HDU 1016 Prime Ring Problem(DFS)

Posted 2020-06-13

题目链接

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

 

题解：一个素数环问题，dfs去遍历所有可能，为了避免重复，把1固定当做第一个数字。前n-1个数字这样判断：1-n循环，如果没有使用过，并且和前一个数字之和是素数，就填进去。最后一个数字，扫描vis数组，哪个没用过就填进去，判断与前后数字是否和为素数，是则输出数组。素数判定可以打表，到40即可。第一发WA，吓死我了==|，仔细一看原来是case没有，注意空行。