UVA 524 素数环【dfs/回溯法】

Description

A ring is composed of n (even number) circles as shown in diagram. Put natural numbers 1,2,3，...，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 <= 16)

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.

You are to write a program that completes above process.

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

【代码】：

/*素数环*/

#include <bits/stdc++.h>

using namespace std;

int n,prime[]={},v[],a[];

void get_prime()

{

    int m=sqrt(*n+0.5);//环-倍增

    memset(prime,,sizeof(prime));//0为素数

    prime[]=prime[]=;//非素数

    for(int i=;i<=m;i++)

    {

        if(prime[i])//素数

        {

            for(int j=i+i;j<=*n;j+=i)

            {

                prime[j]=;//非素数

            }

        }

    }

}

void dfs(int cur)

{

    if(cur == n && prime[ a[]+a[n-] ])

    {

        for(int i=; i<n; i++)

        {

             printf("%d%c", a[i], i == n -  ? '\n' : ' ');

        }

       // printf("\n");

    }

    else

    {

        for(int i=; i<=n; i++)

        {

            if( !v[i] && prime[ i + a[cur-] ] )

            {

                a[cur] = i;

                v[i]=;

                dfs(cur+);

                v[i]=;

            }

        }

    }

}

int main()

{

    scanf("%d",&n);

    //初始化

    memset(v,,sizeof(v));

    a[]=;

    get_prime();

    dfs();

}

巴特西

UVA 524 素数环【dfs/回溯法】

Input

n (0 < n <= 16)

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.

Sample Input

Sample Output

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巴特西

UVA 524 素数环 【dfs/回溯法】

Input

n (0 < n <= 16)

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.

Sample Input

Sample Output

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UVA 524 素数环【dfs/回溯法】