回溯法简介
回溯法按深度优先策略搜索问题的解空间树。首先从根节点出发搜索解空间树，当算法搜索至解空间树的某一节点时，先利用剪枝函数判断该节点是否可行（即能得到问题的解）。如果不可行，则跳过对该节点为根的子树的搜索，逐层向其祖先节点回溯；否则，进入该子树，继续按深度优先策略搜索。
回溯法的基本行为是搜索，搜索过程使用剪枝函数来为了避免无效的搜索。剪枝函数包括两类：
- 1. 使用约束函数，剪去不满足约束条件的路径；
- 2.使用限界函数，剪去不能得到最优解的路径。
问题的关键在于如何定义问题的解空间，转化成树（即解空间树）。解空间树分为两种：子集树和排列树。两种在算法结构和思路上大体相同。
素数环问题
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
C++代码
