hdu1043Eight
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Eight
Time Limit : 10000/5000ms (Java/Other) Memory Limit : 65536/32768K (Java/Other)
Total Submission(s) : 16 Accepted Submission(s) : 1
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 1213 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 1213 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
South Central USA 1998 (Sepcial Judge Module By JGShining)
本来用双向bfs结果tle到死啊~~~
参考别人打表过~~~~用到康托展开
#include <iostream>#include <cstring>#include <cstdio>#include <cstdlib>#include <queue>#define INF 0x3f3f3f3f#define N 400000#define BUG printf("here!\n")using namespace std;struct node{ char num[9]; int cantor; int pos;};int xx[4]={0,1,0,-1};int yy[4]={1,0,-1,0};char temp_str[30];char num[9];char tmp_num[10]="123456780";int fac[10]={1,1,2,6,24,120,720,5040,40320,362880};int vis[N];int route[N];int precantor[N];int cantor(char *num);void bfs(){ queue<node> q; memset(vis,0,sizeof(vis)); memset(precantor,-1,sizeof(precantor)); node temp; int i; for(i=0;i<8;i++) temp.num[i]='1'+i; temp.num[8]='0'; temp.pos=8; temp.cantor=cantor(temp.num); q.push(temp); vis[temp.cantor]=1; while(!q.empty()) { node cur=q.front(); q.pop(); int cx=cur.pos/3; int cy=cur.pos%3; for(i=0;i<4;i++) { int nx=cx+xx[i]; int ny=cy+yy[i]; if(nx<0||nx>=3||ny<0||ny>=3) continue; node next=cur; next.pos=nx*3+ny; next.num[cur.pos]=next.num[next.pos]; next.num[next.pos]='0'; next.cantor=cantor(next.num); if(vis[next.cantor]) continue; vis[next.cantor]=1; if(i==0) { route[next.cantor]='l'; precantor[next.cantor]=cur.cantor; } else if(i==1) { route[next.cantor]='u'; precantor[next.cantor]=cur.cantor; } else if(i==2) { route[next.cantor]='r'; precantor[next.cantor]=cur.cantor; } else { route[next.cantor]='d'; precantor[next.cantor]=cur.cantor; } q.push(next); } } return ;}void print(int tar){ int i; for(i=tar;i!=-1;i=precantor[i]) { printf("%c",route[i]); } printf("\n");}int cantor(char *num){ int i,j,tol=0,sum=0; for(i=0;i<9;i++) { tol=0; for(j=i+1;j<9;j++) { if(num[i]<num[j]) tol++; } sum+=tol*fac[9-i-1]; } return sum;}int main(){ bfs(); while(gets(temp_str)!=NULL) { int k=0; int i,l=strlen(temp_str); for(i=0;i<l;i++) { if(temp_str[i]=='x') { num[k]='0'; k++; } else if(temp_str[i]>='1'&&temp_str[i]<='8') num[k++]=temp_str[i]; } int tt=cantor(num); if(vis[tt]==0) printf("unsolvable\n"); else { print(tt); } } return 0;}
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