HDU 1016 Prime Ring Problem（经典DFS ）

题目链接:    http://acm.hdu.edu.cn/showproblem.php?pid=1016

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

 

Source

Asia 1996, Shanghai (Mainland China)

代码如下：

#include<cstdio>#include<iostream>#include<cmath>const int MAX=100;int prim[MAX],chucun[MAX],mark[MAX];int n,count;using namespace std;bool prime(double x){    int i;    for(i=2;i<=sqrt(x);i++)    {        if(int(x)%i==0)            return false;    }    return true;}void DFS(int x){    if(x==n&&(prime(double(1+chucun[x-1]))))//深搜到结束条件(第一个数字为1，（环）判断最后一个数加1是否为素数)    {        for(int i=0;i<x;i++)        {            if(i==0)                printf("%d",chucun[i]);            else                printf(" %d",chucun[i]);        }        printf("\n");    }    else    {        for(int i=2;i<=n;i++)        {            if(!mark[i] && prime(double(chucun[x-1]+i)))//如果这个数没用过，并且这个数和上一个放到环里的数之和是素数            {                mark[i]=1;                chucun[x]=i;                DFS(x+1);                mark[i]=0;//回溯            }        }    }}int main(){    int i,p=1;    while(~scanf("%d",&n))    {        printf("Case %d:\n",p++);        chucun[0]=1;        memset(mark,0,sizeof(mark));        DFS(1);        printf("\n");    }}