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1 // Core Part about Regular Expression Matching |
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2 //============================================= |
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3 |
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4 object CW8c { |
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5 |
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6 // Regular Expressions |
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7 abstract class Rexp |
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8 case object ZERO extends Rexp |
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9 case object ONE extends Rexp |
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10 case class CHAR(c: Char) extends Rexp |
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11 case class ALT(r1: Rexp, r2: Rexp) extends Rexp |
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12 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp |
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13 case class STAR(r: Rexp) extends Rexp |
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14 |
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15 // some convenience for typing in regular expressions |
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16 |
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17 import scala.language.implicitConversions |
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18 import scala.language.reflectiveCalls |
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19 |
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20 |
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21 def charlist2rexp(s: List[Char]): Rexp = s match { |
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22 case Nil => ONE |
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23 case c::Nil => CHAR(c) |
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24 case c::s => SEQ(CHAR(c), charlist2rexp(s)) |
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25 } |
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26 implicit def string2rexp(s: String): Rexp = charlist2rexp(s.toList) |
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27 |
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28 implicit def RexpOps (r: Rexp) = new { |
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29 def | (s: Rexp) = ALT(r, s) |
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30 def % = STAR(r) |
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31 def ~ (s: Rexp) = SEQ(r, s) |
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32 } |
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33 |
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34 implicit def stringOps (s: String) = new { |
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35 def | (r: Rexp) = ALT(s, r) |
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36 def | (r: String) = ALT(s, r) |
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37 def % = STAR(s) |
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38 def ~ (r: Rexp) = SEQ(s, r) |
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39 def ~ (r: String) = SEQ(s, r) |
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40 } |
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41 |
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42 // (1) Complete the function nullable according to |
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43 // the definition given in the coursework; this |
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44 // function checks whether a regular expression |
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45 // can match the empty string and Returns a boolean |
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46 // accordingly. |
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47 |
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48 def nullable (r: Rexp) : Boolean = r match { |
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49 case ZERO => false |
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50 case ONE => true |
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51 case CHAR(_) => false |
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52 case ALT(r1, r2) => nullable(r1) || nullable(r2) |
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53 case SEQ(r1, r2) => nullable(r1) && nullable(r2) |
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54 case STAR(_) => true |
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55 } |
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56 |
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57 // (2) Complete the function der according to |
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58 // the definition given in the coursework; this |
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59 // function calculates the derivative of a |
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60 // regular expression w.r.t. a character. |
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61 |
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62 def der (c: Char, r: Rexp) : Rexp = r match { |
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63 case ZERO => ZERO |
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64 case ONE => ZERO |
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65 case CHAR(d) => if (c == d) ONE else ZERO |
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66 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
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67 case SEQ(r1, r2) => |
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68 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
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69 else SEQ(der(c, r1), r2) |
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70 case STAR(r1) => SEQ(der(c, r1), STAR(r1)) |
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71 } |
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72 |
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73 // (3) Complete the simp function according to |
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74 // the specification given in the coursework; this |
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75 // function simplifies a regular expression from |
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76 // the inside out, like you would simplify arithmetic |
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77 // expressions; however it does not simplify inside |
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78 // STAR-regular expressions. |
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79 |
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80 def simp(r: Rexp) : Rexp = r match { |
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81 case ALT(r1, r2) => (simp(r1), simp(r2)) match { |
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82 case (ZERO, r2s) => r2s |
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83 case (r1s, ZERO) => r1s |
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84 case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s) |
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85 } |
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86 case SEQ(r1, r2) => (simp(r1), simp(r2)) match { |
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87 case (ZERO, _) => ZERO |
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88 case (_, ZERO) => ZERO |
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89 case (ONE, r2s) => r2s |
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90 case (r1s, ONE) => r1s |
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91 case (r1s, r2s) => SEQ(r1s, r2s) |
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92 } |
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93 case r => r |
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94 } |
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95 |
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96 |
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97 // (4) Complete the two functions below; the first |
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98 // calculates the derivative w.r.t. a string; the second |
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99 // is the regular expression matcher taking a regular |
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100 // expression and a string and checks whether the |
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101 // string matches the regular expression. |
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102 |
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103 def ders (s: List[Char], r: Rexp) : Rexp = s match { |
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104 case Nil => r |
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105 case c::s => ders(s, simp(der(c, r))) |
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106 } |
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107 |
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108 // main matcher function |
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109 def matcher(r: Rexp, s: String) = nullable(ders(s.toList, r)) |
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110 |
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111 // (5) Complete the size function for regular |
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112 // expressions according to the specification |
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113 // given in the coursework. |
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114 |
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115 |
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116 def size(r: Rexp): Int = r match { |
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117 case ZERO => 1 |
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118 case ONE => 1 |
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119 case CHAR(_) => 1 |
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120 case ALT(r1, r2) => 1 + size(r1) + size (r2) |
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121 case SEQ(r1, r2) => 1 + size(r1) + size (r2) |
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122 case STAR(r1) => 1 + size(r1) |
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123 } |
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124 |
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125 |
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126 |
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127 // some testing data |
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128 |
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129 //matcher(("a" ~ "b") ~ "c", "abc") // => true |
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130 //matcher(("a" ~ "b") ~ "c", "ab") // => false |
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131 |
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132 // the supposedly 'evil' regular expression (a*)* b |
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133 val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b')) |
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134 |
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135 //matcher(EVIL, "a" * 1000 ++ "b") // => true |
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136 //matcher(EVIL, "a" * 1000) // => false |
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137 |
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138 // size without simplifications |
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139 //size(der('a', der('a', EVIL))) // => 28 |
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140 //size(der('a', der('a', der('a', EVIL)))) // => 58 |
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141 |
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142 // size with simplification |
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143 //size(simp(der('a', der('a', EVIL)))) // => 8 |
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144 //size(simp(der('a', der('a', der('a', EVIL))))) // => 8 |
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145 |
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146 // Python needs around 30 seconds for matching 28 a's with EVIL. |
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147 // Java 9 and later increase this to an "astonishing" 40000 a's in |
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148 // around 30 seconds. |
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149 // |
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150 // Lets see how long it takes to match strings with |
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151 // 5 Million a's...it should be in the range of a |
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152 // couple of seconds. |
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153 |
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154 def time_needed[T](i: Int, code: => T) = { |
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155 val start = System.nanoTime() |
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156 for (j <- 1 to i) code |
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157 val end = System.nanoTime() |
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158 (end - start)/(i * 1.0e9) |
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159 } |
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160 |
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161 //for (i <- 0 to 5000000 by 500000) { |
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162 // println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i))) + " secs.") |
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163 //} |
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164 |
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165 // another "power" test case |
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166 //simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(100).next) == ONE |
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167 |
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168 // the Iterator produces the rexp |
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169 // |
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170 // SEQ(SEQ(SEQ(..., ONE | ONE) , ONE | ONE), ONE | ONE) |
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171 // |
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172 // where SEQ is nested 100 times. |
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173 |
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174 |
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175 |
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176 } |