八数码
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:
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:
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.
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 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
is described by this list:
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.
Sample Input
2 3 4 1 5 x 7 6 8
Sample Output
ullddrurdllurdruldr
经典的八数码问题，不过这道题的难点主要在于时间限制，如果时间开放为十秒，估计问题也就没那么复杂了，直接用stl中的map去重及标记。
可是时间限制为一秒，这就说明无法采用stl，只能用hash+BFS
开始的时候用hash+BFS 做了一个：
#include"iostream"
#include"cstring"
#include"queue"
#include"stack"
using namespace std;
const int maxn=370000;
int book[maxn];
struct node
{
int status[9]; //记录当前状态
int log; //记录x的位置
int hashd; //记录当前状态哈希值
string path; //记录路径
};
int goal[]={1,2,3,4,5,6,7,8,0};
int aim;
int mov1[4][2]={{-1,0},{1,0},{0,-1},{0,1}};
string mov2="udlr";
string ans;
int HASH[10]={1,1,2,6,24,120,720,5040,40320,362880};
int cantor(int a[])
{
int answer=0;
int number=0;
for(int i=0;i<9;i++)
{
number=0;
for(int j=i+1;j<9;j++)
if(a[i]>a[j]) number++;
answer+=number*HASH[8-i];
}
return answer+1;
}
int BFS(struct node c)
{
queue<struct node> que;
que.push(c);
book[c.hashd]=1;
while(!que.empty())
{
struct node cur,nex;
cur=que.front();
if(cur.hashd==aim)
{
ans=cur.path;
// for(int kk=0;kk<9;kk++) cout<<cur.status[kk]<<' ';
return 1;
}
que.pop();
int x=cur.log/3