# 传送门HDU1043

# 描述

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 xwhere 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

5 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.## 输入

You will receive, several descriptions of configuration of the 8 puzzle. One 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

# 输出

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. Do not print a blank line between cases.

# 样例

Input

2 3 4 1 5 x 7 6 8Output

ullddrurdllurdruldr

# 题解

- 题意：3*3的表格，x可以和上下左右交换，最后通过移动x使整个表格有序且x在最后一格。求移动方案，输出路径，没有则输出-1
- 法一：从输入字符串和目标串开始进行双向bfs（3000+ms）
- 法二：bfs预处理出目标串到其他可达串的路径，然后O(t)查询，t为答案长度(300+ms)
- 因为内存有限，把x视为9，用康托展开存储答案。

# Code（法一）

1 | //双向bfs+康托 |

# Code(法二)

1 | //预处理答案 |