hdu 1016 Prime Ring Problem
2014-07-06 16:38
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Prime Ring Problem
Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 25144 Accepted Submission(s): 11229
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
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
<pre name="code" class="cpp">#include<stdio.h> #include<algorithm> #define max 100 int v[max]; int a[max]; int vis[max]; int i,n; void dfs(int cur) { if(cur==n && v[a[0]+a[n-1]]) //递归边界,测试第一个数和最后一个数。 { for(i=0;i<n;i++) { if(i!=n-1) printf("%d ",a[i]); //注意格式问题 else printf("%d\n",a[i]); } } else { for(int i=2;i<=n;i++) // 尝试放每一个数i if(!vis[i]&&v[i+a[cur-1]]) // 如果i没有用过,并且与前一个数之和为素数 { a[cur]=i; // i满足条件,则放入到数组a中 vis[i]=1; // 设置标记 dfs(cur+1); vis[i]=0; // 清除标记 } } } int isprime(int n) // 素数打表 { int k=1; for(int i=2;i<n/2;i++) { if(n%i==0) k=0; } return k; } int main() { int p=1; while(~scanf("%d",&n)) { for(i=1;i<=2*n;i++) v[i]=isprime(i); //判断 1 到 2*n 中哪些是素数(若是素数则赋值为1)。v[2]=0,v[7]=1..... for(i=0;i<n;i++) a[i]=i+1; //将数 1 到 n 存到数组a里面。 a[0]=1,a[1]=2,a[2]=3,a[3]=4...... printf("Case %d:\n",p); dfs(1); p++; printf("\n"); } return 0; }
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