pku1736 恶心的插头DP，终于被搞定了。括号匹配法+hash+四进制
一个网格图上某些格子是不能到达了，求从左下角到右下角哈密顿路的数量。研究了大牛的论文好久，终于写出了这道题目
首先将哈密顿路径改造成哈密顿回路，这样就可以用联通性DP来求得路径数量。
大概方法间论文 http://www.cppblog.com/Files/yzhw/dp.doc
下面我说点细节部分
首先是行末的转移，最后一个轮廓线不能有右插头，并且需要将状态右移
举例来说
假设行末的状态为()..().，竖着的轮廓线在最后一个格子的右侧
下行第一个格子的状态即为.()..()，竖着的轮廓线在第一个格子的左侧
自认为java跑了500ms还算快的了～
1
import
java.util.
*
;
2 import java.util.Map.Entry;
3 import java.io. * ;
4 public class Main {
5
6 /**
7 * @param args
8 */
9 static int r = 0 ,c = 0 ;
10 static String map[] = new String[ 10 ];
11 static HashMap < Integer,Integer > dp[][] = new HashMap[ 10 ][ 2 ];
12 static final int encode( int code[])
13 {
14 int res = 0 ;
15 for ( int i = 0 ;i < code.length;i ++ )
16 {
17 res <<= 2 ;
18 res |= code[i];
19 }
20 return res;
21 }
22 static final void decode( int code[], int cd)
23 {
24 for ( int i = code.length - 1 ;i >= 0 ;i -- )
25 {
26 code[i] = cd & 3 ;
27 cd >>= 2 ;
28 }
29 }
30 static void print( int i, int j, int code[], int num)
31 {
32 /* System.out.print("row="+i+" col="+j+" code=");
33 for(int k=0;k<code.length;k++)
34 System.out.print(code[k]+" ");
35 System.out.println(num); */
36 }
37 public static void main(String[] args) throws IOException{
38 BufferedReader in = new BufferedReader( new InputStreamReader(System.in));
39 for ( int i = 0 ;i < 10 ;i ++ )
40 for ( int j = 0 ;j < 2 ;j ++ )
41 dp[i][j] = new HashMap < Integer,Integer > ();
42 while ( true )
43 {
44 String tmp[] = in.readLine().split( " " );
45 r = Integer.parseInt(tmp[ 0 ]);
46 c = Integer.parseInt(tmp[ 1 ]);
47 if (r == 0 && c == 0 ) break ;
48 map[ 0 ] = "" ;
49 for ( int i = 0 ;i < c + 4 ;i ++ )
50 map[ 0 ] += ' . ' ;
51 map[ 1 ] = " . " ;
52 for ( int i = 0 ;i < c + 2 ;i ++ )
53 map[ 1 ] += ' # ' ;
54 map[ 1 ] += ' . ' ;
55 for ( int i = 2 ;i < 2 + r;i ++ )
56 {
57 map[i] = in.readLine();
58 if (i != 1 + r) map[i] = " .# " + map[i] + " #. " ;
59 else map[i] = " .. " + map[i] + " .. " ;
60 }
61 c += 4 ;
62 r += 2 ;
63 int last = 0 ;
64 // for(int i=0;i<r;i++)
65 // System.out.println(map[i]);
66 // System.out.println();
67 dp[ 0 ][ 0 ].clear();
68 int code[] = new int [r + 1 ];
69 code[ 0 ] = 1 ;
70 code[ 1 ] = 2 ;
71 dp[ 0 ][ 0 ].put(encode(code), 1 );
72 for ( int j = 0 ;j < c;j ++ )
73 for ( int i = 0 ;i < r;i ++ )
74 {
75 if (i == 0 && j == 0 ) continue ;
76 dp[i][j & 1 ].clear();
77 int p1 = (i == 0 ? r - 1 :i - 1 ),p2 = (i == 0 ? j - 1 :j);
78 for (Entry < Integer, Integer > p:dp[p1][p2 & 1 ].entrySet())
79 {
80 decode(code,p.getKey());
81 print(p1,p2,code,p.getValue());
82 if (map[i].charAt(j) == ' . ' )
83 {
84 last = i * c + j;
85 if (i == r - 1 )
86 {
87 if (code[i] == 2 && code[i + 1 ] == 1 || i == r - 1 && j == c - 1 && code[i] == 1 && code[i + 1 ] == 2 )
