(HDU 1016) Prime Ring Problem

(HDU 1016) Prime Ring Problem

思路：

素数环，用数组来存储，相邻的两个数a[x] + a[x-1]要为素数；

DFS, a[0] = 1, 从位置1开始尝试填入数字，填入的数字和前一个数字之和要为素数且填过数字不能重复，直到a[n-1]放好数字之后， 判断a[n-1]+a[0]是否为素数，如果是则输出结果。

代码：

import java.util.Arrays;
import java.util.Scanner;

public class Main{
	public static int a[];
	public static boolean vis[];
	public static int prime[] = new int[50];
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		gernerate_prime();//生成素数表
		int cnt = 0;
		while(in.hasNext()){
			cnt++;
			int n = in.nextInt();
			a = new int[n];
			vis = new boolean[n+1];
			a[0] = 1;
			vis[1] = true;
			System.out.println("Case "+cnt+":");
			dfs(1, n);
			System.out.println();
		}
	}
	private static void dfs(int i, int n) {
		if(i == n && prime[a[n-1] + a[0]] == 1){
			for(int j = 0; j < n-1; j++) 
				System.out.print(a[j]+" ");
			System.out.println(a[n-1]);
			return ;
		}
		
		for(int j = 1; j <= n; j++){
			if(!vis[j] && prime[j+a[i-1]] == 1){ //判断数字是否填过，并且这个数字填入是否和前面数字之和为素数
				vis[j] = true;
				a[i] = j;
				dfs(i+1, n);
				vis[j] = false;
			}
		}
	}
	private static void gernerate_prime() {
		int size = prime.length - 1;
		Arrays.fill(prime, 1);
		prime[1] = 0;
		prime[2] = 1;
		for(int i = 2; i < size; i++){
			if(prime[i] == 1){
				for(int j = i + i; j < size; j += i)
					prime[j] = 0;
			}
		}
	}
}

 相似题目：

HDU 1015 Safecracker

用大小为5数组的存放数字，可选数字有12个，和上面一样先放0位置，直到5位置填充，判断是否符合题目条件v - w^2 + x^3 - y^4 + z^5 = target

5个位置5层循环也可以代码：

import java.util.Arrays;
import java.util.Scanner;

public class Main{
    public static char a[];
    public static char c[];
    public static boolean ans;
    public static boolean vis[];
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        
        while(in.hasNext()){
            int n = in.nextInt();
            String s = in.next();
            if(n == 0 && s.equals("END"))
                break;
            c = s.toCharArray();
            a = new char[5];
            vis = new boolean[c.length];
            Arrays.sort(c);
            ans = false;
            dfs(0, 5, n);
            if(ans){
                for(int i = 0; i < 5; i++) 
                    System.out.print(a[i]);
                System.out.println();
            }
            else 
                System.out.println("no solution");
        }
    }
    
    private static void dfs(int i, int n, int target) {
        if(i == n){
            int sum = 0;
            for(int j = 0; j < 5; j++){
                sum += pow(a[j]-'A'+1, j+1);
            }
            if(target == sum) 
                ans = true;
            return ;
        }
        
        for(int j = c.length-1; j >= 0; j--){
            if(!vis[j]){
                vis[j] = true;
                a[i] = c[j];
                dfs(i+1, n, target);
                if(ans)
                    return ;
                
                vis[j] = false;
            }
        }
    }
    
    private static int pow(int x, int n) {
        int sum = 1;
        for(int i = 0; i < n; i++)
            sum *= x;
        
        if((n&1) == 1) 
            return sum;
        else 
            return -sum;
    }
}