HDU 1016 Prime Ring Problem 素数环

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

68

Sample Output

Case 1:1 4 3 2 5 61 6 5 2 3 4Case 2:1 2 3 8 5 6 7 41 2 5 8 3 4 7 61 4 7 6 5 8 3 21 6 7 4 3 8 5 2

//回溯法（DFS遍历解答树）#include<iostream>using namespace std;int n,cnt = 1;int vis[21],A[21];//素数表,加快后续判断int primelist[38] = {0,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1};void dfs(int cur){if(cur == n && primelist[A[0] + A[n-1]])//递归边界,别忘了测试第一个数和最后一个数{cout << A[0] ;for(int i = 1;i < n;++i)cout << " "<< A[i];//此题的打印格式,注意,最后一个数字打印出来后不带空格cout <<endl;}else for(int i = 2;i <= n;++i)//尝试放置每一个数iif(!vis[i] && primelist[i + A[cur-1]])//如果u没有用过，并且与前面一个数之和为素数{A[cur] = i;//将该数放进A中vis[i] = 1;//设置使用标志dfs(cur + 1);//递归调用vis[i] = 0;//切记一定要将标志改回来,清除标志!}}int main(){A[0] = 1;//1的位置不变while(cin >> n){memset(vis,0,sizeof(vis));//标记数组清零cout << "Case " << cnt++ <<":/n";dfs(1);cout << endl;}return 0;}