八数码问题——HDU 1043
2014-08-07 10:41
337 查看
对应杭电题目:点击打开链接
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.
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
Sample Output
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 康拓展开判重,反向BFS#include<cstdio> #include<cstdlib> #include<cmath> #include<map> #include<queue> #include<stack> #include<vector> #include<algorithm> #include<cstring> #include<string> #include<iostream> const int MAXN=500000+10; const int MAXNHASH=500000+10; using namespace std; typedef int State[9]; State st[MAXN]; int goal[9]; int vis[370000]; int fact[9]; int fa[MAXN]; int dir[MAXN]; int codestart,codeend; const int dx[]={-1,1,0,0}; const int dy[]={0,0,-1,1}; char cal[5]="durl"; void init_lookup_table() { fact[0]=1; for(int i=1; i<9; i++){ fact[i]=fact[i-1]*i; } } int Code(State &s) { int code=0; for(int i=0; i<9; i++){ int cnt=0; for(int j=i+1; j<9; j++){ if(s[j]<s[i]) cnt++; } code+=fact[8-i]*cnt; } return code; } void bfs() { memset(fa,0,sizeof(fa)); memset(vis,0,sizeof(vis)); int front=1, rear=2; while(front<rear) { //cout<<front<<endl; State& s=st[front]; //if(memcmp(goal, s, sizeof(s))==0) return front; int z; for(z=0; z<9; z++) if(!s[z]) break; int x=z/3, y=z%3; for(int i=0; i<4; i++){ int newx=x+dx[i]; int newy=y+dy[i]; int newz=newx*3+newy; if(newx>=0 && newx<3 && newy>=0 && newy<3){ State&t =st[rear]; memcpy(t,s,sizeof(s)); t[newz]=s[z]; t[z]=s[newz]; int code=Code(t); int code1=Code(s); if(!vis[code]){ vis[code]=1; fa[code]=code1; dir[code]=i; rear++; } } } front++; } } void print(int num) { if(num!=codeend){ cout<<cal[dir[num]]; print(fa[num]); } } int main() { //freopen("in.txt","r",stdin); init_lookup_table(); char ch; for(int i=0; i<8; i++) st[1][i]=i+1; st[1][8]=0; codeend=Code(st[1]); vis[codeend]=1; bfs(); while(cin>>ch) { if(ch=='x') goal[0]=ch-120; else goal[0]=ch-'0'; for(int i=1; i<9; i++){ cin>>ch; if(ch=='x') goal[i]=ch-120; else goal[i]=ch-'0'; } codestart=Code(goal); if(vis[codestart]){ print(codestart); cout<<endl; } else cout<<"unsolvable"<<endl; } return 0; }
相关文章推荐
- HDU 1043 Eight (经典八数码问题,BFS+状态枚举+伪哈希)
- bfs+hash poj 1077/hdu 1043 八数码问题
- HDU-1043 Eight 八数码问题
- [算法入门经典] 7.5.3 八数码问题 | HDU 1043
- HDU 1043 八数码问题 A*搜索
- poj 1077 hdu 1043 Eight 八数码问题 DBFS(双向广度优先搜索)a*算法 康拓展开
- hdu 1043 Eight(八数码问题 高级搜索: A* 搜索)
- hdu 1043 Eight 经典八数码问题
- HDU 1043 Eight ((八数码问题)逆向BFS + 康托定理判重)
- hdu1043 八数码问题
- hdu 1043 /poj 1077 Eight(经典八数码问题,BFS+康托展开)
- HDU 1043 Eight(经典八数码问题)对比POJ 1077
- POJ 1077 Eight && HDU 1043 Eight 八数码问题(A*算法)
- hdu 1043 Eight 经典八数码问题
- Hdu 1043 Eight (八数码问题)
- HDU 1043 八数码问题 A*搜索
- 八数码问题(HDU 1043)
- HDU1043 Eight 八数码问题
- HDU 1043 / POJ 1077 Eight(八数码问题)
- hdu 1043-Eight(经典八数码问题)(单向广搜 A* 状态压缩)