Poj 1077 Eight 八数码

题目描述：求八数码的解，输出x的移动方式（输出步数最少的解，但是也可能会有多解，所以是special judge）

如果判断8数码有没有解可以用逆序数求，找出规律即可求解

解法一：搜索（没写过）

解法二：康托展开，一种hash的方法。

int try_to_insert(int s){
    int code = 0;
    for(int i=0;i<9;i++){
        int cnt=0;
        for(int j=i+1;j<9;j++){
            if(st[s][j]<st[s][i]) cnt++;
        }
        code += cnt*fact[8-i];
    }
    if(vis[code]==1) return 0;
    return vis[code] = 1;
}

如果简单的开一个数组，判重的时候后则需要开一个，则需要开一个九维的数组，一共会耗去9⁹=387420789项，但其实0~8的排列只有9!=362880个，所以可以用一个hash表一一对应起来。

解法3：A*（还不会）

View Code

  1 Source Code
  2 
  3 Problem: 1077  User: celia01 
  4 Memory: 8920K  Time: 141MS 
  5 Language: G++  Result: Accepted 
  6 
  7 Source Code 
  8 #include<iostream>
  9 #include<cstdio>
 10 #include<cmath>
 11 #include<cstring>
 12 #include<algorithm>
 13 #include<queue>
 14 #define see(x) cout<<#x<<":"<<x<<endl;
 15 using namespace std;
 16 typedef int State[9];
 17 const int MAXSIZE = 1000000;
 18 State st[MAXSIZE], goal;
 19 
 20 const int dx[] = {0,-1,0,1};
 21 const int dy[] = {-1,0,1,0};
 22 bool vis[400000];
 23 int fact[9];
 24 int path[MAXSIZE];
 25 int pre[MAXSIZE];
 26 void init_lookup_table(){
 27     memset(vis,0,sizeof(vis));
 28     fact[0] = 1;
 29     for(int i=1;i<9;i++){
 30         fact[i] = fact[i-1]*i;
 31     }
 32 }
 33 int try_to_insert(int s){
 34     int code = 0;
 35     for(int i=0;i<9;i++){
 36         int cnt=0;
 37         for(int j=i+1;j<9;j++){
 38             if(st[s][j]<st[s][i]) cnt++;
 39         }
 40         code += cnt*fact[8-i];
 41     }
 42     if(vis[code]==1) return 0;
 43     return vis[code] = 1;
 44 }
 45 
 46 int bfs(){
 47     init_lookup_table();
 48     int f=1, r=2;
 49     while(f<r){
 50         State& s = st[f];
 51 
 52         if(  memcmp(goal,s,sizeof(s)) == 0  )  return f;
 53         int z;
 54         for(z=0;z<9;z++) if(s[z]==0) break;
 55         int x=z/3, y=z%3;
 56         for(int d=0;d<4;d++){
 57             int newx = x+dx[d];
 58             int newy = y+dy[d];
 59             int newz = newx*3+newy;
 60             if(newx>=0&&newx<3&&newy>=0&&newy<3){
 61                 State &t = st[r];
 62                 memcpy(&t,&s,sizeof(s));
 63                 t[newz] = s[z];
 64                 t[z] = s[newz];
 65                 pre[r] = f;
 66                 path[r] = d;
 67                 if(try_to_insert(r)) r++;
 68             }
 69         }
 70         f++;
 71     }
 72     return 0;
 73 }
 74 
 75 void Path(int r){
 76     if(r<=1) return;
 77     Path(pre[r]);
 78     if(path[r]==0)
 79         printf("l");
 80     else if(path[r]==1)
 81         printf("u");
 82     else if(path[r]==2)
 83         printf("r");
 84     else
 85         printf("d");
 86 }
 87 int main(){
 88     int i, j, k, l;
 89     char ch[3];
 90     for(i=0;i<9;i++){
 91         scanf("%s",ch);
 92         if(ch[0]=='x'){
 93             st[1][i] = 0;
 94         }
 95         else st[1][i] = ch[0]-'0';
 96         goal[i]=i+1;
 97     }
 98     goal[8] = 0;
 99     
100     int ans = bfs();
101     if(ans>0) Path(ans);
102     else printf("-1");
103     puts("");
104     return 0;
105 }