88 {
89 code[i] = 0 ;
90 code[i + 1 ] = 0 ;
91 if (dp[i][j & 1 ].containsKey(encode(code) >> 2 ))
92 dp[i][j & 1 ].put(encode(code) >> 2 , dp[i][j & 1 ].get(encode(code) >> 2 ) + p.getValue());
93 else
94 dp[i][j & 1 ].put(encode(code) >> 2 , p.getValue());
95 }
96 else if (code[i] == 0 && code[i + 1 ] != 0 || code[i + 1 ] == 0 && code[i] != 0 )
97 {
98 code[i] = (code[i] != 0 ? code[i]:code[i + 1 ]);
99 code[i + 1 ] = 0 ;
100 if (dp[i][j & 1 ].containsKey(encode(code) >> 2 ))
101 dp[i][j & 1 ].put(encode(code) >> 2 , dp[i][j & 1 ].get(encode(code) >> 2 ) + p.getValue());
102 else
103 dp[i][j & 1 ].put(encode(code) >> 2 , p.getValue());
104 }
105 else if (code[i] == 2 && code[i + 1 ] == 2 )
106 {
107 int t = 0 ;
108 code[i] = code[i + 1 ] = 0 ;
109 for ( int k = i - 1 ;k >= 0 ;k -- )
110 {
111 if (code[k] == 1 ) t ++ ;
112 else if (code[k] == 2 ) t -- ;
113 if (t == 1 )
114 {
115 code[k] = 2 ;
116 break ;
117 }
118 }
119 if (dp[i][j & 1 ].containsKey(encode(code) >> 2 ))
120 dp[i][j & 1 ].put(encode(code) >> 2 , dp[i][j & 1 ].get(encode(code) >> 2 ) + p.getValue());
121 else
122 dp[i][j & 1 ].put(encode(code) >> 2 , p.getValue());
123 }
124 }
125 else
126 {
127 if (code[i] == 0 && code[i + 1 ] == 0 )
128 {
129 code[i] = 1 ;
130 code[i + 1 ] = 2 ;
131 if (dp[i][j & 1 ].containsKey(encode(code)))
132 dp[i][j & 1 ].put(encode(code), dp[i][j & 1 ].get(encode(code)) + p.getValue());
133 else
134 dp[i][j & 1 ].put(encode(code), p.getValue());
135 }
136 else if (code[i] == 2 && code[i + 1 ] == 1 || i == r - 1 && j == c - 1 && code[i] == 1 && code[i + 1 ] == 2 )
137 {
138 code[i] = code[i + 1 ] = 0 ;
139 if (dp[i][j & 1 ].containsKey(encode(code)))
140 dp[i][j & 1 ].put(encode(code), dp[i][j & 1 ].get(encode(code)) + p.getValue());
141 else
142 dp[i][j & 1 ].put(encode(code), p.getValue());
143 }
144 else if (code[i] == 0 || code[i + 1 ] == 0 )
145 {
146 if (dp[i][j & 1 ].containsKey(encode(code)))
147 dp[i][j & 1 ].put(encode(code), dp[i][j & 1 ].get(encode(code)) + p.getValue());
148 else
149 dp[i][j & 1 ].put(encode(code), p.getValue());
150 int t = code[i];
151 code[i] = code[i + 1 ];
152 code[i + 1 ] = t;
153 if (dp[i][j & 1 ].containsKey(encode(code)))
154 dp[i][j & 1 ].put(encode(code), dp[i][j & 1 ].get(encode(code)) + p.getValue());
155 else
156 dp[i][j & 1 ].put(encode(code), p.getValue());
157 }
158 else if (code[i] == 1 && code[i + 1 ] == 1 )
159 {
160 int t = 0 ;
161 code[i] = code[i + 1 ] = 0 ;
162 for ( int k = i + 2 ;k < code.length;k ++ )
163 {
164 if (code[k] == 1 ) t ++ ;
165 else if (code[k] == 2 ) t -- ;
166 if (t ==- 1 )
167 {
168 code[k] = 1 ;
169 break ;
170 }
171 }
