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.
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.
You are to write a program that completes above process.
Print a blank line after each case.
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
Source
Recommend
题意:给你一个小于20的数n,让你用1-n的数去形成一个素数环,这个素数环定义第一个数为1,任意相邻两个数之和为素数。
思路:简单dfs,标记每个数用还是不用,不满足条件时候回溯去掉标记就是了。
代码:
#include<bits/stdc++.h>
using namespace std;
const int maxn=30;
int a[maxn];
bool vis[maxn];
int n;
bool check(int num)
{
for(int i=2;i*i<=num;i++)
{
if(num%i==0) return false;
}
return true;
}
void dfs(int num)//填到第i个数
{
if(num==n&&check(a[0]+a[n-1]))
{
for(int i=0;i<n;i++)
{
if(i!=n-1) printf("%d ",a[i]);
else printf("%d\n",a[i]);
}
}
else
{
for(int i=2;i<=n;i++)
{
if(!vis[i]&&check(i+a[num-1]))
{
a[num]=i;
vis[i]=true;
dfs(num+1);
vis[i]=false;//回溯去标记
}
}
}
}
int main()
{
while(~scanf("%d",&n))
{
memset(vis,false,sizeof(false));
memset(a,0,sizeof(a));
static int t=1;
printf("Case %d:\n",t++);
a[0]=1;
dfs(1);
printf("\n");
}
return 0;
}