POJ1077 Eight —— 正向BFS

主页面：http://www.cnblogs.com/DOLFAMINGO/p/7538588.html

代码一：以数组充当队列，利用结构体中的pre追溯上一个状态在数组（队列）中的下标：

 #include <iostream>
 #include <cstdio>
 #include <cstring>
 #include <cmath>
 #include <algorithm>
 #include <vector>
 #include <queue>
 #include <stack>
 #include <map>
 #include <string>
 #include <set>
 #define ms(a,b) memset((a),(b),sizeof((a)))
 using namespace std;
 typedef long long LL;
 const int INF = 2e9;
 const LL LNF = 9e18;
 const int MOD = 1e9+;
 const int MAXN = 1e6+;
 #define AIM  1     //123456789的哈希值为1

 struct node
 {
     int status;
     int s[];
     int loc;
     char path;
     int pre;  //pre为上一个操作在队列中的下标，用于输出路径
 };

 int vis[MAXN], fac[] = { , , , , , , , , };
 int dir[][] = { -,, ,, ,-, , };
 char op[] = {'u', 'd', 'l', 'r'  };

 int cantor(int s[])  //获得哈希函数值
 {
     int sum = ;
     for(int i = ; i<; i++)
     {
         int num = ;
         for(int j = i+; j<; j++)
             if(s[j]<s[i])
                 num++;
         sum += num*fac[-i];
     }
     return sum+;
 }

 node que[MAXN];
 int front, rear;
 int bfs(node now)
 {
     ms(vis,);
     front = rear = ;

     now.status = cantor(now.s);
     vis[now.status] = ;
     que[rear++] = now;

     node tmp;
     while(front!=rear)
     {
         now = que[front++];
         if(now.status==AIM)
             return front-;

         int x = now.loc/;
         int y = now.loc%;
         for(int i = ; i<; i++)
         {
             int xx = x + dir[i][];
             int yy = y + dir[i][];
             if(xx>= && xx<= && yy>= && yy<=)
             {
                 tmp = now;
                 tmp.s[x*+y] = tmp.s[xx*+yy];  //交换位置，下同
                 tmp.s[xx*+yy] = ;
                 tmp.status = cantor(tmp.s);
                 if(!vis[tmp.status])
                 {
                     vis[tmp.status] = ;
                     tmp.loc = xx*+yy;
                     tmp.path = op[i];     //保存操作
                     tmp.pre = front-;  //保存当前结点的状态的上一个状态所在的结点在数组（队列）的下标
                     que[rear++] = tmp;
                 }
             }
         }
     }
     return -;
 }

 void Print(int i)   //利用递归的特点（压栈），输出路径
 {
     if(i==) return;    //到了目的状态，则退出。目的状态的结点在数组（队列）中的下标为0
     Print(que[i].pre);  //访问上一步
     putchar(que[i].path); //输出操作
 }

 int main()
 {
     char tmp[];
     while(gets(tmp))
     {
         node beg;
         int cnt = ;
         for(int i = ; tmp[i]; i++)
         {
             if(tmp[i]==' ') continue;
             if(tmp[i]=='x') beg.s[cnt] = , beg.loc = cnt++;
             else  beg.s[cnt++] = tmp[i]-'';

         }
         int i = bfs(beg);
         if(i==-)
             puts("unsolvable");
         else
             Print(i), putchar('\n');
     }
 }

代码二（推荐）：把pre和path放在结构体外，利用当前状态status追溯上一个状态status：

 #include <iostream>
 #include <cstdio>
 #include <cstring>
 #include <cmath>
 #include <algorithm>
 #include <vector>
 #include <queue>
 #include <stack>
 #include <map>
 #include <string>
 #include <set>
 #define ms(a,b) memset((a),(b),sizeof((a)))
 using namespace std;
 typedef long long LL;
 const int INF = 2e9;
 const LL LNF = 9e18;
 const int MOD = 1e9+;
 const int MAXN = 1e6+;
 #define AIM  1     //123456789的哈希值为1

 struct node
 {
     int status;
     int s[];
     int loc;
 };

 int vis[MAXN], fac[] = { , , , , , , , , };
 int dir[][] = { -,, ,, ,-, , };
 char op[] = {'u', 'd', 'l', 'r'  };
 char path[MAXN];
 int pre[MAXN];

 int cantor(int s[])  //获得哈希函数值
 {
     int sum = ;
     for(int i = ; i<; i++)
     {
         int num = ;
         for(int j = i+; j<; j++)
             if(s[j]<s[i])
                 num++;
         sum += num*fac[-i];
     }
     return sum+;
 }

 queue<node>que;
 bool bfs(node now)
 {
     ms(vis,);
     while(!que.empty()) que.pop();

     now.status = cantor(now.s);
     pre[now.status] = -;   //开始状态的上一个状态为-1，用于输出路径时“刹车”
     vis[now.status] = ;
     que.push(now);

     node tmp;
     while(!que.empty())
     {
         now = que.front();
         que.pop();
         if(now.status==AIM) //找到了123456789的状态
             return true;

         int x = now.loc/;
         int y = now.loc%;
         for(int i = ; i<; i++)
         {
             int xx = x + dir[i][];
             int yy = y + dir[i][];
             if(xx>= && xx<= && yy>= && yy<=)
             {
                 tmp = now;
                 tmp.s[x*+y] = tmp.s[xx*+yy];  //交换位置，下同
                 tmp.s[xx*+yy] = ;
                 tmp.status = cantor(tmp.s);
                 if(!vis[tmp.status])
                 {
                     vis[tmp.status] = ;
                     tmp.loc = xx*+yy;
                     pre[tmp.status] = now.status;   //tmp.status的上一个状态为now.status
                     path[tmp.status] = op[i];   //保存操作
                     que.push(tmp);
                 }
             }
         }
     }
     return ;
 }

 void Print(int status)
 {
     if(pre[status]==-) return;
     Print(pre[status]);     //追溯上一个状态
     putchar(path[status]);
 }

 int main()
 {
     char str[];
     while(gets(str))
     {
         node now;
         int cnt = ;
         for(int i = ; str[i]; i++)
         {
             if(str[i]==' ') continue;
             if(str[i]=='x') now.s[cnt] = , now.loc = cnt++;
             else  now.s[cnt++] = str[i]-'';
         }
         if(!bfs(now))
             puts("unsolvable");
         else
             Print(AIM), putchar('\n');
     }
 }