1089 Insert or Merge (25 分) 插入排序or归并排序

梦里梦外; 2024-04-17 05:33 10阅读 0赞

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.

**Merge sort** works as follows: Divide the unsorted list into N sublists, each containing 1 element (a list of 1 element is considered sorted). Then repeatedly merge two adjacent sublists to produce new sorted sublists until there is only 1 sublist remaining.

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 "Merge 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 0 6
    1 3 2 8 5 7 4 9 0 6

### Sample Output 2: ###

Merge Sort
    1 2 3 8 4 5 7 9 0 6

**题意：**给定一个序列，判断这个序列是插入排序or归并排序的过程序列

判断输出排序方法后，输出该排序的下一个序列。

**思路：**插入排序的过程序列特点比较明显：前k个数有序，后n-k个数与原序列相同。可依此来判断排序方法。

插入排序的下一个序列即为p+1个有序，可以直接用sort解决。

归并排序因为步长未知，所以需要for找到现有的步长，然后一直循环下去，知道和已知序列相同。

#include <stdio.h>
    #include <string.h>
    #include <string>
    #include <map>
    #include <vector>
    #include <queue>
    #include <math.h>
    #include <algorithm>
    #include <iostream>
    #define INF 0x3f3f3f3f
    using namespace std;
    int a[105],b[105];
    int main()
    {
    	int n,i,j,k,p;
    	scanf("%d",&n);
    	for(i=1;i<=n;i++)
    	scanf("%d",&a[i]);
    	for(i=1;i<=n;i++)
    	scanf("%d",&b[i]);
    	k=1;
    	while(k<=n&&b[k-1]<=b[k])k++; //若没有等号，测试点4过不去 
    	p=k;
    	while(k<=n&&a[k]==b[k])k++;
    	if(k==n+1)
    	{
    		printf("Insertion Sort\n");
    		sort(b+1,b+p+1);	
    		for(i=1;i<=n;i++)
    		{
    			if(i!=1)printf(" ");
    			printf("%d",b[i]);
    		}
    	}
    	else
    	{
    		printf("Merge Sort\n");
    		int flag=0;
    		for(i=2;i/2<=n;i*=2) //i-步长 
    		{
    			if(i!=2)
    			{
    				for(j=1;j<=n;j++)
    				{
    					if(a[j]!=b[j])
    					break;
    				}
    				if(j==n+1)flag=1;
    			} 			
    			for(j=1;j<=n;j+=i)
    			sort(a+j,a+min(j+i,n+1));	
    			if(flag)break;		
    		}		
    		for(i=1;i<=n;i++)
    		{
    			if(i!=1)printf(" ");
    			printf("%d",a[i]);
    		}
    	}
    }