HDU 1016 Prime Ring Problem

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

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

 

时间复杂度：$O(n!)$

代码：

#include <stdio.h>
#include <string.h>
int book[30], a[30], n;
int prime(int x) {
    int i;
    for (i = 2; i <= x / 2; i ++)
        if (x % i == 0) return 0;
    return 1;
}

void dfs(int step) {
    if (step == n + 1 && prime(a[1] + a[n])) {
        for (int i = 1; i <= n - 1; i ++)
            printf("%d ", a[i]);
        printf("%d\n", a[n]);
        return;
    }
    
    for (int i = 2; i <= n; i ++) {
        if (book[i] == 0) {
            if (prime(i + a[step - 1])) {
                book[i] = 1;
                a[step] = i;
                dfs(step + 1);
                book[i] = 0;
            }
        }
    }
    return;
}

int main() {
    int kase = 0;
    a[1] = 1;
    while (~scanf("%d", &n)) {
        memset(book, 0, sizeof(book));
        printf("Case %d:\n", ++kase);
        dfs(2);
        printf("\n");
    }
    return 0;
}