172 if (dp[i][j & 1 ].containsKey(encode(code)))
173 dp[i][j & 1 ].put(encode(code), dp[i][j & 1 ].get(encode(code)) + p.getValue());
174 else
175 dp[i][j & 1 ].put(encode(code), p.getValue());
176 }
177 else if (code[i] == 2 && code[i + 1 ] == 2 )
178 {
179 int t = 0 ;
180 code[i] = code[i + 1 ] = 0 ;
181 for ( int k = i - 1 ;k >= 0 ;k -- )
182 {
183 if (code[k] == 1 ) t ++ ;
184 else if (code[k] == 2 ) t -- ;
185 if (t == 1 )
186 {
187 code[k] = 2 ;
188 break ;
189 }
190 }
191 if (dp[i][j & 1 ].containsKey(encode(code)))
192 dp[i][j & 1 ].put(encode(code), dp[i][j & 1 ].get(encode(code)) + p.getValue());
193 else
194 dp[i][j & 1 ].put(encode(code), p.getValue());
195 }
196 }
197 }
198 else
199 {
200 if (code[i] == 0 && code[i + 1 ] == 0 )
201 if (i == r - 1 )
202 {
203 if (code[i] == 0 && code[i + 1 ] == 0 )
204 if (dp[i][j & 1 ].containsKey(p.getKey() >> 2 ))
205 dp[i][j & 1 ].put(p.getKey() >> 2 , dp[i][j & 1 ].get(p.getKey() >> 2 ) + p.getValue());
206 else
207 dp[i][j & 1 ].put(p.getKey() >> 2 , p.getValue());
208 }
209 else
210 {
211 if (code[i] == 0 && code[i + 1 ] == 0 )
212 if (dp[i][j & 1 ].containsKey(p.getKey()))
213 dp[i][j & 1 ].put(p.getKey(), dp[i][j & 1 ].get(p.getKey()) + p.getValue());
214 else
215 dp[i][j & 1 ].put(p.getKey(), p.getValue());
216 }
217 }
218 }
219 }
220 if (last == (r - 1 ) * c + c - 1 )
221 System.out.println(dp[r - 1 ][(c - 1 ) & 1 ].containsKey( 0 ) ? dp[r - 1 ][(c - 1 ) & 1 ].get( 0 ): 0 );
222 else
223 System.out.println( 0 );
224 }
225
226 }
227
228 }
229
2 import java.util.Map.Entry;
3 import java.io. * ;
4 public class Main {
5
6 /**
7 * @param args
8 */
9 static int r = 0 ,c = 0 ;
10 static String map[] = new String[ 10 ];
11 static HashMap < Integer,Integer > dp[][] = new HashMap[ 10 ][ 2 ];
12 static final int encode( int code[])
13 {
14 int res = 0 ;
15 for ( int i = 0 ;i < code.length;i ++ )
16 {
17 res <<= 2 ;
18 res |= code[i];
19 }
20 return res;
21 }
22 static final void decode( int code[], int cd)
23 {
24 for ( int i = code.length - 1 ;i >= 0 ;i -- )
25 {
26 code[i] = cd & 3 ;
27 cd >>= 2 ;
28 }
29 }
30 static void print( int i, int j, int code[], int num)
31 {
32 /* System.out.print("row="+i+" col="+j+" code=");
33 for(int k=0;k<code.length;k++)
34 System.out.print(code[k]+" ");
35 System.out.println(num); */
36 }
37 public static void main(String[] args) throws IOException{
38 BufferedReader in = new BufferedReader( new InputStreamReader(System.in));
39 for ( int i = 0 ;i < 10 ;i ++ )
40 for ( int j = 0 ;j < 2 ;j ++ )
41 dp[i][j] = new HashMap < Integer,Integer > ();
42 while ( true )
43 {
44 String tmp[] = in.readLine().split( " " );
45 r = Integer.parseInt(tmp[ 0 ]);
