Prime Ring Problem（杭電1016）（DFS）

Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 28204 Accepted Submission(s): 12561


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 Asia 1996, Shanghai (Mainland China)

#include
#include
#include
int visit[40],a[40],n;
int fun(int x)
{
	for(int i=2;i<=sqrt(x);i++)
	    if(x%i==0)
	        return 0;
	return 1;
}
void dfs(int k)
{
	if(fun(a[0]+a[n-1])&&k==n)
	{
		printf("%d",a[0]);
		for(int i=1;i