Prime Ring Problem HDU - 1016

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. 

 

Inputn (0 < n < 20). 
OutputThe 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

思路：DFS遍历所有结果
AC Code:

#include<iostream>
#include<cstring>
using namespace std;
int num[100];
int vis[100];
int n;
bool isPrime (int k) {
    for (int i = 2; i * i <= k; i++)
        if (k % i == 0)
            return false;
    return true;
}
void dfs (int k) {
    if (k > n) {
        if (isPrime (num[1] + num[n])) {
            for (int i = 1; i < n; i++)
                printf("%d ", num[i]);
            printf("%d\n", num[n]);
        }
        return ;
    }
    for (int i = 2; i <= n; i++) {
        if (vis[i] == false) {
            if (isPrime (num[k - 1] + i)) {
                num[k] = i;
                vis[i] = true;
                dfs (k + 1);
                vis[i] = false;
            }
        }
    }
    return ;
}
int main() {
    int sum = 1;
    while(~scanf ("%d", &n)){
        printf ("Case %d:\n", sum++);
        memset (vis, false, sizeof(vis));
        num[1] = 1;
        vis[1] = true;
        dfs(2);
        putchar('\n');
    }
}