 

 

 

 

 

 

View Code

  1 Source Code
  2 
  3 Problem: 1077  User: celia01 
  4 Memory: 12840K  Time: 110MS 
  5 Language: G++  Result: Accepted 
  6 
  7 Source Code 
  8 
  9 
 10 #include<iostream>
 11 #include<cstdio>
 12 #include<cmath>
 13 #include<cstring>
 14 #include<algorithm>
 15 #include<queue>
 16 #define see(x) cout<<#x<<":"<<x<<endl;
 17 using namespace std;
 18 typedef int State[9];
 19 const int MAXSIZE = 1000000;
 20 State st[MAXSIZE], goal;
 21 int dist[MAXSIZE];
 22 
 23 const int dx[] = {0,-1,0,1};
 24 const int dy[] = {-1,0,1,0};
 25 bool vis[400000];
 26 int fact[9];
 27 int path[MAXSIZE];
 28 int pre[MAXSIZE];
 29 void init_lookup_table(){
 30     memset(vis,0,sizeof(vis));
 31     memset(dist,0,sizeof(dist));
 32     fact[0] = 1;
 33     for(int i=1;i<9;i++){
 34         fact[i] = fact[i-1]*i;
 35     }
 36 }
 37 int try_to_insert(int s){
 38     int code = 0;
 39     for(int i=0;i<9;i++){
 40         int cnt=0;
 41         for(int j=i+1;j<9;j++){
 42             if(st[s][j]<st[s][i]) cnt++;
 43         }
 44         code += cnt*fact[8-i];
 45     }
 46 //    see(vis[code])
 47     if(vis[code]==1) return 0;
 48     return vis[code] = 1;
 49 }
 50 
 51 int bfs(){
 52     init_lookup_table();
 53     int f=1, r=2;
 54     while(f<r){
 55         //see(f) see(r)
 56         State& s = st[f];
 57 
 58         if(  memcmp(goal,s,sizeof(s)) == 0  )  return f;
 59         int z;
 60         for(z=0;z<9;z++) if(s[z]==0) break;
 61         int x=z/3, y=z%3;
 62         for(int d=0;d<4;d++){
 63         //    system("pause");
 64             int newx = x+dx[d];
 65             int newy = y+dy[d];
 66             int newz = newx*3+newy;
 67         //    see(z) see(newz)
 68             if(newx>=0&&newx<3&&newy>=0&&newy<3){
 69                 State &t = st[r];
 70                 memcpy(&t,&s,sizeof(s));
 71                 t[newz] = s[z];
 72                 t[z] = s[newz];
 73             //    dist[r] = dist[f]+1;
 74                 pre[r] = f;
 75                 path[r] = d;
 76                 if(try_to_insert(r)) r++;
 77             }
 78         }
 79         f++;
 80     //    see(f)
 81     }
 82     return 0;
 83 }
 84 
 85 void Path(int r){
 86     if(r<=1) return;
 87     Path(pre[r]);
 88     if(path[r]==0)
 89         printf("l");
 90     else if(path[r]==1)
 91         printf("u");
 92     else if(path[r]==2)
 93         printf("r");
 94     else
 95         printf("d");
 96 }
 97 int main(){
 98     int i, j, k, l;
 99     char ch[3];
100     for(i=0;i<9;i++){
101         scanf("%s",ch);
102         if(ch[0]=='x'){
103             st[1][i] = 0;
104         }
105         else st[1][i] = ch[0]-'0';
106         goal[i]=i+1;
107     }
108     goal[8] = 0;
109 //    for(i=0;i<9;i++) cout<<st[1][i]; cout<<endl;
110 //    for(i=0;i<9;i++) cout<<goal[i]; cout<<endl;
111     
112     int ans = bfs();//see(ans)
113     if(ans>0) Path(ans);
114     else printf("-1");
115     puts("");
116     return 0;
117 }