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  • Coprime Array

    Description

    You are given an array of n elements, you must make it a co-prime array in as few moves as possible.

    In each move you can insert any positive integral number you want not greater than 109 in any place in the array.

    An array is co-prime if any two adjacent numbers of it are co-prime.

    In the number theory, two integers a and b are said to be co-prime if the only positive integer that divides both of them is 1.

    Input

    The first line contains integer n (1 ≤ n ≤ 1000) — the number of elements in the given array.

    The second line contains n integers ai (1 ≤ ai ≤ 109) — the elements of the array a.

    Output

    Print integer k on the first line — the least number of elements needed to add to the array a to make it co-prime.

    The second line should contain n + k integers aj — the elements of the array a after adding k elements to it. Note that the new array should be co-prime, so any two adjacent values should be co-prime. Also the new array should be got from the original array a by addingk elements to it.

    If there are multiple answers you can print any one of them.

    Sample Input

    Input
    3
    2 7 28
    
    Output
    1
    

    2 7 9 28

    给出一个序列 为了保证相邻的两个数互质(最大公约数为1) 可以再任意两个数之间插入一个数

    输出最少需要插入的数的数量 和插入新数后的序列

    1和任意一个数都互质 只要在不互质的两个数之间插入一个1即可

    #include<cstdio>
    #include<cstring>
    #include<cmath>
    #include<queue>
    #include<algorithm>
    using namespace std;
    int vis[10001];
    int gcd(int a,int b)
    {
    	 if(a%b==0)
    	 return b;
    	 return gcd(b,a%b);
    }
    int s[10000];
    int main()
    {
    	int n;
    	scanf("%d",&n);
    	int sum=0;
    	for(int i=0;i<n;i++)
    	{
    		vis[i]=0;
    		scanf("%d",&s[i]);
    	}
    	for(int i=0;i<n-1;i++)
    	{
    		if(gcd(s[i],s[i+1])!=1)
    		{
    			vis[i]=1;
    			sum++;
    		}
    	}
    	 printf("%d\n",sum);
    	for(int i=0;i<n;i++)
    	{
    		printf("%d",s[i]);
    		if(vis[i]==1)
    		printf(" 1");
    		if(i!=n)
    		printf(" ");
    	}
    	return 0;
    }
    


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  • 原文地址:https://www.cnblogs.com/kingjordan/p/12027040.html
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