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1 package takuzu |
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2 |
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3 import ( |
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4 "bytes" |
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5 "fmt" |
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6 "log" |
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7 "math" |
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8 "runtime" |
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9 "sync" |
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10 "time" |
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11 |
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12 "github.com/pkg/errors" |
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13 ) |
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14 |
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15 var verbosity int |
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16 var schrodLvl uint |
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17 |
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18 // Cell is a single cell of a Takuzu game board |
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19 type Cell struct { |
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20 Defined bool |
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21 Value int |
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22 } |
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23 |
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24 // Takuzu is a Takuzu game board (Size x Size) |
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25 type Takuzu struct { |
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26 Size int |
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27 Board [][]Cell |
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28 } |
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29 |
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30 // New creates a new Takuzu board |
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31 func New(size int) Takuzu { |
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32 t := Takuzu{Size: size} |
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33 t.Board = make([][]Cell, size) |
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34 for l := range t.Board { |
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35 t.Board[l] = make([]Cell, size) |
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36 } |
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37 return t |
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38 } |
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39 |
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40 // NewFromString creates a new Takuzu board from a string definition |
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41 func NewFromString(s string) (*Takuzu, error) { |
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42 l := len(s) |
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43 // TODO: validate chars ([.01OI]) |
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44 size := int(math.Sqrt(float64(l))) |
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45 if size*size != l { |
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46 return nil, errors.New("bad string length") |
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47 } |
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48 |
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49 i := 0 |
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50 t := New(size) |
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51 |
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52 for line := 0; line < size; line++ { |
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53 for col := 0; col < size; col++ { |
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54 switch s[i] { |
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55 case '0', 'O': |
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56 t.Board[line][col].Defined = true |
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57 t.Board[line][col].Value = 0 |
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58 case '1', 'I': |
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59 t.Board[line][col].Defined = true |
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60 t.Board[line][col].Value = 1 |
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61 case '.': |
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62 default: |
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63 return nil, errors.New("invalid char in string") |
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64 } |
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65 i++ |
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66 } |
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67 } |
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68 return &t, nil |
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69 } |
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70 |
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71 // ToString converts a takuzu board to its string representation |
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72 func (b Takuzu) ToString() string { |
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73 var sbuf bytes.Buffer |
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74 for line := 0; line < b.Size; line++ { |
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75 for col := 0; col < b.Size; col++ { |
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76 if b.Board[line][col].Defined { |
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77 sbuf.WriteString(fmt.Sprintf("%d", b.Board[line][col].Value)) |
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78 continue |
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79 } |
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80 sbuf.WriteByte('.') |
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81 } |
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82 } |
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83 return sbuf.String() |
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84 } |
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85 |
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86 // DumpString writes the content of the board as a stream |
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87 func (b Takuzu) DumpString() { |
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88 fmt.Println(b.ToString()) |
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89 } |
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90 |
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91 // Clone returns a copy of the Takuzu board |
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92 func (b Takuzu) Clone() Takuzu { |
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93 c := New(b.Size) |
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94 for line := range b.Board { |
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95 for col := range b.Board[line] { |
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96 c.Board[line][col] = b.Board[line][col] |
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97 } |
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98 } |
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99 return c |
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100 } |
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101 |
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102 // Copy copies a Takuzu board to another existing board |
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103 func Copy(src, dst *Takuzu) error { |
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104 if src.Size != dst.Size { |
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105 return errors.New("sizes do not match") |
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106 } |
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107 for line := range src.Board { |
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108 for col := range src.Board[line] { |
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109 dst.Board[line][col] = src.Board[line][col] |
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110 } |
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111 } |
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112 return nil |
