Prime Ring Problem 素数环问题

Prime Ring Problem

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

 

  题意不难理解，即一个环，由1~n组成，任意相邻的两个数之和为素数

主要是代码方面，原以为写了很多dfs这方面的代码，但是这次写仍然遇到了问题：

         1.dfs里自己写的很乱

         2.不够优化，比如判断素数时，想到了素数打表，但没想到用0,1代表是否为素数，下标代表这个数。

         3.还可以更优化—n为奇数的时候不可能形成素数环，此处优化下面代码中未体现

附代码如下

#include<stdio.h>#include<string.h>int is_prime[]= {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},n;int visited[21],a[21];int flog;void dfs(int step){    if(step==n&&is_prime[a[n-1]+1])    {        flog=0;        for(int i=0; i<n-1; i++)            printf("%d ",a[i]);        printf("%d\n",a[n-1]);    return;    }        for(int i=2; i<=n; i++)        {           if(visited[i]==0)            {                if(is_prime[a[step-1]+i])                {                    visited[i]=1;                    a[step++]=i;                    dfs(step);                    visited[i]=0;                    step--;//写的时候把这条语句没写，汗···                }            }      }}int main(){    int j=1;    while(~scanf("%d",&n))    {        flog=1;        printf("Case %d:\n",j++);        memset(visited,0,sizeof(visited));        a[0]=1;        dfs(1);         if(flog==1)         printf("No Answer\n");     }}