Prime Ring Problem
Time Limit : 4000/2000ms (Java/Other) Memory Limit : 65536/32768K (Java/Other)
Total Submission(s) : 99 Accepted Submission(s) : 47
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.<br><br>Note: the number of first circle should always be 1.<br><br><img src=../../data/images/1016-1.gif><br>
Input
n (0 < n < 20).<br>
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.<br><br>You are to write a program that completes above process.<br><br>Print a blank line after each case.<br>
Sample Input
6<br>8<br>
Sample Output
Case 1:<br>1 4 3 2 5 6<br>1 6 5 2 3 4<br><br>Case 2:<br>1 2 3 8 5 6 7 4<br>1 2 5 8 3 4 7 6<br>1 4 7 6 5 8 3 2<br>1 6 7 4 3 8 5 2<br>
Source
Asia 1996, Shanghai (Mainland China)