HDU-1016 Prime Ring Problem

Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 12124    Accepted Submission(s): 5506

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

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#include <iostream>#include <cstring>using namespace std;int n,visited[30],buffer[30],ans,flag;bool is_prime(int x,int y){    int sum=x+y;    for(int i=2;i*i<=sum;i++)    {        if(sum%i==0)            return 0;    }    return 1;}void dfs(int cur){    visited[1]=1;    if(cur>n && is_prime(buffer[1],buffer[n]))    {        if(!flag)        {            printf("Case %d:\n",ans);            flag=1;        }        for(int i=1;i<n;i++)        {            printf("%d ",buffer[i]);        }        printf("%d\n",buffer[n]);    }    else    {        for(int i=2;i<=n;i++)        {            buffer[cur]=i;            if(!visited[i] && is_prime(buffer[cur-1],buffer[cur]))            {                visited[i]=1;                dfs(cur+1);                visited[i]=0;            }        }    }}int main(){    ans=0;    while(scanf("%d",&n)!=EOF)    {        ans++;        flag=0;        memset(visited,0,sizeof(visited));        buffer[1]=1;        dfs(2);        printf("\n");    }    return 0;}