1 // Core Part about Regular Expression Matching |
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2 //============================================= |
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3 |
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4 object CW9c { |
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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 // alternative |
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12 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp // sequence |
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13 case class STAR(r: Rexp) extends Rexp // star |
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14 |
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15 |
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16 // some convenience for typing regular expressions |
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17 |
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18 import scala.language.implicitConversions |
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19 import scala.language.reflectiveCalls |
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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 // (5) 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 = ... |
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49 |
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50 |
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51 // (6) Complete the function der according to |
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52 // the definition given in the coursework; this |
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53 // function calculates the derivative of a |
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54 // regular expression w.r.t. a character. |
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55 |
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56 //def der (c: Char, r: Rexp) : Rexp = ... |
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57 |
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58 |
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59 // (7) Complete the simp function according to |
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60 // the specification given in the coursework; this |
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61 // function simplifies a regular expression from |
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62 // the inside out, like you would simplify arithmetic |
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63 // expressions; however it does not simplify inside |
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64 // STAR-regular expressions. |
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65 |
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66 //def simp(r: Rexp) : Rexp = ... |
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67 |
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68 |
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69 // (8) Complete the two functions below; the first |
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70 // calculates the derivative w.r.t. a string; the second |
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71 // is the regular expression matcher taking a regular |
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72 // expression and a string and checks whether the |
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73 // string matches the regular expression |
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74 |
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75 //def ders (s: List[Char], r: Rexp) : Rexp = ... |
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76 |
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77 //def matcher(r: Rexp, s: String): Boolean = ... |
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78 |
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79 |
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80 // (9) Complete the size function for regular |
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81 // expressions according to the specification |
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82 // given in the coursework. |
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83 |
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84 //def size(r: Rexp): Int = ... |
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85 |
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86 |
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87 // some testing data |
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88 |
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89 /* |
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90 matcher(("a" ~ "b") ~ "c", "abc") // => true |
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91 matcher(("a" ~ "b") ~ "c", "ab") // => false |
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92 |
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93 // the supposedly 'evil' regular expression (a*)* b |
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94 val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b')) |
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95 |
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96 matcher(EVIL, "a" * 1000 ++ "b") // => true |
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97 matcher(EVIL, "a" * 1000) // => false |
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98 |
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99 // size without simplifications |
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100 size(der('a', der('a', EVIL))) // => 28 |
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101 size(der('a', der('a', der('a', EVIL)))) // => 58 |
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102 |
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103 // size with simplification |
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104 size(simp(der('a', der('a', EVIL)))) // => 8 |
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105 size(simp(der('a', der('a', der('a', EVIL))))) // => 8 |
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106 |
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107 // Python needs around 30 seconds for matching 28 a's with EVIL. |
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108 // Java 9 and later increase this to an "astonishing" 40000 a's in |
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109 // 30 seconds. |
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110 // |
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111 // Lets see how long it really takes to match strings with |
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112 // 5 Million a's...it should be in the range of a couple |
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113 // of seconds. |
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114 |
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115 def time_needed[T](i: Int, code: => T) = { |
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116 val start = System.nanoTime() |
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117 for (j <- 1 to i) code |
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118 val end = System.nanoTime() |
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119 (end - start)/(i * 1.0e9) |
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120 } |
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121 |
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122 for (i <- 0 to 5000000 by 500000) { |
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123 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i)))) |
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124 } |
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125 |
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126 // another "power" test case |
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127 simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(50).next) == ONE |
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128 |
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129 // the Iterator produces the rexp |
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130 // |
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131 // SEQ(SEQ(SEQ(..., ONE | ONE) , ONE | ONE), ONE | ONE) |
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132 // |
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133 // where SEQ is nested 50 times. |
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134 |
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135 */ |
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136 |
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137 } |
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