|
1 // 2 x 2 x 2 Rubik's Cube |
|
2 //======================== |
|
3 |
|
4 // for more memory for the JVM, call |
|
5 // |
|
6 // JAVA_OPTS="-Xmx2g" scala |
|
7 |
|
8 |
|
9 // for measuring memory usage |
|
10 val mb = 1024*1024 |
|
11 val runtime = Runtime.getRuntime |
|
12 |
|
13 def memory() = { |
|
14 println(s" ** Used Memory: ${(runtime.totalMemory - runtime.freeMemory) / mb}") |
|
15 println(s" ** Free Memory: ${runtime.freeMemory / mb}") |
|
16 println(s" ** Total Memory: ${runtime.totalMemory / mb}") |
|
17 println(s" ** Max Memory: ${runtime.maxMemory / mb}") |
|
18 } |
|
19 |
|
20 |
|
21 abstract class Colour |
|
22 case object White extends Colour |
|
23 case object Yellow extends Colour |
|
24 case object Orange extends Colour |
|
25 case object Red extends Colour |
|
26 case object Green extends Colour |
|
27 case object Blue extends Colour |
|
28 |
|
29 // Faces |
|
30 // ------- |
|
31 // |c11 c12| |
|
32 // |c21 c22| |
|
33 // ------- |
|
34 case class Face(c11: Colour, c12: Colour, |
|
35 c21: Colour, c22: Colour) |
|
36 |
|
37 |
|
38 // Cubes |
|
39 // +--+ |
|
40 // |f2| |
|
41 // +--+ +--+ |
|
42 // |f5 f1 f6| |
|
43 // +--+ +--+ |
|
44 // |f3| |
|
45 // |f4| |
|
46 // +--+ |
|
47 case class Cube(f1: Face, f2: Face, f3: Face, |
|
48 f4: Face, f5: Face, f6: Face) |
|
49 |
|
50 |
|
51 // starting cube |
|
52 val init = |
|
53 Cube(Face(White, Green, White, White), |
|
54 Face(Blue, Yellow, Orange, Red), |
|
55 Face(Red, Blue, Red, Blue), |
|
56 Face(White, Yellow, Red, Orange), |
|
57 Face(Yellow, Green, Blue, Green), |
|
58 Face(Yellow, Green, Orange, Orange)) |
|
59 |
|
60 // solved cube |
|
61 val solved = |
|
62 Cube(Face(Yellow, Yellow, Yellow, Yellow), |
|
63 Face(Orange, Orange, Orange, Orange), |
|
64 Face(Red, Red, Red, Red), |
|
65 Face(White, White, White, White), |
|
66 Face(Blue, Blue, Blue, Blue), |
|
67 Face(Green, Green, Green, Green)) |
|
68 |
|
69 |
|
70 |
|
71 // actions |
|
72 def up(c: Cube) : Cube = |
|
73 Cube(Face(c.f1.c11, c.f3.c12, c.f1.c21, c.f3.c22), |
|
74 Face(c.f2.c11, c.f1.c12, c.f2.c21, c.f1.c22), |
|
75 Face(c.f3.c11, c.f4.c12, c.f3.c21, c.f4.c22), |
|
76 Face(c.f4.c11, c.f2.c12, c.f4.c21, c.f2.c22), |
|
77 Face(c.f5.c11, c.f5.c12, c.f5.c21, c.f5.c22), |
|
78 Face(c.f6.c21, c.f6.c11, c.f6.c22, c.f6.c12)) |
|
79 |
|
80 def clock(c: Cube) : Cube = |
|
81 Cube(Face(c.f1.c21, c.f1.c11, c.f1.c22, c.f1.c12), |
|
82 Face(c.f2.c11, c.f2.c12, c.f5.c22, c.f5.c12), |
|
83 Face(c.f6.c21, c.f6.c11, c.f3.c21, c.f3.c22), |
|
84 Face(c.f4.c11, c.f4.c12, c.f4.c21, c.f4.c22), |
|
85 Face(c.f5.c11, c.f3.c11, c.f5.c21, c.f3.c12), |
|
86 Face(c.f2.c21, c.f6.c12, c.f2.c22, c.f6.c22)) |
|
87 |
|
88 def right(c: Cube) : Cube = |
|
89 Cube(Face(c.f5.c11, c.f5.c12, c.f1.c21, c.f1.c22), |
|
90 Face(c.f2.c12, c.f2.c22, c.f2.c11, c.f2.c21), |
|
91 Face(c.f3.c11, c.f3.c12, c.f3.c21, c.f3.c22), |
|
92 Face(c.f4.c11, c.f4.c12, c.f6.c12, c.f6.c11), |
|
93 Face(c.f4.c22, c.f4.c21, c.f5.c21, c.f5.c22), |
|
94 Face(c.f1.c11, c.f1.c12, c.f6.c21, c.f6.c22)) |
|
95 |
|
96 |
|
97 // simple bf-search without generating a solution, just true |
|
98 |
|
99 def actions(c: Cube) : List[Cube] = |
|
100 List(up(c), clock(c), right(c)) |
|
101 |
|
102 def search(cs: List[Cube], d: Int) : Boolean = { |
|
103 println(s"Depth: $d Cands: ${cs.length}") |
|
104 //memory() |
|
