Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 63806 Accepted Submission(s): 27457

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

Source

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分析：

经典的素数环问题

dfs

就是全排列的基础上加上素数环要求的检测

code：

#include
      
       using namespace std;typedef long long LL;#define max_v 105int a[max_v];int vis[max_v];int n;int isp(int x)//素数检测{    for(int i=2;i<=sqrt(x);i++)    {        if(x%i==0)            return 0;    }    return 1;}void dfs(int cur)//素数环问题 全排列思想加素数的检测{    if(cur==n&&isp(a[0]+a[n-1]))//判断到最后一个数了    {        printf("%d",a[0]);//打印        for(int i=1;i

转载于:https://www.cnblogs.com/yinbiao/p/9313350.html

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