Prime Ring Problem（dfs）_problem description a ring is compose of n circles-优快云博客

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 Input6
8

Sample OutputCase 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

Source Asia 1996, Shanghai (Mainland China)

#include<stdio.h>
#include<string.h>
#include<stdlib.h>
int book[25];
int result[25];
int n;
int num;
//判断是否为素数
int prime(int n)
{
    if(n<=1)
        return 0;
    int i;
    for(i=2;i*i<=n;i++)
    {
        if(n%i==0)
            break;
    }
    if(i*i>n)
        return 1;
    return 0;
}
//判断是否能将当前的数字放到当前的圈内
int check(int i,int step)
{
    if((book[i]==0) && prime(i+result[step-1])==1)//如果该数用过了，
                                         //则book[i]对其已标注过，为1。
    {
        if(step==n-1)
        {
            if(!prime(i+result[0]))
                return 0;
        }
        return 1;
    }
    return 0;
}
void dfs(int step)
{
    if(step==n)//判断边界
    {
        int a;
        printf("%d",result[0]);
        for(a=1;a<n;a++)
        {
            printf(" %d",result[a]);
        }
        printf("\n");
        return ;
    }
    int i;
    for(i=2;i<=n;i++)//遍历每一种情况
    {
        if(check(i,step))//check是否满足
        {
            book[i]=1;//标记
            result[step]=i;//记录结果
            dfs(step+1);//搜索下一个
            book[i]=0;//恢复初始状态，回到上一层
        }
    }
}
int main(void)
{
    while(scanf("%d",&n)!=EOF)
    {
        num++;
        memset(result,0,sizeof(result));
        memset(book,0,sizeof(book));
        result[0]=1;
        printf("Case %d:\n",num);
        dfs(1);
        printf("\n");

> 这里是引用

    }
    return 0;
}

深度优先搜索算法（Depth First Search，简称DFS）：一种用于遍历或搜索树或图的算法。
沿着树的深度遍历树的节点，尽可能深的搜索树的分支。当节点v的所在边都己被探寻过或者在搜寻时结点不满足条件，搜索将回溯到发现节点v的那条边的起始节点。整个进程反复进行直到所有节点都被访问为止。属于盲目搜索,最糟糕的情况算法时间复杂度为O(!n)。