Prime Ring Problem-蒲公英云

Prime Ring Problem

小灰灰 2022-05-16 09:06 309阅读 0赞

Prime Ring Problem

A ring is compose of n circles as shown in diagram. Put natural number 1, 2, …, n into each circle separately, and the sum of numbers in two adjacent circles should be a prime.

Note: the number of first circle should always be 1.

这里写图片描述

Input
n (0 < n < 20).

Output
The output format is shown as sample below. Each row represents a series of circle numbers in the ring beginning from 1 clockwisely and anticlockwisely. The order of numbers must satisfy the above requirements. Print solutions in lexicographical order.

You are to write a program that completes above process.

Print a blank line after each case.

Sample Input
6
8

Sample Output
Case 1:
1 4 3 2 5 6
1 6 5 2 3 4

Case 2:
1 2 3 8 5 6 7 4
1 2 5 8 3 4 7 6
1 4 7 6 5 8 3 2
1 6 7 4 3 8 5 2

#include <cstdio>
#include <iostream>
#include <cmath>
using namespace std;
//判断素数 
int isprime(int n)
{
    int i;
    if(n==1) return false;
    for(i=2;i<=sqrt(n);i++)
     if(n%i==0)
     return false;
     return true;
}
//判断当前序列是否满足条件 
int isok(int a[],int last,int curvalue)//curvalue是当前值,a[last]是前一个值 
{
    if(last<0) return true;//第一个元素没有前驱元素 返回真
    if(!((curvalue+a[last])&1))//相邻元素和为偶数,偶数肯定不是素数! 
    return false;
    if(!(isprime(curvalue+a[last])))//相邻元素和不为素数 
    return false; 
    for(int i=0;i<=last;i++)
    if(a[i]==curvalue)//去重curvalue没有出现过
     return false;
      return true; 
}
//输出 
void print(int a[],int n)
{
    for(int i=0;i<n-1;i++)
    printf("%d ",a[i]);
    printf("%d\n",a[n-1]);
}
void primecircle(int a[],int n,int t)
{
    if(n&1)//输入N为奇数,肯定不满足,因为肯定会有两个奇数排在一起~
    return ;
    if(t==n)
    {
        if(isprime(a[0]+a[n-1]))
        print(a,n);
    }
    else{
        for(int i=2;i<=n;i++)
        {
            a[t]=i;
            if(isok(a,t-1,i))//如果当前元素满足条件
            primecircle(a,n,t+1); 
        } 
    }
}
int main()
{
    int a[30],n,k=1,i,j;
    while(scanf("%d",&n)!=EOF){
        printf("Case %d:\n",k++);
        a[0]=1;
        isprime(a[0]);
        for(i=1,j=2;i<n;i++,j++){
          a[i]=j;
         isprime(a[i]);
        }
        primecircle(a,n,1);
        printf("\n");
    }
    return 0;
}