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