HDU 1043 Eight（双向BFS+康托展开）

  1 #include<iostream>
  2 #include<string>
  3 #include<cstring>
  4 #include<queue>
  5 #include<algorithm>
  6 using namespace std;
  7 
  8 const int maxn = 400000;
  9 const char* DIR1 = "udlr";
 10 const char* DIR2 = "durl";
 11 
 12 int fac[] = { 1, 1, 2, 6, 24, 120, 720, 5040, 40320 };  //阶乘值
 13 
 14 int x; //x的位置
 15 
 16 int dir[] = { -3, 3, -1, 1 };
 17 
 18 int vis1[maxn];
 19 int vis2[maxn];
 20 
 21 char ss[] = "123456780";
 22 char str[30];
 23 
 24 struct Node
 25 {
 26     int x;
 27     char str[30];
 28 };
 29 
 30 struct Step
 31 {
 32     int cnt;
 33     char dir;
 34 }pre[maxn];  //记录路径
 35 
 36 
 37 int sequence(char a[])  //计算康托展开值
 38 {
 39     int sum = 0;
 40     for (int i = 0; i < 9; i++)
 41     {
 42         int k = 0;
 43         for (int j = i + 1; j < 9; j++)
 44         {
 45             if (a[j] < a[i])
 46                 k++;
 47         }
 48         sum += fac[9 - 1 - i] * k;
 49     }
 50     return sum;
 51 }
 52 
 53 
 54 void printfff(int x)  //追溯到起点输出路径
 55 {
 56     if (pre[x].cnt == -1)  return;
 57     printfff(pre[x].cnt);
 58     cout << pre[x].dir;
 59 }
 60 
 61 int judge(int x, int i)   //判断是否越界
 62 {
 63     int xx = x / 3;  //行
 64     int yy = x % 3;  //列
 65     if (i == 3)
 66     {
 67         int yyy = yy + 1;
 68         if (yyy > 2)  return 0;
 69     }
 70     if (i == 2)
 71     {
 72         int yyy = yy - 1;
 73         if (yyy < 0)   return 0;
 74     }
 75     if (i == 1)
 76     {
 77         int xxx = xx + 1;
 78         if (xxx>2)    return 0;
 79     }
 80     if (i == 0)
 81     {
 82         int xxx = xx - 1;
 83         if (xxx < 0) return 0;
 84     }
 85     return 1;
 86 }
 87 
 88 void bfs()
 89 {
 90     memset(vis1, 0, sizeof(vis1));
 91     memset(vis2, 0, sizeof(vis2));
 92 
 93     queue<Node> q1, q2;
 94     Node p1, p2;
 95 
 96     int count = 2;
 97     strcpy(p1.str, str);  //初始
 98     p1.x = x;             //初始x的位置
 99     //cout << p1.str << endl;
100     strcpy(p2.str, ss);   //终极
101     p2.x = 8;             //终极x的位置
102     //cout << p2.str << endl;
103     q1.push(p1);
104     q2.push(p2);
105     vis1[sequence(str)] = 1;
106     vis2[sequence(ss)] = 2;
107     pre[1].cnt = -1;  //起点标记
108     pre[2].cnt = -1;  //终点标记
109     while (!q1.empty() && !q2.empty())
110     {
111         Node u = q1.front();
112         q1.pop();
113         int p = sequence(u.str);
114         if (vis2[p])  //找到目标状态
115         {
116             printfff(vis1[p]);
117             int k = vis2[p];
118             while (pre[k].cnt != -1)
119             {
120                 cout << pre[k].dir;
121                 k = pre[k].cnt;
122             }
123             cout << endl;
124             return;
125         }
126         else //未找到目标状态
127         {
128             Node u2;
129             for (int i = 0; i < 4; i++)
130             {
131                 u2 = u;
132                 if (!judge(u.x, i))  continue;
133                 int xx = u.x + dir[i]; //x的新地址
134                 swap(u2.str[u.x], u2.str[xx]);
135                 u2.x = xx;
136                 int v = sequence(u2.str);
137                 if (vis1[v])  continue; //已访问
138                 vis1[v] = ++count;
139                 pre[count].dir = DIR1[i]; //记录方向
140                 pre[count].cnt = vis1[p];
141                 q1.push(u2);
142             }
143         }
144 
145         u = q2.front();
146         q2.pop();
147         p = sequence(u.str);
148         if (vis1[p])
149         {
150             printfff(vis1[p]);
151             int k = vis2[p];
152             while (pre[k].cnt != -1)
153             {
154                 cout << pre[k].dir;
155                 k = pre[k].cnt;
156             }
157             cout << endl;
158             return;
159         }
160         else //未找到目标状态
161         {
162             Node u2;
163             for (int i = 0; i < 4; i++)
164             {
165                 u2 = u;
166                 if (!judge(u.x, i))  continue;
167                 int xx = u.x + dir[i]; //x的新地址
168                 swap(u2.str[u.x], u2.str[xx]);
169                 u2.x = xx;
170                 int v = sequence(u2.str);
171                 if (vis2[v])  continue; //已访问
172                 vis2[v] = ++count;
173                 pre[count].dir = DIR2[i]; //记录方向
174                 pre[count].cnt = vis2[p];
175                 q2.push(u2);
176             }
177         }
178     }
179     cout << "unsolvable" << endl;
180 }
181 
182 
183 int main()
184 {
185     //freopen("D:\\txt.txt", "r", stdin);
186     char s[30];
187     while (gets(s))
188     {
189         int k = 0;
190         int t = 0;
191         for (int i = 0; s[i] != NULL; i++)
192         {
193             if (s[i] == ‘x‘)  { str[k] = ‘0‘; x = k; }
194             else if (s[i] >= ‘1‘ && s[i] <= ‘8‘)  str[k] = s[i];
195             else continue;
196             k++;
197         }
198         str[k] = ‘\0‘;
199         //int result = sequence(ss);
200         //cout << result << endl;
201         //cout << str << endl << ss << endl << x << endl;
202 
203         for (int i = 0; i<9; i++)  //逆序数判断是否可行
204         {
205             if (str[i] == ‘0‘)continue;
206             for (int j = 0; j<i; j++)
207             {
208                 if (str[j] == ‘0‘)continue;
209                 if (str[j]>str[i])t++;
210             }
211         }
212         if (t & 1) cout << "unsolvable" << endl;
213         else bfs();
214     }
215     return 0;
216 }