HDU 1016 Prime Ring Problem 【DFS】

Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 27775    Accepted Submission(s): 12342

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

 

Source

Asia 1996, Shanghai (Mainland China)

 

/*题解：
    第一个自己用DFS解决的搜索问题，一次AC，但感觉对搜索仍然不是很懂。 
*/

#include<cstdio>int a[22],vis[22],n;int prime[12]={2,3,5,7,11,13,17,19,23,29,31,37};int is_prime(int x){    for(int i=2; i*i<=x; i++)        if(x%i==0)            return 0;    return 1;}void dfs(int pos){    if(pos==n&&a[0]==1&&is_prime(a[0]+a[n-1]))    {        printf("%d",a[0]);        for(int i=1; i<n; i++)            printf(" %d",a[i]);        printf("\n");        return;    }     for(int i=1; i<=n; i++)    {        if(vis[i]&&is_prime(a[pos-1]+i))        {            vis[i]=0;            a[pos]=i;            dfs(pos+1);            vis[i]=1;        }    }}                 int main(){    int k;    k=1;    while(scanf("%d",&n)!=EOF)    {        printf("Case %d:\n",k++);         for(int i=1; i<=n; i++)            vis[i]=1;        a[0]=1;         dfs(0);        printf("\n");    }    return 0;}