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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 |
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6 case object NULL extends Rexp |
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7 case object EMPTY extends Rexp |
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8 case object ALLCHAR extends Rexp |
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9 case class CHAR(c: Char) extends Rexp |
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10 case class STR(s: String) 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 case class NOT(r: Rexp) extends Rexp |
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15 case class REP(r: Rexp, n: Int) extends Rexp |
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16 |
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17 // some convenience for typing in regular expressions |
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18 implicit def string2rexp(s : String) : Rexp = STR(s) |
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19 |
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20 implicit def RexpOps(r: Rexp) : Rexp = new { |
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21 def | (s: Rexp) = ALT(r, s) |
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22 def % = STAR(r) |
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23 def %(n: Int) = REP(r, n) |
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24 def %%(n: Int) = SEQ(REP(r, n), STAR(r)) |
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25 def ? = ALT(EMPTY, r) |
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26 def unary_! = NOT(r) |
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27 def ~ (s: Rexp) = SEQ(r, s) |
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28 } |
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29 |
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30 implicit def stringOps(s: String) : Rexp = new { |
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31 def | (r: Rexp) = ALT(s, r) |
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32 def | (r: String) = ALT(s, r) |
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33 def % = STAR(s) |
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34 def %(n: Int) = REP(s, n) |
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35 def %%(n: Int) = SEQ(REP(s, n), STAR(s)) |
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36 def ? = ALT(EMPTY, s) |
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37 def unary_! = NOT(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 |
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43 // nullable function: tests whether the regular |
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44 // expression can recognise the empty string |
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45 |
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46 def nullable (r: Rexp) : Boolean = r match { |
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47 case NULL => false |
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48 case EMPTY => true |
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49 case ALLCHAR => false |
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50 case CHAR(_) => false |
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51 case STR(s) => s.isEmpty |
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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 case NOT(r) => !(nullable(r)) |
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56 case REP(r, i) => if (i == 0) true else nullable(r) |
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57 } |
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58 |
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59 // derivative of a regular expression w.r.t. a character |
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60 def der (c: Char, r: Rexp) : Rexp = r match { |
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61 case NULL => NULL |
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62 case EMPTY => NULL |
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63 case ALLCHAR => EMPTY |
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64 case CHAR(d) => if (c == d) EMPTY else NULL |
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65 case STR(s) => if (s.isEmpty || s.head != c) NULL else STR(s.tail) |
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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(r) => SEQ(der(c, r), STAR(r)) |
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71 case NOT(r) => NOT(der (c, r)) |
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72 case REP(r, i) => |
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73 if (i == 0) NULL else SEQ(der(c, r), REP(r, i - 1)) |
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74 } |
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75 |
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76 |
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77 // derivative w.r.t. a string (iterates der) |
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78 @tailrec |
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79 def ders (s: List[Char], r: Rexp) : Rexp = s match { |
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80 case Nil => r |
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81 case c::s => ders(s, der(c, r)) |
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82 } |
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83 |
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84 // main matcher function |
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85 def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r)) |
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86 |
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87 //examples |
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88 val digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" |
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89 val int = ("+" | "-").? ~ digit.%%(1) |
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90 val real = ("+" | "-").? ~ digit.%%(1) ~ ("." ~ digit.%%(1)).? ~ (("e" | "E") ~ ("+" | "-").? ~ digit.%%(1)).? |
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91 |
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92 val ints = List("0", "-4534", "+049", "99") |
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93 val reals = List("0.9", "-12.8", "+91.0", "9e12", "+9.21E-12", "-512E+01") |
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94 val errs = List("", "-", "+", "+-1", "-+2", "2-") |
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95 |
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96 ints.map(s => matcher(int, s)) |
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97 reals.map(s => matcher(int, s)) |
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98 errs.map(s => matcher(int, s)) |
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99 |
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100 ints.map(s => matcher(real, s)) |
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101 reals.map(s => matcher(real, s)) |
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102 errs.map(s => matcher(real, s)) |
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103 |
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104 |
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105 |
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106 def RTEST(n: Int) = ("a".? %(n)) ~ ("a" %(n)) |
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107 |
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108 def time_needed[T](i: Int, code: => T) = { |
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109 val start = System.nanoTime() |
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110 for (j <- 1 to i) code |
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111 val end = System.nanoTime() |
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112 (end - start)/(i * 1.0e9) |
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113 } |
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114 |
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115 for (i <- 1 to 12000 by 500) { |
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116 println(i + ": " + "%.5f".format(time_needed(1, matcher(RTEST(i), "a" * i)))) |
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117 } |
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118 |
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119 |