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113 } |
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114 |
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115 // BoardsMatch compares a Takuzu board to another, optionally ignoring |
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116 // empty cells. Returns true if the two boards match. |
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117 func BoardsMatch(t1, t2 *Takuzu, ignoreUndefined bool) (match bool, line, col int) { |
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118 match = true |
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119 |
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120 if t1.Size != t2.Size { |
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121 line, col = -1, -1 |
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122 match = false |
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123 return |
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124 } |
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125 for line = range t1.Board { |
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126 for col = range t1.Board[line] { |
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127 if !t1.Board[line][col].Defined || !t2.Board[line][col].Defined { |
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128 // At least one of the cells is empty |
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129 if ignoreUndefined || |
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130 !(t1.Board[line][col].Defined || t2.Board[line][col].Defined) { |
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131 // Both cells are empty or we ignore empty cells |
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132 continue |
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133 } |
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134 match = false |
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135 return |
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136 } |
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137 // Both cells are defined |
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138 if t1.Board[line][col].Value != t2.Board[line][col].Value { |
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139 match = false |
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140 return |
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141 } |
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142 } |
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143 } |
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144 |
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145 line, col = -1, -1 |
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146 return |
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147 } |
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148 |
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149 // Set sets the value of the cell; a value -1 will set the cell as undefined |
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150 func (c *Cell) Set(value int) { |
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151 if value != 0 && value != 1 { |
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152 c.Defined = false |
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153 return |
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154 } |
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155 c.Defined = true |
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156 c.Value = value |
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157 } |
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158 |
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159 // Set sets the value of a specific cell |
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160 // A value -1 will undefine the cell |
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161 func (b Takuzu) Set(l, c, value int) { |
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162 if value != 0 && value != 1 { |
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163 b.Board[l][c].Defined = false |
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164 return |
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165 } |
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166 b.Board[l][c].Defined = true |
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167 b.Board[l][c].Value = value |
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168 } |
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169 |
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170 // GetLine returns a slice of cells containing the ith line of the board |
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171 func (b Takuzu) GetLine(i int) []Cell { |
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172 return b.Board[i] |
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173 } |
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174 |
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175 // GetColumn returns a slice of cells containing the ith column of the board |
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176 func (b Takuzu) GetColumn(i int) []Cell { |
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177 c := make([]Cell, b.Size) |
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178 for l := range b.Board { |
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179 c[l] = b.Board[l][i] |
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180 } |
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181 return c |
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182 } |
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183 |
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184 // GetLinePointers returns a slice of pointers to the cells of the ith line of the board |
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185 func (b Takuzu) GetLinePointers(i int) []*Cell { |
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186 r := make([]*Cell, b.Size) |
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187 for l := range b.Board[i] { |
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188 r[l] = &b.Board[i][l] |
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189 } |
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190 return r |
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191 } |
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192 |
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193 // GetColumnPointers returns a slice of pointers to the cells of the ith column of the board |
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194 func (b Takuzu) GetColumnPointers(i int) []*Cell { |
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195 r := make([]*Cell, b.Size) |
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196 for l := range b.Board { |
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197 r[l] = &b.Board[l][i] |
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198 } |
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199 return r |
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200 } |
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201 |
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202 // FillLineColumn add missing 0s or 1s if all 1s or 0s are there. |
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203 // Note: This method can update b. |
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204 func (b Takuzu) FillLineColumn(l, c int) { |
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205 fillRange := func(r []*Cell) { |
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206 size := len(r) |
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207 var notFull bool |
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208 var n [2]int |
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209 for x := 0; x < size; x++ { |
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210 if r[x].Defined { |
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211 n[r[x].Value]++ |
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212 } else { |
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213 notFull = true |
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214 } |
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215 } |
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216 if !notFull { |
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217 return |
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218 } |
