1098. Insertion or Heap Sort (25)

Posted 2020-10-23 给杰瑞一块奶酪~

According to Wikipedia:

Insertion sort iterates, consuming one input element each repetition, and growing a sorted output list. At 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

如果是插入排序，t序列分为两部分前半部分是排好序的后半部分与s一一对应不变，通过这一点判断是什么排序。
插入排序，就是把排好序的后一个元素，插入前面的序列，堆排序，就是把堆顶放入排好序的序列，也就是尾部已经sorted的序列（比堆顶大的元素都在sorted的序列中），把unsorted的序列中最后一个元素放到堆顶，然后从头往下调成最大堆。

代码：

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <iomanip>

using namespace std;
int s[101],t[101];
int n;
int check(int d)
{
    for(int i = d;i <= n;i ++)
        if(s[i] != t[i])return 0;
    return 1;
}
void insertsort(int m)
{
    int d = t[m + 1];
    for(;m >= 1;m --)
    {
        if(t[m] > d)t[m + 1] = t[m];
        else break;
    }
    t[m + 1] = d;
}
void heapsort(int m)
{
    swap(t[1],t[m]);
    int flag = 1,i = 1;
    while(flag)
    {
        flag = 0;
        int d = i;
        if(i * 2 < m && t[d] < t[i * 2])d = i * 2;
        if(i * 2 + 1 < m && t[d] < t[i * 2 + 1])d = i * 2 + 1;
        if(i != d)
        {
            flag = 1;
            swap(t[i],t[d]);
            i = d;
        }
    }
}
int main()
{
    scanf("%d",&n);
    for(int i = 1;i <= n;i ++)
        scanf("%d",&s[i]);
    for(int i = 1;i <= n;i ++)
        scanf("%d",&t[i]);
    int m;
    for(m = 1;m <= n - 1;m ++)
    {
        if(t[m] > t[m + 1])break;
    }
    if(check(m + 1))
    {
        printf("Insertion Sort\n");
        insertsort(m);
    }
    else
    {
        printf("Heap Sort\n");
        for(m = n;m > 1;m --)
        {
            if(t[m] < t[1])break;
        }
        heapsort(m);
    }
    printf("%d",t[1]);
    for(int i = 2;i <= n;i ++)
        printf(" %d",t[i]);
}