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1 import scala.annotation.tailrec |
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2 import scala.language.implicitConversions |
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3 |
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4 abstract class Rexp { |
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5 def simp : Rexp = this |
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6 } |
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7 |
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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 override def simp = (r1.simp, r2.simp) match { |
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13 case (ZERO, r) => r |
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14 case (r, ZERO) => r |
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15 case (r, ONE) => if (nullable(r)) r else ALT(r, ONE) |
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16 case (ONE, r) => if (nullable(r)) r else ALT(r, ONE) |
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17 case (r1, r2) => if (r1 == r2) r1 else ALT(r1, r2) |
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18 } |
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19 } |
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20 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp { |
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21 override def simp = (r1.simp, r2.simp) match { |
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22 case (ZERO, _) => ZERO |
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23 case (_, ZERO) => ZERO |
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24 case (ONE, r) => r |
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25 case (r, ONE) => r |
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26 case (r1, r2) => SEQ(r1, r2) |
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27 } |
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28 } |
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29 case class STAR(r: Rexp) extends Rexp { |
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30 override def simp = r.simp match { |
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31 case ZERO => ONE |
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32 case ONE => ONE |
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33 case r => STAR(r) |
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34 } |
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35 } |
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36 case class NTIMES(r: Rexp, n: Int) extends Rexp { |
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37 override def simp = if (n == 0) ONE else |
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38 r.simp match { |
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39 case ZERO => ZERO |
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40 case ONE => ONE |
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41 case r => NTIMES(r, n) |
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42 } |
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43 } |
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44 |
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45 // some convenience for typing in regular expressions |
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46 def charlist2rexp(s : List[Char]) : Rexp = s match { |
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47 case Nil => ONE |
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48 case c::Nil => CHAR(c) |
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49 case c::s => SEQ(CHAR(c), charlist2rexp(s)) |
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50 } |
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51 implicit def string2rexp(s : String) : Rexp = charlist2rexp(s.toList) |
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52 |
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53 |
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54 // nullable function: tests whether the regular |
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55 // expression can recognise the empty string |
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56 def nullable (r: Rexp) : Boolean = r match { |
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57 case ZERO => false |
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58 case ONE => true |
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59 case CHAR(_) => false |
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60 case ALT(r1, r2) => nullable(r1) || nullable(r2) |
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61 case SEQ(r1, r2) => nullable(r1) && nullable(r2) |
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62 case STAR(_) => true |
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63 case NTIMES(r, i) => if (i == 0) true else nullable(r) |
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64 } |
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65 |
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66 // derivative of a regular expression w.r.t. a character |
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67 def der (c: Char, r: Rexp) : Rexp = r match { |
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68 case ZERO => ZERO |
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69 case ONE => ZERO |
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70 case CHAR(d) => if (c == d) ONE else ZERO |
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71 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
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72 case SEQ(r1, r2) => |
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73 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
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74 else SEQ(der(c, r1), r2) |
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75 case STAR(r) => SEQ(der(c, r), STAR(r)) |
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76 case NTIMES(r, i) => |
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77 if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1)) |
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78 } |
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79 |
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80 // derivative w.r.t. a string (iterates der) |
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81 def ders2(s: List[Char], r: Rexp) : Rexp = (s, r) match { |
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82 case (Nil, r) => r |
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83 case (s, ZERO) => ZERO |
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84 case (s, ONE) => if (s == Nil) ONE else ZERO |
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85 case (s, CHAR(c)) => if (s == List(c)) ONE else |
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86 if (s == Nil) CHAR(c) else ZERO |
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87 case (s, ALT(r1, r2)) => ALT(ders2(s, r2), ders2(s, r2)) |
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88 case (c::s, r) => ders2(s, der(c, r).simp) |
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89 } |
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90 |
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91 // main matcher function |
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92 def matcher(r: Rexp, s: String) : Boolean = nullable(ders2(s.toList, r)) |
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93 |
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94 |
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95 //one or zero |
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96 def OPT(r: Rexp) = ALT(r, ONE) |
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97 |
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98 def EVIL1(n: Int) = SEQ(NTIMES(OPT("a"), n), NTIMES("a", n)) |
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99 val EVIL2 = SEQ(STAR("a"), "b") |
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100 |
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101 def time_needed[T](i: Int, code: => T) = { |
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102 val start = System.nanoTime() |
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103 for (j <- 1 to i) code |
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104 val end = System.nanoTime() |
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105 (end - start)/(i * 1.0e9) |
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106 } |
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107 |
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108 val i = 5000 |
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109 println(i + " " + "%.5f".format(time_needed(10, matcher(EVIL1(i), "a" * i)))) |
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110 |
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111 for (i <- 1 to 80000 by 10000) { |
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112 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i)))) |
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113 } |
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114 |
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115 for (i <- 1 to 10000001 by 1000000) { |
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116 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i)))) |
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117 } |
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118 |