Prime ring problem

Description

 

A ring is composed of n (even number) circles as shown in diagram. Put natural numbers  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 <= 16)

 

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.

 

You are to write a program that completes above process.

 

Sample Input 

6

8

 

Sample Output 

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

 

 这个先用深搜求n个数的全排列，这样就枚举了每一种情况，在对素数打表，以进行快速判断。

这个UVA上需要注意输出的最后一组数据不能有多余的空行

 

#include"iostream" #include"cstring" #include"cstdio" using namespace std; int n,book[21],a[21]; int ca=1; int dic[52]={0,1,1,1,0,1, 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, 0,1,0,0,0, 1,0,1,0,0, 0,1,0,0,0, 0 }; void dfs(int step) { if ((step == n) && dic[a[1] + a[n]]) { for(int i=1;i<n;i++) cout<<a[i]<<' '; cout<<a[n]<<endl; return; return; } for(int i=2;i<=n;i++) if(!book[i] && dic[a[step] + i]) { a[step+1]=i; book[i]=1; dfs(step+1); book[i]=0; } } int main() { int x=1; while(scanf("%d",&n)!=EOF) { a[1]=1; if(x>1) cout<<endl;x++; cout<<"Case "<<ca++<<':'<<endl; dfs(1); } return 0; } 

 

也可以用暴力的方法求数全排，不过会超时，暂且贴上来吧

#include"iostream"
#include"cstring"
#include"cstdio"
using namespace std;
int n,book[21],a[21];
int ca=1;
int dic[52]={0,1,1,1,0,1,
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,
0,1,0,0,0,
1,0,1,0,0,
0,1,0,0,0,
0
};

void print(int step)
{
if ((step == n+1))
{
int okk=1;
for(int k=1;k<n;k++) if(dic[a[k]+a[k+1]]==0) okk=0;
if(dic[a[n]+a[1]]==0) okk=0;
if(okk)
{
for(int i=1;i<n;i++) cout<<a[i]<<' ';
cout<<a[n]<<endl;
}
}

for(int i=1;i<=n;i++)
{
int ok=1;
for(int j=1;j<step;j++)
if(a[j]==i) ok=0;
if(ok)
{
a[step]=i;
print(step+1);
}
}
}

int main()
{
int x=1;
while(scanf("%d",&n)!=EOF)
{
memset(a,0,sizeof(a));
a[1]=1;
if(x>1) cout<<endl;x++;
cout<<"Case "<<ca++<<':'<<endl;
print(2);
}
return 0;
}