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219 if n[0] == size/2 { |
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220 // Let's fill the 1s |
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221 for _, x := range r { |
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222 if !x.Defined { |
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223 x.Defined = true |
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224 x.Value = 1 |
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225 } |
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226 } |
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227 } else if n[1] == size/2 { |
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228 // Let's fill the 0s |
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229 for _, x := range r { |
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230 if !x.Defined { |
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231 x.Defined = true |
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232 x.Value = 0 |
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233 } |
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234 } |
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235 } |
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236 } |
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237 |
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238 var cells []*Cell |
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239 |
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240 // Fill line |
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241 cells = b.GetLinePointers(l) |
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242 fillRange(cells) |
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243 // Fill column |
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244 cells = b.GetColumnPointers(c) |
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245 fillRange(cells) |
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246 } |
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247 |
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248 // DumpBoard displays the Takuzu board |
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249 func (b Takuzu) DumpBoard() { |
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250 fmt.Println() |
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251 for i := range b.Board { |
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252 dumpRange(b.Board[i]) |
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253 } |
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254 } |
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255 |
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256 // CheckLine returns an error if the line i fails validation |
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257 func (b Takuzu) CheckLine(i int) error { |
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258 _, err := checkRange(b.GetLine(i)) |
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259 return err |
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260 } |
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261 |
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262 // CheckColumn returns an error if the column i fails validation |
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263 func (b Takuzu) CheckColumn(i int) error { |
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264 _, err := checkRange(b.GetColumn(i)) |
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265 return err |
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266 } |
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267 |
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268 // Validate checks a whole board for errors (not completeness) |
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269 // Returns true if all cells are defined. |
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270 func (b Takuzu) Validate() (bool, error) { |
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271 finished := true |
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272 |
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273 computeVal := func(cells []Cell) (val int) { |
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274 for i := 0; i < len(cells); i++ { |
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275 val += cells[i].Value * 1 << uint(i) |
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276 } |
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277 return |
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278 } |
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279 |
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280 lineVals := make(map[int]bool) |
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281 colVals := make(map[int]bool) |
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282 |
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283 for i := 0; i < b.Size; i++ { |
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284 var d []Cell |
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285 var full bool |
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286 var err error |
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287 |
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288 // Let's check line i |
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289 d = b.GetLine(i) |
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290 full, err = checkRange(d) |
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291 if err != nil { |
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292 return false, errors.Wrapf(err, "line %d", i) |
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293 } |
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294 if full { |
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295 hv := computeVal(d) |
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296 if lineVals[hv] { |
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297 return false, fmt.Errorf("duplicate lines (%d)", i) |
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298 } |
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299 lineVals[hv] = true |
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300 } else { |
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301 finished = false |
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302 } |
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303 |
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304 // Let's check column i |
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305 d = b.GetColumn(i) |
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306 full, err = checkRange(d) |
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307 if err != nil { |
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308 return false, errors.Wrapf(err, "column %d", i) |
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309 } |
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310 if full { |
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311 hv := computeVal(d) |
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312 if colVals[hv] { |
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313 return false, fmt.Errorf("duplicate colums (%d)", i) |
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314 } |
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315 colVals[hv] = true |
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316 } else { |
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317 finished = false |
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318 } |
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319 } |
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320 return finished, nil |
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321 } |
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322 |
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323 func dumpRange(cells []Cell) { |
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324 for _, c := range cells { |
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325 if !c.Defined { |
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326 fmt.Printf(". ") |
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327 continue |
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328 } |
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329 fmt.Printf("%d ", c.Value) |
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330 } |
