Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 48837    Accepted Submission(s): 21529

Problem Description

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.

 

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

68

 

Sample Output

Case 1:1 4 3 2 5 61 6 5 2 3 4Case 2:1 2 3 8 5 6 7 41 2 5 8 3 4 7 61 4 7 6 5 8 3 21 6 7 4 3 8 5 2
/*分类：dp来源：prime ring problem思路：输入奇数无解，剪枝 We are giants.create by Lee_SD on 2017/4/*/#include<queue>#include<iostream>#include<algorithm>#include<cmath>#include<stack>#include<string.h>#include<stdio.h>using namespace std;using namespace std;int ring[25];int vis[25];int n;int isprime(int a){for(int i=2;i*i<=a;i++)if(a%i==0) return 0;return 1;}void dfs(int k,int n){if(k==n+1&&isprime(1+ring[n])==1){printf("1");for(int i=2;i<=n;i++){printf(" %d",ring[i]);}printf("\n");return ;}for(int i=2;i<=n;i++){if(!vis[i]&&isprime(i+ring[k-1])==1){vis[i]=1;ring[k]=i;dfs(k+1,n);vis[i]=0;}}}int main(){int kase=1;while(scanf("%d",&n)!=EOF){printf("Case %d:\n",kase++);if(n==1){printf("1\n");continue;}if(n&1)return 0;memset(vis,0,sizeof(vis));vis[1]=ring[1]=1;dfs(2,n);printf("\n");}}