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)

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      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

Prime Ring Problem（杭电1016）（DFS）

Prime Ring Problem