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331 fmt.Println() |
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332 } |
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333 |
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334 // checkRange returns true if the range is completely defined, and an error |
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335 // if it doesn't follow the rules for a takuzu line or column |
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336 // Note that the boolean might be invalid if the error is not nil. |
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337 func checkRange(cells []Cell) (bool, error) { |
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338 full := true |
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339 size := len(cells) |
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340 counters := []int{0, 0} |
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341 |
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342 var prevCell Cell |
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343 var prevCellCount int |
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344 |
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345 for _, c := range cells { |
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346 if !c.Defined { |
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347 full = false |
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348 prevCell.Defined = false |
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349 prevCellCount = 0 |
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350 continue |
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351 } |
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352 counters[c.Value]++ |
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353 if prevCellCount == 0 { |
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354 prevCellCount = 1 |
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355 } else { |
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356 if c.Value == prevCell.Value { |
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357 prevCellCount++ |
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358 if prevCellCount > 2 { |
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359 return full, errors.Errorf("3+ same values %d", c.Value) |
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360 } |
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361 } else { |
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362 prevCellCount = 1 |
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363 } |
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364 |
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365 } |
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366 prevCell = c |
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367 } |
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368 if counters[0] > size/2 { |
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369 return full, errors.Errorf("too many zeroes") |
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370 } |
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371 if counters[1] > size/2 { |
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372 return full, errors.Errorf("too many ones") |
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373 } |
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374 return full, nil |
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375 } |
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376 |
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377 func checkRangeCounts(cells []Cell) (full bool, n0, n1 int) { |
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378 counters := []int{0, 0} |
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379 full = true |
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380 |
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381 for _, c := range cells { |
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382 if c.Defined { |
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383 counters[c.Value]++ |
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384 } else { |
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385 full = false |
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386 } |
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387 } |
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388 return full, counters[0], counters[1] |
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389 } |
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390 |
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391 func (b Takuzu) guessPos(l, c int) int { |
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392 if b.Board[l][c].Defined { |
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393 return b.Board[l][c].Value |
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394 } |
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395 |
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396 bx := b.Clone() |
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397 bx.Set(l, c, 0) |
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398 bx.FillLineColumn(l, c) |
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399 if bx.CheckLine(l) != nil || bx.CheckColumn(c) != nil { |
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400 return 1 |
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401 } |
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402 Copy(&b, &bx) |
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403 bx.Set(l, c, 1) |
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404 bx.FillLineColumn(l, c) |
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405 if bx.CheckLine(l) != nil || bx.CheckColumn(c) != nil { |
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406 return 0 |
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407 } |
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408 |
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409 return -1 // dunno |
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410 } |
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411 |
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412 // trySolveTrivialPass does 1 pass over the takuzu board and tries to find |
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413 // values using simple guesses. |
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414 func (b Takuzu) trySolveTrivialPass() (changed bool) { |
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415 for line := 0; line < b.Size; line++ { |
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416 for col := 0; col < b.Size; col++ { |
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417 if b.Board[line][col].Defined { |
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418 continue |
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419 } |
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420 if guess := b.guessPos(line, col); guess != -1 { |
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421 b.Set(line, col, guess) |
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422 if verbosity > 3 { |
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423 log.Printf("Trivial: Setting [%d,%d] to %d", line, col, guess) |
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424 } |
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425 changed = true // Ideally remember l,c |
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426 } |
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427 } |
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428 } |
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429 return changed |
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430 } |
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431 |
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432 // TrySolveTrivial tries to solve the takuzu using a loop over simple methods |
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433 // It returns true if all cells are defined, and an error if the grid breaks the rules. |
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434 func (b Takuzu) TrySolveTrivial() (bool, error) { |
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435 for { |
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436 changed := b.trySolveTrivialPass() |
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437 if verbosity > 3 { |
