hdu 1016 Prime Ring Problem

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

思路：终于考完了冬季“大雪崩”的考试，现在水平也就做做基础题了，本题dfs，用筛法筛出质数然后每次dfs当前的没有被用过数和层数，当转一圈层数正好等于n时再输出，用fa[]记录每个点的父亲结点方便输出，不符合条件的dfs之后要消去访问标记。

#include<iostream>#include<cstring>#define CLR(a,b) memset(a,b,sizeof(a))using namespace std;const int MAXN=2e2+5;int n,phi[MAXN],ans[MAXN],fa[MAXN],vis[MAXN];void eular(){for(int i = 0; i<MAXN;i++) phi[i] = i;for(int i = 2; i<MAXN;i++) if(phi[i] == i) for(int j = i+i;j<MAXN;j+=i) phi[j] = 0;}void print(int cur){int n=0;while(cur!=1){ans[n++]=cur;cur=fa[cur];}cout<<1;for(int i=n-1;i>=0;i--)cout<<' '<<ans[i];cout<<endl;}void dfs(int cur,int k){if(k==n && phi[cur+1]){print(cur);}//cout<<cur<<' '<<k<<endl;for(int i=2;i<=n;i++){if(phi[cur+i] && !vis[i]){vis[i]=1;fa[i]=cur; dfs(i,k+1);vis[i]=0;}}}void init(){CLR(ans,0);CLR(fa,0);CLR(vis,0);}int main(){int ca=1;eular();while(cin>>n){cout<<"Case "<<ca++<<":"<<endl;init();dfs(1,1);cout<<endl;}return 0;}