【PAT】A1089 Insert or Merge【插入排序】【归并排序】

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

给出一个初始序列和一个中间序列，判断这是插入排序还是归并排序，并输出确定的排序方法下一个轮排序后的序列。

思路

模拟插入排序和归并排序的过程，使用一个布尔变量flag标记输入使用的是否是当前的排序方法，每一步排序都和目标序列做比较，如果发现相同，则将flag置为true，并在下一轮判断到flag为true时输出当前序列（即上一轮序列的下一个序列）。由于归并排序的复杂度比插入排序低，先判断是否是归并排序。因为题目输入较小，归并排序的归并过程可以使用sort()代替。注意归并排序的边界条件，插入排序默认从第二个元素开始插入（从第一个元素插入其实不会使序列发生变化，经测试，从第一个元素开始插入会有一组数据错误）。

代码

#include <cstdio>
#include <algorithm>
#define MAX_N 100
using namespace std;
int N;
int origin[MAX_N], target[MAX_N