; i>=2; i--)
56         {
57             if(sorted[i-1] > sorted[i])
58                 swap(sorted[i-1],sorted[i]);
59             else
60                 break;
61         }
62     }
63     else
64     {
65         printf("Heap Sort\\n");
66         pt=n;
67         while(pt>=1 && sorted[1]<=sorted[pt])
68             pt--;
69         swap(sorted[1], sorted[pt]);
70         pt--;
71         for(int i=pt; i>pt/2; i--)
72             DownAdjust(1,i);
73     }
74     for(int i=1; i<=n; i++)
75         printf("%d%c", sorted[i], i==n?‘\\n‘:‘ ‘);
76 
77 
78     return 0;
79 }