46 c = Integer.parseInt(tmp[ 1 ]);
47 if (r == 0 && c == 0 ) break ;
48 map[ 0 ] = "" ;
49 for ( int i = 0 ;i < c + 4 ;i ++ )
50 map[ 0 ] += ' . ' ;
51 map[ 1 ] = " . " ;
52 for ( int i = 0 ;i < c + 2 ;i ++ )
53 map[ 1 ] += ' # ' ;
54 map[ 1 ] += ' . ' ;
55 for ( int i = 2 ;i < 2 + r;i ++ )
56 {
57 map[i] = in.readLine();
58 if (i != 1 + r) map[i] = " .# " + map[i] + " #. " ;
59 else map[i] = " .. " + map[i] + " .. " ;
60 }
61 c += 4 ;
62 r += 2 ;
63 int last = 0 ;
64 // for(int i=0;i<r;i++)
65 // System.out.println(map[i]);
66 // System.out.println();
67 dp[ 0 ][ 0 ].clear();
68 int code[] = new int [r + 1 ];
69 code[ 0 ] = 1 ;
70 code[ 1 ] = 2 ;
71 dp[ 0 ][ 0 ].put(encode(code), 1 );
72 for ( int j = 0 ;j < c;j ++ )
73 for ( int i = 0 ;i < r;i ++ )
74 {
75 if (i == 0 && j == 0 ) continue ;
76 dp[i][j & 1 ].clear();
77 int p1 = (i == 0 ? r - 1 :i - 1 ),p2 = (i == 0 ? j - 1 :j);
78 for (Entry < Integer, Integer > p:dp[p1][p2 & 1 ].entrySet())
79 {
80 decode(code,p.getKey());
81 print(p1,p2,code,p.getValue());
82 if (map[i].charAt(j) == ' . ' )
83 {
84 last = i * c + j;
85 if (i == r - 1 )
86 {
87 if (code[i] == 2 && code[i + 1 ] == 1 || i == r - 1 && j == c - 1 && code[i] == 1 && code[i + 1 ] == 2 )
88 {
89 code[i] = 0 ;
90 code[i + 1 ] = 0 ;
91 if (dp[i][j & 1 ].containsKey(encode(code) >> 2 ))
92 dp[i][j & 1 ].put(encode(code) >> 2 , dp[i][j & 1 ].get(encode(code) >> 2 ) + p.getValue());
93 else
94 dp[i][j & 1 ].put(encode(code) >> 2 , p.getValue());
95 }
96 else if (code[i] == 0 && code[i + 1 ] != 0 || code[i + 1 ] == 0 && code[i] != 0 )
97 {
98 code[i] = (code[i] != 0 ? code[i]:code[i + 1 ]);
99 code[i + 1 ] = 0 ;
100 if (dp[i][j & 1 ].containsKey(encode(code) >> 2 ))
101 dp[i][j & 1 ].put(encode(code) >> 2 , dp[i][j & 1 ].get(encode(code) >> 2 ) + p.getValue());
102 else
103 dp[i][j & 1 ].put(encode(code) >> 2 , p.getValue());
104 }
105 else if (code[i] == 2 && code[i + 1 ] == 2 )
106 {
107 int t = 0 ;
108 code[i] = code[i + 1 ] = 0 ;
109 for ( int k = i - 1 ;k >= 0 ;k -- )
110 {
111 if (code[k] == 1 ) t ++ ;
112 else if (code[k] == 2 ) t -- ;
113 if (t == 1 )
114 {
115 code[k] = 2 ;
116 break ;
117 }
118 }
119 if (dp[i][j & 1 ].containsKey(encode(code) >> 2 ))
120 dp[i][j & 1 ].put(encode(code) >> 2 , dp[i][j & 1 ].get(encode(code) >> 2 ) + p.getValue());
121 else
122 dp[i][j & 1 ].put(encode(code) >> 2 , p.getValue());
123 }
124 }
125 else
126 {
127 if (code[i] == 0 && code[i + 1 ] == 0 )
128 {
129 code[i] = 1 ;
130 code[i + 1 ] = 2 ;
131 if (dp[i][j & 1 ].containsKey(encode(code)))
132 dp[i][j & 1 ].put(encode(code), dp[i][j & 1 ].get(encode(code)) + p.getValue());
133 else
134 dp[i][j & 1 ].put(encode(code), p.getValue());
135 }
