【HDU 1016】Prime Ring Problem（DFS）

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

题目大意

给你一个n，问你能否将1~n中的各个数字拼成一个素数环，要求相邻两个元素之间相加为素数。

思路

对于每一种情况都去跑一边DFS，记录步数，看最后步数和N是否相等，相等即为一种可行情况。

代码

#include <iostream>#include <cstdio>#include <algorithm>using namespace std;int CaseTime;int Number;int direction[21];int DoneNumber;int num[21];int chess[21];bool IsLeagal( int tmp ){    if( tmp == 3 || tmp == 5 || tmp == 7 || tmp == 11 || tmp == 13 || tmp == 17 || tmp == 19 )        return true;    if( tmp == 23 || tmp == 31 || tmp == 37 )        return true;    return false;}void solve(int startnum,int overnum,int settime){    if(overnum == Number)    {        for(int i=0;i<Number;i++)        {            if(i==0) printf("%d",num[i]);            else printf(" %d",num[i]);        }        printf("\n");        return ;    }    int i;    for(i=1;i<=Number;i++)    {        if(overnum==Number-1)        {            if(IsLeagal(startnum+direction[i])&&IsLeagal(direction[i]+1)&&!chess[i])            {                chess[i]=1;                num[settime] = i;                solve(i,overnum+1,settime+1);                chess[i]=0;            }        }        else if(IsLeagal(startnum+direction[i])&&!chess[i])        {                chess[i]=1;                num[settime] = i;                solve(i,overnum+1,settime+1);                chess[i]=0;        }    }}int main(){    for(int i=1;i<=20;i++)        direction[i]=i;    CaseTime=0;    while(scanf("%d",&Number)!=EOF)    {        memset(chess,0,sizeof(chess));        chess[1]=1;        num[0]=1;        printf("Case %d:\n",++CaseTime);        solve(1,1,1);        printf("\n");    }    return 0;}