HDUOJ1016 Prime Ring Problem

Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others)Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 8087Accepted Submission(s): 3620

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.

HDUOJ1016 Prime Ring Problem
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
【解题思路】素数环是典型的DFS题目,DFS函数的参数为(int c, int cnt),
c代表遍历时所在环上节点的数,cnt代表结点个数。当节点个数位n时并且环末节点
和首节点相加也为素数则打印环。

根据本题总结dfs的主要步骤和方法:

1. 找搜索出口条件,即搜索到最深层时的操作

2. Dfs采用递归搜索,在遍历后返回时标记已经遍历的节点

3. 注意入口条件的满足

4. 画出递归搜索图查看函数是否满足要求

5. 注意回溯的条件,适当的时候需要剪枝

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