ZOJ 1457 Prime Ring Problem (dfs + pruning)

Zookeeper

Prime Ring Problem Time Limit: 10 Seconds Memory Limit: 32768 KB

A ring is compose of n circles as shown in digoal. put natural number 1, 2 ,..., n into each circle separately, and the sum of numbers in two adjacent circles shoshould be a prime.

Note: the number of first circle shoshould 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 abve 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

# Include
 
  
# Include
  
   
# Include
   
    
# Include
    
     
Using namespace std; int n, test = 0; int cir [30]; int vis [30]; int prime [50] = {0}; void dfs (int k) {if (k = n) {if (! Prime [cir [k] + cir [1]) return; for (int I = 1; I