HDU 1016 Prime Ring Problem(DFS)

Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 48783    Accepted Submission(s): 21502

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

 

Source

Asia 1996, Shanghai (Mainland China)

 

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直接素数打表会快一点吧，反正只是40以内的素数

#include<stdio.h>#include<string.h>#include<stdlib.h>#include<algorithm>using namespace std;int prime[40]={0,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0};int n;int vis[25];    //存储是否遍历过int a[25];      //存储正确的序列void dfs(int num){int i;if(num==n&&prime[a[n-1]+a[0]]){for(i=0;i<n-1;i++){printf("%d ",a[i]);}printf("%d\n",a[n-1]);}else {for(i=2;i<=n;i++){if(vis[i]==0&&prime[i+a[num-1]]){vis[i]=1;a[num++]=i;dfs(num);vis[i]=0;num--;} }}}int main(){int k=0;while(~scanf("%d",&n)){k++;printf("Case %d:\n",k);memset(vis,0,sizeof(vis));a[0]=1;dfs(1);printf("\n");}return 0;}