105 if (cs.exists(solved == _)) true |
|
106 else search(cs.flatMap(actions), d + 1) |
|
107 } |
|
108 |
|
109 search(List(init), 0) |
|
110 |
|
111 |
|
112 // set version |
|
113 def actions_set(c: Cube) : Set[Cube] = |
|
114 Set(up(c), clock(c), right(c)) |
|
115 |
|
116 def search_set(cs: Set[Cube], d: Int) : Boolean = { |
|
117 println(s"Depth: $d candidates: ${cs.size}") |
|
118 //memory() |
|
119 if (cs.contains(solved)) true |
|
120 else search_set(cs.flatMap(actions_set), d + 1) |
|
121 } |
|
122 |
|
123 search_set(Set(init), 0) |
|
124 |
|
125 |
|
126 // for generating list of actions |
|
127 abstract class Action |
|
128 case object Up extends Action |
|
129 case object Right extends Action |
|
130 case object Clock extends Action |
|
131 |
|
132 type Actions = List[Action] |
|
133 |
|
134 // list version generating a list of actions |
|
135 def actions_list(c: Cube, act: Actions) : List[(Cube, Actions)] = |
|
136 List((up(c), Up::act), |
|
137 (clock(c), Clock::act), |
|
138 (right(c), Right::act)) |
|
139 |
|
140 |
|
141 def search_list(cs: List[(Cube, Actions)], d: Int) : (Cube, Actions) = { |
|
142 println(s"Depth: $d Cands: ${cs.length}") |
|
143 val res = cs.find(_._1 == solved) |
|
144 if (res.isDefined) res.get |
|
145 else search_list(cs.flatMap{case (c, as) => actions_list(c, as) }, d + 1) |
|
146 } |
|
147 |
|
148 search_list(List((init, Nil)), 0)._2.reverse.mkString("\n") |
|
149 |
|
150 |
|
151 // map version generating a list of actions |
|
152 def actions_map(c: Cube, as: Actions) : Map[Cube, Actions] = |
|
153 Map(up(c) -> (Up::as), |
|
154 clock(c) -> (Clock::as), |
|
155 right(c) -> (Right::as)) |
|
156 |
|
157 |
|
158 def search_map(cs: Map[Cube, Actions], d: Int) : Actions = { |
|
159 println(s"Depth: $d Cands: ${cs.keySet.size}") |
|
160 val res = cs.keySet.find(_ == solved) |
|
161 if (res.isDefined) cs(res.get) |
|
162 else search_map(cs.flatMap{case (c, as) => actions_list(c, as) }, d + 1) |
|
163 } |
|
164 |
|
165 |
|
166 search_map(Map(init -> Nil), 0).reverse.mkString("\n") |
|
167 |
|
168 |
|
169 |
|
170 // bidirectional breadth-first search |
|
171 def bsearch(cs: Map[Cube, Actions], |
|
172 bs: Map[Cube, Actions], d: Int) : Actions = { |
|
173 println(s"Depth: $d Cands: ${cs.keySet.size}/${bs.keySet.size}") |
|
174 val res = cs.keySet intersect bs.keySet |
|
175 if (!res.isEmpty) (cs(res.head).reverse ::: bs(res.head)) |
|
176 else bsearch(cs.flatMap{case (c, as) => actions_map(c, as) }, |
|
177 bs.flatMap{case (c, as) => actions_map(c, as) }, d + 1) |
|
178 } |
|
179 |
|
180 bsearch(Map(init -> Nil), Map(solved -> Nil), 0).mkString("\n") |
|
181 |
|
182 |
|
183 |
|
184 // bidirectional breadth-first search |
|
185 def bsearch(cs: Map[Cube, Actions], |
|
186 bs: Map[Cube, Actions], d: Int) : Actions = { |
|
187 println(s"Depth: $d Cands: ${cs.keySet.size}/${bs.keySet.size}") |
|
188 val res = cs.keySet intersect bs.keySet |
|
189 if (!res.isEmpty) (cs(res.head).reverse ::: bs(res.head)) |
|
190 else bsearch(cs.flatMap{ (c, as) => actions_map(c, as) }, |
|
191 bs.flatMap{ (c, as) => actions_map(c, as) }, d + 1) |
|
192 } |
|
193 |
|
194 bsearch(Map(init -> Nil), Map(solved -> Nil), 0).mkString("\n") |
|
195 |
|
196 |
|
197 |
|
198 |
|
199 |
|
200 |
|
201 |
|
202 |
|
203 |
|
204 |
|
205 |
|
206 |
|
207 |
|
208 |
|
209 |
|
210 |
|
211 |
|
212 |
|
213 |
|
214 |