PAT甲級：1089 Insert or Merge (25分)

PAT甲級：1089 Insert or Merge (25分)

題幹

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

思路

根據兩個排序的特性，我們不難發現：

1. 插入排序中，總會是前半段有序，後半段無序。
2. 歸併排序中，則是一段一段的有序。

由於題目保證唯一解，我們不考慮兩者交叉的情況。實際上是兩者在很多情況下是無法分清的。

所以首先利用兩者的特性，找到第一個次序不對的位置。再繼續調查剩下的序列情況，如果與原數列都相同，說明是插入排序。否則一定是歸併排序。

插入排序只需要用sort函數處理0到剛剛找到的位置即可。

而歸併排序就直接對數據進行排序，等到某一步與給出的第二列數據相同，就再進行一步即可。

code

#include <iostream>
#include <vector>
#include <algorithm>
/* run this program using the console pauser or add your own getch, system("pause") or input loop */
using namespace std;
void merge(vector<int>& sorted, vector<int>& init){
	int k = 1, flag = 1;
	while(flag){
		flag = 0;
		int i;
		if(sorted != init) flag = 1;
		k *= 2;
		for(i = 0; i + k < init.size(); i += k) sort(init.begin() + i, init.begin() + i + k);
		sort(init.begin() + i, init.end());
	}
}
int main(int argc, char** argv) {
	int n = 0, temp_split = 0;
	scanf("%d", &n);
	vector<int> init(n), sorted(n);
	for(int i = 0; i < n; i++) scanf("%d", &init[i]);
	for(int i = 0; i < n; i++) scanf("%d", &sorted[i]);
	for(int i = 1; i < n; i++){
		if(sorted[i] < sorted[i-1]){
			temp_split = i;
			break;
		} 
	}
	for(int i = temp_split; i < n; i++){
		if(init[i] != sorted[i]){
			printf("Merge Sort\n");
			merge(sorted, init);
			for(auto it = init.begin(); it != init.end(); it++){
				if(it != init.begin()) printf(" ");
				printf("%d", *it);
			}
			return 0;
		}
	}
	printf("Insertion Sort\n");
	sort(sorted.begin(), sorted.begin() + temp_split + 1);
	for(auto it = sorted.begin(); it != sorted.end(); it++){
		if(it != sorted.begin()) printf(" ");
		printf("%d", *it);
	}
	return 0;
}