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438 var status string |
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439 if changed { |
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440 status = "ongoing" |
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441 } else { |
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442 status = "stuck" |
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443 } |
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444 log.Println("Trivial resolution -", status) |
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445 } |
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446 if !changed { |
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447 break |
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448 } |
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449 |
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450 if verbosity > 3 { |
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451 b.DumpBoard() |
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452 fmt.Println() |
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453 } |
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454 } |
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455 full, err := b.Validate() |
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456 if err != nil { |
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457 return full, errors.Wrap(err, "the takuzu looks wrong") |
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458 } |
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459 return full, nil |
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460 } |
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461 |
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462 // TrySolveRecurse tries to solve the takuzu recursively, using trivial |
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463 // method first and using guesses if it fails. |
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464 func (b Takuzu) TrySolveRecurse(allSolutions *[]Takuzu, timeout time.Duration) (*Takuzu, error) { |
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465 |
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466 var solutionsMux sync.Mutex |
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467 var singleSolution *Takuzu |
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468 var solutionMap map[string]*Takuzu |
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469 |
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470 var globalSearch bool |
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471 // globalSearch doesn't need to use a mutex and is more convenient |
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472 // to use than allSolutions. |
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473 if allSolutions != nil { |
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474 globalSearch = true |
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475 solutionMap = make(map[string]*Takuzu) |
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476 } |
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477 |
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478 startTime := time.Now() |
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479 |
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480 var recurseSolve func(level int, t Takuzu, errStatus chan<- error) error |
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481 |
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482 recurseSolve = func(level int, t Takuzu, errStatus chan<- error) error { |
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483 |
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484 reportStatus := func(failure error) { |
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485 // Report status to the caller's channel |
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486 if errStatus != nil { |
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487 errStatus <- failure |
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488 } |
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489 } |
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490 |
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491 // In Schröndinger mode we check concurrently both values for a cell |
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492 var schrodinger bool |
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493 concurrentRoutines := 1 |
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494 if level < int(schrodLvl) { |
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495 schrodinger = true |
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496 concurrentRoutines = 2 |
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497 } |
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498 |
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499 var status [2]chan error |
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500 status[0] = make(chan error) |
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501 status[1] = make(chan error) |
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502 |
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503 for { |
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504 // Try simple resolution first |
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505 full, err := t.TrySolveTrivial() |
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506 if err != nil { |
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507 reportStatus(err) |
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508 return err |
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509 } |
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510 |
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511 if full { // We're done |
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512 if verbosity > 1 { |
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513 log.Printf("{%d} The takuzu is correct and complete.", level) |
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514 } |
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515 solutionsMux.Lock() |
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516 singleSolution = &t |
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517 if globalSearch { |
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518 solutionMap[t.ToString()] = &t |
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519 } |
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520 solutionsMux.Unlock() |
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521 |
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522 reportStatus(nil) |
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523 return nil |
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524 } |
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525 |
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526 if verbosity > 2 { |
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527 log.Printf("{%d} Trivial resolution did not complete.", level) |
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528 } |
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529 |
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530 // Trivial method is stuck, let's use recursion |
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531 |
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532 changed := false |
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533 |
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534 // Looking for first empty cell |
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535 var line, col int |
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536 firstClear: |
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537 for line = 0; line < t.Size; line++ { |
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538 for col = 0; col < t.Size; col++ { |
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539 if !t.Board[line][col].Defined { |
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540 break firstClear |
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541 } |
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542 } |
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543 } |
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544 |
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545 if line == t.Size || col == t.Size { |
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546 break |
