八数码问题（HDU 1043）（搜索、A*、IDA*、康托展开）（过一段时间二刷）_the 15-puzzle has been around for over 100 years; -优快云博客

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Problem Description 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.

Input 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

Output 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.

Sample Input 2 3 4 1 5 x 7 6 8

Sample Output ullddrurdllurdruldr