杭电1016Prime Ring Problem DFS 搜索-优快云博客

本文链接：https://blog.youkuaiyun.com/qq_35109846/article/details/71438721

本文探讨了素数环问题，即在一个由多个圆组成的环中填入从1到n的自然数，使得相邻圆内的数字之和为素数。通过递归深度优先搜索算法寻找所有可能的解决方案，并按字典序输出。

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Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 25200 Accepted Submission(s): 11252

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

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 <stdio.h>  
#include <string.h>  
int p[]={0,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1};  
int a[30],vis[30],n;  
void dfs(int num,int count)  
{  
    int i;  
    vis[num]=1;  
    a[count]=num;  
    if(count==n){//总数为n，输出答案  
        if(p[a[count]+a[1]]){//判断是否构成圆环  
            printf("1");  
            for(i=2;i<=n;i++)  
                printf(" %d",a[i]);  
            printf("\n");  
        }  
        return ;  
    }  
    for(i=1;i<=n;i++){  
        if(!vis[i]&&p[a[count]+i]){  
            dfs(i,count+1);  
            vis[i]=0;//回溯访问要重新为0  
        }  
    }  
}  
  
int main(){  
    int t=1;  
    while(~scanf("%d",&n)){  
        memset(vis,0,sizeof(vis));  
        printf("Case %d:\n",t++);  
        dfs(1,1);  
        printf("\n");  
    }  
    return 0;  
}