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.
![](http://acm.hdu.edu.cn/data/images/1016-1.gif)
Note: the number of first circle should always be 1.
![](http://acm.hdu.edu.cn/data/images/1016-1.gif)
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.
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; }