(PAT 1089) Insert or Merge (排序算法原理)

蔚落 2022-03-26 10:24 129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

解题原理:

把插入排序和归并排序(非递归)写出,中间排序过程每进行一次,就和部分已序数组比较,如果完全匹配,就说明是插入/归并排序

这里判断归并排序要用非递归法才行的通.非递归写法见

[https://blog.csdn.net/alex1997222/article/details/86514999][https_blog.csdn.net_alex1997222_article_details_86514999]

#include<iostream>
    #include<algorithm>
    using namespace std;
    const int MAXN = 110;
    int tempArray[MAXN];
    int tempArray2[MAXN];
    int partialArray[MAXN];
    //插入排序
    int N;
    bool isPartial = false;
    bool isMerge = false;
    void InsetSort(int a[], int n) {
    	for (int i = 1; i < n; ++i) {
    		int j = i;
    		int mtemp = a[i];
    		while (j > 0 && mtemp < a[j - 1]) {
    			a[j] = a[j - 1];
    			j--;
    		}
    		a[j] = mtemp;
    		if (isPartial) {
    			cout << "Insertion Sort" << endl;
    			for (int i = 0; i < n; ++i) {
    				cout << a[i];
    				if (i < n - 1) cout << " ";
    			}
    			break;
    		}
    		//比较部分
    		int idex;
    		for (idex = 0; idex < n; ++idex) {
    			if (a[idex] != partialArray[idex]) {
    				break;
    			}
    		}
    		if (idex == n) {
    			isPartial = true;
    		}
    	}
    }
    //归并排序:非递归实现
    void nMergeSortPlus(int nums[], int n) {
    	for (int step = 2; step / 2 <= n; step *= 2) {
    		for (int i = 0; i < n; i += step) {
    			sort(nums + i, nums + min(i + step, n));
    		}
    		if (isMerge) {
    			for (int i = 0; i < n; ++i) {
    				cout << nums[i];
    				if (i < n - 1) cout << " ";
    			}
    			return;
    		}
    		//比较部分
    		int idex;
    		for (idex = 0; idex < n; ++idex) {
    			if (nums[idex] != partialArray[idex]) {
    				break;
    			}
    		}
    		if (idex == n) {
    			isMerge = true;
    		}
    	}
    }
    
    int main() {
    	cin >> N;
    	for (int i = 0; i < N; ++i) {
    		cin >> tempArray[i];
    		tempArray2[i] = tempArray[i];
    	}
    	for (int i = 0; i < N; ++i) {
    		cin >> partialArray[i];
    	}
    	InsetSort(tempArray,N);
    	if (!isPartial) {
    		cout << "Merge Sort" << endl;
    		nMergeSortPlus(tempArray2, N);
    	}
    	system("PAUSE");
    	return 0;
    }

[https_blog.csdn.net_alex1997222_article_details_86514999]: https://blog.csdn.net/alex1997222/article/details/86514999