1 题目

1098 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

2 解析

2.1 题意

给定一个初始序列以及经过一定排序步骤的序列，判断是插入排序还是堆排序，并输出下一步步骤后的序列

2.2 思路

  • 1 模拟插入排序，比较每步排序后与部分排序的序列是否相同，如果相同，则输出”Insertion Sort“以及下一步排序后的序列，并结束；
  • 2 模拟堆排序，比较每步排序后的序列与部分序列是否相同，如果相同，则输出Heap Sort以及下一步排序后的序列
  • 注意：初始序列不参与比较是否与目标序列相同（也就是中间序列不包括初始序列）
  • eg：
Sample Input:
4
3 4 2 1 
3 4 2 1  

Sample Output:
Insertion Sort
2 3 4 1

3 参考代码

#include 
#include 

using std::swap;

const int MAXN = 110;
int heap[MAXN], sortSeq[MAXN], insertSeq[MAXN];
int N;
bool isSort = false;

void showArray(int A[]){
    for (int i = 1; i <= N; ++i) {
        printf("%d", A[i]);
        if(i < N) printf(" ");
    }
    printf("\n");
}

bool isSame(int A[], int B[]){
    for (int i = 1; i <= N; ++i) {
        if(A[i] != B[i]) return  false;
    }
    return true;
}

bool insertSort(){
    bool flag = false;
    for (int i = 2; i <= N; ++i)
    {
        if(i != 2 && isSame(sortSeq, insertSeq)){
            flag = true;
        }

        int temp = insertSeq[i], j = i;
        while(j > 1 && temp < insertSeq[j - 1]){
            insertSeq[j] = insertSeq[j - 1];
            j--;
        }
        insertSeq[j] = temp;

        if(flag == true){
            return true;
        }

    }
    return false;
}

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

void CreateHeap(){
    for (int i = N / 2; i >= 1; --i) {
        downAjdjust(i, N);
    }
}

void heapSort(){
    bool flag = false;
    CreateHeap();
    for (int i = N; i > 1; --i) {
        if(i != N && isSame(heap, sortSeq)){
            flag = true;
        }
        swap(heap[i], heap[1]);
        downAjdjust(1, i - 1);

        if(flag == true){
            showArray(heap);
            return;
        }
    }
}

int main(int argc, char const *argv[])
{
    scanf("%d", &N);
    for (int i = 1; i <= N; ++i)
    {
        scanf("%d", &heap[i]);
        insertSeq[i] = heap[i];
    }
    for (int i = 1; i <= N; ++i)
    {
        scanf("%d", &sortSeq[i]);
    }

    if(insertSort()){
        printf("Insertion Sort\n");
        showArray(insertSeq);
    }else{
        printf("Heap Sort\n");
        heapSort();
    }
    return 0;
}