UVA - 524 Prime Ring Problem

朱雀 2022-07-10 11:28 141阅读 0赞

Description

A ring is composed of n (even number) circles as shown in diagram. Put natural numbers  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][Input]  ##

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][Input]  ##

6
    8

## [Sample Output][Input]  ##

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

#include <iostream>
    #include <cstdio>
    
    using namespace std;
    
    const int maxn = 50;
    int n,A[maxn] = {1},isp[maxn], vis[maxn];
    void dfs(int cur)
    {
        if(cur == n&& isp[A[0] + A[n - 1]]) {
            for(int i = 0; i < n; i++) {
                i ? printf(" %d", A[i]) : printf("%d", A[i]);
            }
            printf("\n");
        } else for(int i = 2; i <= n; i++) {
            if(!vis[i]&& isp[i + A[cur - 1]]) {
                A[cur] = i;
                vis[i] = 1;
                dfs(cur + 1);
                vis[i] = 0;
            }
        }
    }
    int main()
    {
        for(int i =2;i<=50;i++)
        {
            isp[i] = 1;
        }
        for(int i = 2;i<=50;i++)
        {
            for(int j = i + i; j + i <= 50; j +=i)
            {
                isp[j] = 0;
            }
        }
        int kase = 0;
        while(cin>>n)
        {
            if(kase++)
            {
                cout<<"\n";
            }
            cout<<"Case "<<kase<<":\n";
            dfs(1);
        }
        return 0;
    }

[Input]: http://acm.hust.edu.cn/vjudge/contest/view.action?cid=84562