136 else if (code[i] == 2 && code[i + 1 ] == 1 || i == r - 1 && j == c - 1 && code[i] == 1 && code[i + 1 ] == 2 )
137 {
138 code[i] = code[i + 1 ] = 0 ;
139 if (dp[i][j & 1 ].containsKey(encode(code)))
140 dp[i][j & 1 ].put(encode(code), dp[i][j & 1 ].get(encode(code)) + p.getValue());
141 else
142 dp[i][j & 1 ].put(encode(code), p.getValue());
143 }
144 else if (code[i] == 0 || code[i + 1 ] == 0 )
145 {
146 if (dp[i][j & 1 ].containsKey(encode(code)))
147 dp[i][j & 1 ].put(encode(code), dp[i][j & 1 ].get(encode(code)) + p.getValue());
148 else
149 dp[i][j & 1 ].put(encode(code), p.getValue());
150 int t = code[i];
151 code[i] = code[i + 1 ];
152 code[i + 1 ] = t;
153 if (dp[i][j & 1 ].containsKey(encode(code)))
154 dp[i][j & 1 ].put(encode(code), dp[i][j & 1 ].get(encode(code)) + p.getValue());
155 else
156 dp[i][j & 1 ].put(encode(code), p.getValue());
157 }
158 else if (code[i] == 1 && code[i + 1 ] == 1 )
159 {
160 int t = 0 ;
161 code[i] = code[i + 1 ] = 0 ;
162 for ( int k = i + 2 ;k < code.length;k ++ )
163 {
164 if (code[k] == 1 ) t ++ ;
165 else if (code[k] == 2 ) t -- ;
166 if (t ==- 1 )
167 {
168 code[k] = 1 ;
169 break ;
170 }
171 }
172 if (dp[i][j & 1 ].containsKey(encode(code)))
173 dp[i][j & 1 ].put(encode(code), dp[i][j & 1 ].get(encode(code)) + p.getValue());
174 else
175 dp[i][j & 1 ].put(encode(code), p.getValue());
176 }
177 else if (code[i] == 2 && code[i + 1 ] == 2 )
178 {
179 int t = 0 ;
180 code[i] = code[i + 1 ] = 0 ;
181 for ( int k = i - 1 ;k >= 0 ;k -- )
182 {
183 if (code[k] == 1 ) t ++ ;
184 else if (code[k] == 2 ) t -- ;
185 if (t == 1 )
186 {
187 code[k] = 2 ;
188 break ;
189 }
190 }
191 if (dp[i][j & 1 ].containsKey(encode(code)))
192 dp[i][j & 1 ].put(encode(code), dp[i][j & 1 ].get(encode(code)) + p.getValue());
193 else
194 dp[i][j & 1 ].put(encode(code), p.getValue());
195 }
196 }
197 }
198 else
199 {
200 if (code[i] == 0 && code[i + 1 ] == 0 )
201 if (i == r - 1 )
202 {
203 if (code[i] == 0 && code[i + 1 ] == 0 )
204 if (dp[i][j & 1 ].containsKey(p.getKey() >> 2 ))
205 dp[i][j & 1 ].put(p.getKey() >> 2 , dp[i][j & 1 ].get(p.getKey() >> 2 ) + p.getValue());
206 else
207 dp[i][j & 1 ].put(p.getKey() >> 2 , p.getValue());
208 }
209 else
210 {
211 if (code[i] == 0 && code[i + 1 ] == 0 )
212 if (dp[i][j & 1 ].containsKey(p.getKey()))
213 dp[i][j & 1 ].put(p.getKey(), dp[i][j & 1 ].get(p.getKey()) + p.getValue());
214 else
215 dp[i][j & 1 ].put(p.getKey(), p.getValue());
216 }
217 }
218 }
219 }
220 if (last == (r - 1 ) * c + c - 1 )
221 System.out.println(dp[r - 1 ][(c - 1 ) & 1 ].containsKey( 0 ) ? dp[r - 1 ][(c - 1 ) & 1 ].get( 0 ): 0 );
222 else
223 System.out.println( 0 );
224 }
225
226 }
227
228 }
229