[HDOJ1043]Eight（康托展开 BFS 打表）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=1043

　　八数码问题，因为固定了位置所以以目标位置开始搜索，把所有情况（相当于一个排列）都记录下来，用康托展开来完成序列的记录问题开始BFS。打好表后按给出序列的康托数确定开始位置，逆向查找。

 #include <algorithm>
 #include <iostream>
 #include <iomanip>
 #include <cstring>
 #include <climits>
 #include <complex>
 #include <fstream>
 #include <cassert>
 #include <cstdio>
 #include <bitset>
 #include <vector>
 #include <deque>
 #include <queue>
 #include <stack>
 #include <ctime>
 #include <set>
 #include <map>
 #include <cmath>

 using namespace std;

 typedef struct Node1 {
     char s;
     int pre;
     Node1() { pre = -; }
 }Node1;
 typedef struct Node2 {
     int status[];
     int n, son;
 }Node2;

 Node1 path[];
 int dx[] = {, -, , };
 int dy[] = {, , , -};
 int fac[];

 void init() {
     fac[] = fac[] = ;
     for(int i = ; i <= ; i++) {
         fac[i] = fac[i-] * i;
     }
 }

 int ecantor(int* s, int n = ) {
     int num = ;
     for(int i = ; i < n; i++) {
         int tmp = ;
         for(int j = i + ; j < n; j++) {
             if(s[j] < s[i]) {
                 tmp++;
             }
         }
         num += fac[n--i] * tmp;
     }
     return num;
 }

 void bfs() {
     queue<Node2> q;
     Node2 a, b;
     int t = ;
     for(int i = ; i < ; i++) {
         a.status[i] = i + ;
     }
     a.n = ; a.son = ;
     path[a.son].pre = ;
     q.push(a);
     while(!q.empty()) {
         a = q.front(); q.pop();
         for(int i = ; i < ; i++) {
             b = a;
             int xx = a.n %  + dx[i];
             int yy = a.n /  + dy[i];
             if(!(xx >=  && xx <  && yy >=  && yy < )) continue;
             b.n = yy *  + xx;
             swap(b.status[b.n], b.status[a.n]);
             b.son = ecantor(b.status);
             if(path[b.son].pre == -) {
                 path[b.son].pre = a.son;
                 if(i == ) path[b.son].s = 'l';
                 if(i == ) path[b.son].s = 'r';
                 if(i == ) path[b.son].s = 'u';
                 if(i == ) path[b.son].s = 'd';
                 q.push(b);
             }
         }
     }
 }

 int main() {
     // freopen("in", "r", stdin);
     init();
     int s, ss[];
     char ch[];
     bfs();
     while(gets(ch)) {
         int cnt = ;
         for(int i = ; ch[i]; i++) {
             if(ch[i] == 'x') {
                 ss[cnt++] = ;
             }
             else if(ch[i] >= '' && ch[i] <= '') {
                 ss[cnt++] = ch[i] - '';
             }
         }
         s = ecantor(ss);
         if(path[s].pre == -) {
             printf("unsolvable\n");
             continue;
         }
         while(s != ) {
             printf("%c", path[s].s);
             s = path[s].pre;
         }
         printf("\n");
     }
     return ;
 }