九度oj 题目1459：Prime ring problem

题目描述：

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.

输入：

n (1 < n < 17).

输出：

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.

样例输入：

6
8

样例输出：

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

提示：

用printf打印输出。

 

此题应该用深搜来求解，代码如下

#include <cstdio>
#include <iostream>
#include <cstring>
#include <queue>
#include <algorithm>
using namespace std;

int n;

int isPrime[42];
void getPrime() {
    memset(isPrime, 0, sizeof(isPrime));
    for (int i = 2; i <= 40; i++) {
        if (isPrime[i] == 0) {
            for (int j = i*2; j <= 40; j += i) {
                isPrime[j] = 1;
            }
        }
    }

}

int flag[20];
int ans[20];

void dfs(int step) {
    if (step == n) {
        int tmp = ans[0] + ans[n - 1];
        if (isPrime[tmp] == 0) {
            printf("%d", ans[0]);
            for (int j = 1; j < n; j++) {
                printf(" %d", ans[j]);
            }
            puts("");
        }
        return;
    }
    for (int i = 2; i <= n; i++) {
        if (flag[i] == 0) {
            if (step == 0) {
                flag[i] = 1;
                ans[step] = i;
                dfs(step + 1);
                flag[i] = 0;
            }
            else {
                int tmp = ans[step - 1] + i;
                if (isPrime[tmp] == 0) {
                    flag[i] = 1;
                    ans[step] = i;
                    dfs(step + 1);
                    flag[i] = 0;
                }
            }
        }
    }
}
int main(int argc, char const *argv[])
{
    getPrime();
    memset(flag, 0, sizeof(flag));
    int p = 1;
    while (scanf("%d", &n) != EOF) {
        printf("Case %d:\n", p);
        flag[1] = 1;
        ans[0] = 1;
        dfs(1);
        p++;
        puts("");
    }

    return 0;
}