HDU 1016 Prime Ring Problem

Prime Ring Problem

 Time Limit : 4000/2000ms (Java/Other) Memory Limit : 65536/32768K (Java/Other)

Total Submission(s) : 101 Accepted Submission(s) : 21

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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) 

    相对简单的一道题，dfs深搜。即在N个数的全排列，找出符合提议的素数组。

    注意：一边排列 一边检查

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#include<stdio.h>#include<math.h>int num;bool use[20];int CP[20];bool isprime(int a){for(int i=2;i<=sqrt(a+0.0);i++){if(a%i==0)return false;}return true;}void dfs(int n){if(n==num&&isprime(1+CP[n-1])){for(int i=0;i<num;i++){printf(i==num-1?"%d\n":"%d ",CP[i]);}}else{for(int i=2;i<=num;i++){if(!use[i]&&isprime(i+CP[n-1])){CP[n]=i;use[i]=true;dfs(n+1);use[i]=false;}}}}void init(){for(int i=1;i<=num;i++){use[i]=false;}CP[0]=1;use[1]=true;}int main(){int time=0;while(scanf("%d",&num)!=EOF){init();printf("Case %d:\n",++time);dfs(1);puts("");}}