HD 1016 Prime Ring Problem（素数环问题）

题目来源 ：HD 1016

[align=left]Problem Description[/align]
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.



 

[align=left]Input[/align]
n (0 < n < 20).

 

[align=left]Output[/align]
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.

 

[align=left]Sample Input[/align]

6
8

 

[align=left]Sample Output[/align]

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

题意就是输入一个数n，在 1 到 n 里面找数字围成一个圈，使得相邻的两个数字加起来是素数，每个环都有1，输出的结果按字典序输出，每个答案都从1 开始。

这里有一个值得注意的地方就是，最后一个数跟1的和要是素数。每个case之后都要有空行。

很显然，要用for循环进行深搜。

#include <stdio.h>
#include <string.h>
#include <math.h>
#include <iostream>
using namespace std;

int num[20],ans[20],bj[20];
int n,len;
void get(){ //这里是得到素数，如果一个个判断素数，会做很多重复的工作
len=0;
int leap,i,j;
for(j=2;j<25;j++){
leap=0;
int ma=sqrt(j)+1;
for(i=2;i<ma;i++){

if(j%i==0) {
leap=1;break;
}
}
if(!leap)
num[len++]=j;
}
}

int prim(int a){
for(int i=0;i<len;i++)
if(a==num[i]) return 1;
return 0;
}

int dfs(int pre,int ord,int k){

if(!prim(pre+ord)) return 0;
ans[k]=ord;

 if(k==n&&prim(ord+1)){
for(int i=1;i<n;i++)
printf("%d ",ans[i]);
printf("%d\n",ans
);
return 1;
}
bj[ord]=1;
for(int i=2;i<=n;i++)
if(bj[i]==0&&dfs(ord,i,k+1))
break;
bj[ord]=0;
return 0;
}

int main(){
int cc=1;
get();
while(scanf("%d",&n)!=EOF){
printf("Case %d:\n",cc++);
if(n==1){
        printf("1\n");
        continue;
        }
memset(bj,0,sizeof(bj));
ans[1]=1;
for(int i=2;i<=n;i++)
dfs(1,i,2);
printf("\n");
}
return 0;
}