2013
11-09

# Eight

The 15-puzzle has been around for over 100 years; even if you don’t know it by that name, you’ve seen it. It is constructed with 15 sliding tiles, each with a number from 1 to 15 on it, and all packed into a 4 by 4 frame with one tile missing. Let’s call the missing tile ‘x’; the object of the puzzle is to arrange the tiles so that they are ordered as:
 1  2  3  4
5  6  7  8
9 10 11 12
13 14 15  x 

where the only legal operation is to exchange ‘x’ with one of the tiles with which it shares an edge. As an example, the following sequence of moves solves a slightly scrambled puzzle:

 1  2  3  4    1  2  3  4    1  2  3  4    1  2  3  4
5  6  7  8    5  6  7  8    5  6  7  8    5  6  7  8
9  x 10 12    9 10  x 12    9 10 11 12    9 10 11 12
13 14 11 15   13 14 11 15   13 14  x 15   13 14 15  x
r->           d->           r-> 

The letters in the previous row indicate which neighbor of the ‘x’ tile is swapped with the ‘x’ tile at each step; legal values are ‘r’,'l’,'u’ and ‘d’, for right, left, up, and down, respectively.

Not all puzzles can be solved; in 1870, a man named Sam Loyd was famous for distributing an unsolvable version of the puzzle, and

frustrating many people. In fact, all you have to do to make a regular puzzle into an unsolvable one is to swap two tiles (not counting the missing ‘x’ tile, of course).

In this problem, you will write a program for solving the less well-known 8-puzzle, composed of tiles on a three by three

arrangement.

You will receive a description of a configuration of the 8 puzzle. The description is just a list of the tiles in their initial positions, with the rows listed from top to bottom, and the tiles listed from left to right within a row, where the tiles are represented by numbers 1 to 8, plus ‘x’. For example, this puzzle
 1  2  3
x  4  6
7  5  8 

is described by this list:

 1 2 3 x 4 6 7 5 8

You will print to standard output either the word “unsolvable”, if the puzzle has no solution, or a string consisting entirely of the letters ‘r’, ‘l’, ‘u’ and ‘d’ that describes a series of moves that produce a solution. The string should include no spaces and start at the beginning of the line.

 2  3  4  1  5  x  7  6  8

ullddrurdllurdruldr

//* @author: [email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */
import java.util.*;
public class Main
{
static int[][] arr;
static boolean[] bb=new boolean[10000000];
static Queue< my> qu=new LinkedList< my>();
public static void main(String[] args)
{
Scanner in=new Scanner(System.in);
arr=new int[5][5];
String s;
for(int i=1;i< 4;i++)
{
for(int j=1;j< 4;j++)
{
s=in.next();
if(s.equals("x"))arr[i][j]=0;
else arr[i][j]=Integer.parseInt(s);
}
}
int u=getNum();
bfs(u);

}
static void bfs(int t)
{
while(!qu.isEmpty())
{
my h=qu.poll();
int u=h.u;
String s=h.s;
if(u==123456780)
{
System.out.println(s);
return;
}
if(bb[u%9999991])continue;
bb[u%9999991]=true;
int i=-1,j=-1,p=u;
for(int u1=3;u1>0;u1--)
{
for(int u2=3;u2>0;u2--)
{
arr[u1][u2]=p%10;
if(arr[u1][u2]==0)
{
i=u1;
j=u2;
}
p/=10;
}
}
change(i,j,i-1,j);
int y=getNum();
change(i-1,j,i,j);

change(i,j,i+1,j);
y=getNum();
change(i+1,j,i,j);

change(i,j,i,j+1);
y=getNum();
change(i,j+1,i,j);

change(i,j,i,j-1);
y=getNum();
change(i,j-1,i,j);
}
System.out.println("unsolvable");
}
static int getNum()
{
int t=0;
for(int i=1;i< 4;i++)
for(int j=1;j< 4;j++)
{
t*=10;
t+=arr[i][j];
}
return t;
}
static void change(int x1,int y1,int x2,int y2)
{
arr[x1][y1]=arr[x2][y2];
arr[x2][y2]=0;
}
}
class my
{
String s="";
int u;
public my(String t,int a)
{
u=a;
s=t;
}
}