Eight
Time Limit: 10000/5000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 10778 Accepted Submission(s):
2873
Special Judge
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:
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, 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
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
Source
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康托展开优化,代码自己写的过了,做EIGHTII的时候,发现别人bfs()很简单,而且map[4][2]写的看不懂。
1 #include<iostream> 2 #include<stdio.h> 3 #include<cstring> 4 #include<cstdlib> 5 #include<string> 6 #include<queue> 7 using namespace std; 8 9 struct node 10 { 11 bool flag; 12 char str; 13 int father; 14 }hash[363001]; 15 struct st 16 { 17 char t[10]; 18 }; 19 queue<st>Q; 20 int ans[10]={1}; 21 22 int ktzk(char *c) 23 { 24 int i,j,k,sum=0; 25 for(i=0;i<=8;i++) 26 { 27 k=0; 28 for(j=i+1;j<=8;j++) 29 if(c[i]>c[j]) 30 k++; 31 sum=sum+k*ans[8-i]; 32 } 33 return sum; 34 } 35 void bfs() 36 { 37 int i,k,num,val; 38 struct st cur,t; 39 k=ktzk("123456780"); 40 hash[k].flag=true; 41 hash[k].str='