学步园

注意起点可以是素数，但是终点不可以是素数，终点是素数则到达不了，开数组要开到200*200才可以

描述

Xiaod has recently discovered the grid named "spiral grid".

Construct the grid like the following figure. (The grid is actually infinite. The figure is only a small part of it.)

Considering traveling in it, you are free to any cell containing a composite number or 1, but traveling to any cell containing a prime number is disallowed. In addition, traveling
from a prime number is disallowed, either. You can travel up, down, left or right, but not diagonally. Write a program to find the length of the shortest path between pairs of nonprime numbers, or report it's impossible.

输入

Each test case is described by a line of input containing two nonprime integer 1 <=x, y<=10,000.

输出

For each test case, display its case number followed by the length of the shortest path or "impossible" (without quotes) in one line.

样例输入

1 4
9 32
10 12

样例输出

Case 1: 1
Case 2: 7
Case 3: impossible

 
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;
class node
{
    int x,y,step;
    public node(int x,int y,int step) {
        // TODO Auto-generated constructor stub
        this.x=x;
        this.y=y;
        this.step=step;
    }
}
public class Main {
    static int map[][],startx,starty,endx,endy,n=40400,size=210;
    static boolean prim[],mark[][],vis[][];
    static int directions[][]={{-1,0},{1,0},{0,-1},{0,1}};
    public static void isprim()
    {
        prim[1]=true;
        for(int i=2;i*i<=10009;i++)
        {
            if(!prim[i])
            {
                for(int j=2*i;j<=10009;j+=i)
                {
                    prim[j]=true;
                }
            }
        }
    }
    public static void constructmap()
    {
        int data=40000;
        int x=200;
        map[0][0]=data;
        int i=0,k=0;
        while(data>1)
        {
            while(k<x-1&&map[i][k+1]==0)map[i][k++]=data--;
            while(i<x-1&&map[i+1][k]==0)map[i++][k]=data--;
            while(k>0&&map[i][k-1]==0)map[i][k--]=data--;
            while(i>0&&map[i-1][k]==0)map[i--][k]=data--;
            
        }
        map[i][k]=1;
        
    }
    public static boolean overmap(int x,int y)
    {
        if(x<0||x>=200||y<0||y>=200)return true;
        return false;
                
    }
    public static int bfs(int x,int y)
    {
    	if(x==y)return 0;
        //注意终点不可以是素数
    	if(!prim[y])
    		return -1;
    	
        node first=new node(startx, starty, 0);
        Queue<node>queue=new LinkedList<node>();
        queue.add(first);
        while(!queue.isEmpty())
        {
            first=queue.remove();
                  vis[first.x][first.y]=true;
            for(int i=0;i<4;i++)
            {
                node next=new node(first.x+directions[i][0], first.y+directions[i][1],first.step+1);
                 if(next.x==endx&&next.y==endy)return next.step;
                if(overmap(next.x,next.y)||!prim[map[next.x][next.y]]||vis[next.x][next.y])continue;
                queue.add(next);
                vis[next.x][next.y]=true;
            }
        }
        return -1;
    }
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        Scanner scanner = new Scanner(System.in);
        
        map=new int[size][size]; 
        prim=new boolean[n];
        constructmap();
        isprim();
        int count=1;
        while(scanner.hasNext())
        {
            vis=new boolean[size][size];
            int x=scanner.nextInt();
            int y=scanner.nextInt();
            for(int i=0;i<200;i++)
            {
                for(int j=0;j<200;j++)
                {
                    if(map[i][j]==x)
                    {
                        startx=i;
                        starty=j;
                    }
                    if(map[i][j]==y)
                    {
                        endx=i;
                        endy=j;
                    }
                }
            }
            System.out.printf("Case %d: ",count++);
            int result=bfs(x,y);
            if(result==-1)
            System.out.println("impossible");
            else {
                System.out.println(result);
            }
        }
        
    }
}