Pat(A) 1089. Insert or Merge (25)

原题目:

原题链接:https://www.patest.cn/contests/pat-a-practise/1089

1089. Insert or Merge (25)


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 resulting 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

题目大意

给出一个原序列,一个进行了一部分排序的序列,判断是插入排序还是归并排序。并输出再排一次后的结果。

解题报告

根据插入排序结果的性质,前k个必然是递增的,从k+1开始与原序列一致。若符合这个性质,程序判断是插入,否则是归并排序。

再排一次,对于插入排序来说,找到k,并使将0到k+1排序一下即可。 对于归并排序,先找到已经排到第k层(k=$2^i$,i = 0,1,2……),然后每将每k*2个元素排序即可。

代码

#include "iostream"
#include "algorithm"
using namespace std;

int initial[100 + 5];
int sorted[100 + 5];
int N,i,j;

void print_ans(int f){
    if(f)
        cout<<"Insertion Sort"<<endl;
    else
        cout<<"Merge Sort"<<endl;
    cout<<sorted[0];
    for(int i = 1; i < N; i++)
        cout<<" "<<sorted[i];
}

bool isKisOk(int k){
    int i,j;
    for(i = 0; i < N/k; i++){
        for(j = i * k + 1; j < N && j < i * k + k; j++){
            if(sorted[j] < sorted[j -1])
                return false;
        }
    }
    return true;
}

void sortMerge(){
    int k = 1;
    while(isKisOk(k)){
        k *= 2;
    }
    for(i = 0; i <= N/k; i++){
        sort(sorted + i * k, sorted + min(i*k+k,N));
    }
}

int main(){
    bool flag; //true是insert
    cin>>N;
    for(i = 0; i < N; i++){
        cin >> initial[i];
    }
    for(i = 0; i < N; i++){
        cin >> sorted[i];
    }
    for(i = 1; i < N; i++){
        if(sorted[i] < sorted[i - 1])
            break;
    }
    flag = true;
    for(j = i; j < N; j++){
        if(initial[j] != sorted[j]){
            flag = false;
            break;
        }
    }
    if(flag){
        sort(sorted,sorted+i+1);
        print_ans(flag);
    }else{
        sortMerge();
        print_ans(flag);
    }
    //system("pause");
}

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