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547 } |
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548 |
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549 if verbosity > 2 { |
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550 log.Printf("{%d} GUESS - Trying values for [%d,%d]", level, line, col) |
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551 } |
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552 |
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553 var val int |
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554 err = nil |
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555 errCount := 0 |
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556 |
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557 for testval := 0; testval < 2; testval++ { |
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558 if !globalSearch && t.Board[line][col].Defined { |
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559 // No need to "guess" here anymore |
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560 break |
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561 } |
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562 |
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563 // Launch goroutines for cell values of 0 and/or 1 |
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564 for testCase := 0; testCase < 2; testCase++ { |
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565 if schrodinger || testval == testCase { |
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566 tx := t.Clone() |
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567 tx.Set(line, col, testCase) |
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568 go recurseSolve(level+1, tx, status[testCase]) |
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569 } |
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570 } |
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571 |
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572 // Let's collect the goroutines' results |
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573 for i := 0; i < concurrentRoutines; i++ { |
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574 if schrodinger && verbosity > 1 { // XXX |
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575 log.Printf("{%d} Schrodinger waiting for result #%d for cell [%d,%d]", level, i, line, col) |
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576 } |
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577 select { |
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578 case e := <-status[0]: |
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579 err = e |
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580 val = 0 |
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581 case e := <-status[1]: |
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582 err = e |
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583 val = 1 |
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584 } |
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585 |
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586 if schrodinger && verbosity > 1 { // XXX |
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587 log.Printf("{%d} Schrodinger result #%d/2 for cell [%d,%d]=%d - err=%v", level, i+1, line, col, val, err) |
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588 } |
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589 |
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590 if err == nil { |
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591 if !globalSearch { |
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592 reportStatus(nil) |
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593 if i+1 < concurrentRoutines { |
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594 // Schröndinger mode and we still have one status to fetch |
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595 <-status[1-val] |
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596 } |
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597 return nil |
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598 } |
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599 continue |
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600 } |
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601 if timeout > 0 && level > 2 && time.Since(startTime) > timeout { |
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602 if errors.Cause(err).Error() != "timeout" { |
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603 if verbosity > 0 { |
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604 log.Printf("{%d} Timeout, giving up", level) |
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605 } |
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606 err := errors.New("timeout") |
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607 reportStatus(err) |
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608 if i+1 < concurrentRoutines { |
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609 // Schröndinger mode and we still have one status to fetch |
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610 <-status[1-val] |
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611 } |
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612 // XXX actually can't close the channel and leave, can I? |
|
613 return err |
|
614 } |
|
615 } |
|
616 |
|
617 // err != nil: we can set a value -- unless this was a timeout |
|
618 if errors.Cause(err).Error() == "timeout" { |
|
619 if verbosity > 1 { |
|
620 log.Printf("{%d} Timeout propagation", level) |
|
621 } |
|
622 reportStatus(err) |
|
623 if i+1 < concurrentRoutines { |
|
624 // Schröndinger mode and we still have one status to fetch |
|
625 <-status[1-val] |
|
626 } |
|
627 // XXX actually can't close the channel and leave, can I? |
|
628 return err |
|
629 } |
|
630 |
|
631 errCount++ |
|
632 if verbosity > 2 { |
|
633 log.Printf("{%d} Bad outcome (%v)", level, err) |
|
634 log.Printf("{%d} GUESS was wrong - Setting [%d,%d] to %d", |
|
635 level, line, col, 1-val) |
|
636 } |
|
637 |
|
638 t.Set(line, col, 1-val) |
|
639 changed = true |
|
640 |
|
641 } // concurrentRoutines |
|
642 |
|
643 if (changed && !globalSearch) || schrodinger { |
|
644 // Let's loop again with the new board |
|
645 break |
|
646 } |
|
647 } |
|
648 |
|
649 if verbosity > 2 { |
|
650 log.Printf("{%d} End of cycle.\n\n", level) |
|
651 } |
|
652 |
|
653 if errCount == 2 { |
|
654 // Both values failed |
|
655 err := errors.New("dead end") |
|
656 reportStatus(err) |
|
657 return err |
|
658 } |
|
659 |
|
660 // If we cannot fill more cells (!changed) or if we've made a global search with |
|
661 // both values, the search is complete. |
|
662 if schrodinger || globalSearch || !changed { |
|
663 break |
|
664 } |
|
665 |
|
666 if verbosity > 2 { |
|
667 t.DumpBoard() |
|
668 fmt.Println() |
|
669 } |
|
670 } |
|
671 |
|
672 // Try to force garbage collection |
|
673 runtime.GC() |
|
674 |
|
675 full, err := t.Validate() |
|
676 if err != nil { |
|
677 if verbosity > 1 { |
|
678 log.Println("The takuzu looks wrong - ", err) |
|
679 } |
|
680 err := errors.Wrap(err, "the takuzu looks wrong") |
|
681 reportStatus(err) |
|
682 return err |
|
683 } |
|
684 if full { |
|
685 if verbosity > 1 { |
|
686 log.Println("The takuzu is correct and complete") |
|
687 } |
|
688 solutionsMux.Lock() |
|
689 singleSolution = &t |
|
690 if globalSearch { |
|
691 solutionMap[t.ToString()] = &t |
|
692 } |
|
693 solutionsMux.Unlock() |
|
694 } |
|
695 |
|
696 reportStatus(nil) |
|
697 return nil |
|
698 } |
|
699 |
|
700 status := make(chan error) |
|
701 go recurseSolve(0, b, status) |
|
702 |
|
703 err := <-status // Wait for it... |
|
704 |
|
705 firstSol := singleSolution |
|
706 if globalSearch { |
|
707 for _, tp := range solutionMap { |
|
708 *allSolutions = append(*allSolutions, *tp) |
|
709 } |
|
710 } |
|
711 |
|
712 if err != nil { |
|
713 return firstSol, err |
|
714 } |
|
715 |
|
716 if globalSearch && len(*allSolutions) > 0 { |
|
717 firstSol = &(*allSolutions)[0] |
|
718 } |
|
719 return firstSol, nil |
|
720 } |
|
721 |
|
722 // SetSchrodingerLevel initializes the "Schrödinger" level (0 means disabled) |
|
723 // It must be called before any board generation or reduction. |
|
724 func SetSchrodingerLevel(level uint) { |
|
725 schrodLvl = level |
|
726 } |
|
727 |
|
728 // SetVerbosityLevel initializes the verbosity level |
|
729 func SetVerbosityLevel(level int) { |
|
730 verbosity = level |
|
731 } |