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1 // A Version with an explicit n-times regular expression; |
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2 // this keeps the size of the regular expression in the |
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3 // EVIL1 test-case quite small |
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4 |
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5 abstract class Rexp |
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6 case object ZERO extends Rexp |
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7 case object ONE extends Rexp |
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8 case class CHAR(c: Char) extends Rexp |
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9 case class ALT(r1: Rexp, r2: Rexp) extends Rexp |
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10 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp |
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11 case class STAR(r: Rexp) extends Rexp |
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12 case class NTIMES(r: Rexp, n: Int) extends Rexp //explicit constructor for n-times |
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13 |
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14 |
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15 def nullable (r: Rexp) : Boolean = r match { |
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16 case ZERO => false |
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17 case ONE => true |
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18 case CHAR(_) => false |
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19 case ALT(r1, r2) => nullable(r1) || nullable(r2) |
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20 case SEQ(r1, r2) => nullable(r1) && nullable(r2) |
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21 case STAR(_) => true |
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22 case NTIMES(r, i) => if (i == 0) true else nullable(r) |
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23 } |
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24 |
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25 |
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26 def der (c: Char, r: Rexp) : Rexp = r match { |
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27 case ZERO => ZERO |
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28 case ONE => ZERO |
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29 case CHAR(d) => if (c == d) ONE else ZERO |
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30 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
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31 case SEQ(r1, r2) => |
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32 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
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33 else SEQ(der(c, r1), r2) |
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34 case STAR(r1) => SEQ(der(c, r1), STAR(r1)) |
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35 case NTIMES(r1, i) => |
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36 if (i == 0) ZERO else SEQ(der(c, r1), NTIMES(r1, i - 1)) |
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37 } |
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38 |
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39 def ders (s: List[Char], r: Rexp) : Rexp = s match { |
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40 case Nil => r |
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41 case c::s => ders(s, der(c, r)) |
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42 } |
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43 |
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44 def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r)) |
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45 |
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46 |
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47 // the optional regular expression: one or zero times |
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48 // this regular expression is still defined in terms of ALT |
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49 def OPT(r: Rexp) = ALT(r, ONE) |
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50 |
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51 |
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52 // Test Cases |
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53 |
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54 // evil regular expressions |
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55 def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n)) |
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56 val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b')) |
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57 |
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58 def time_needed[T](i: Int, code: => T) = { |
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59 val start = System.nanoTime() |
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60 for (j <- 1 to i) code |
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61 val end = System.nanoTime() |
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62 (end - start) / (i * 1.0e9) |
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63 } |
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64 |
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65 |
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66 |
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67 // test: (a?{n}) (a{n}) |
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68 for (i <- 0 to 1000 by 100) { |
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69 println(f"$i: ${time_needed(2, matcher(EVIL1(i), "a" * i))}%.5f") |
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70 } |
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71 |
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72 // test: (a*)* b |
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73 for (i <- 0 to 20) { |
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74 println(f"$i: ${time_needed(2, matcher(EVIL2, "a" * i))}%.5f") |
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75 } |
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76 |
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77 |
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78 // the size of a regular expressions - for testing purposes |
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79 def size(r: Rexp) : Int = r match { |
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80 case ZERO => 1 |
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81 case ONE => 1 |
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82 case CHAR(_) => 1 |
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83 case ALT(r1, r2) => 1 + size(r1) + size(r2) |
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84 case SEQ(r1, r2) => 1 + size(r1) + size(r2) |
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85 case STAR(r) => 1 + size(r) |
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86 case NTIMES(r, _) => 1 + size(r) |
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87 } |
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88 |
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89 // EVIL1(n) has now a constant size, no matter |
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90 // what n is; also the derivative only grows |
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91 // moderately |
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92 |
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93 size(EVIL1(1)) // 7 |
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94 size(EVIL1(3)) // 7 |
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95 size(EVIL1(5)) // 7 |
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96 size(EVIL1(7)) // 7 |
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97 size(EVIL1(20)) // 7 |
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98 |
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99 size(ders("".toList, EVIL1(5))) // 7 |
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100 size(ders("a".toList, EVIL1(5))) // 16 |
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101 size(ders("aa".toList, EVIL1(5))) // 35 |
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102 size(ders("aaa".toList, EVIL1(5))) // 59 |
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103 size(ders("aaaa".toList, EVIL1(5))) // 88 |
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104 size(ders("aaaaa".toList, EVIL1(5))) // 122 |
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105 size(ders("aaaaaa".toList, EVIL1(5))) // 151 |
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106 |
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107 // but the size of the derivatives can still grow |
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108 // quite dramatically in case of EVIL2 |
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109 |
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110 size(ders("".toList, EVIL2)) // 5 |
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111 size(ders("a".toList, EVIL2)) // 12 |
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112 size(ders("aa".toList, EVIL2)) // 28 |
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113 size(ders("aaa".toList, EVIL2)) // 58 |
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114 size(ders("aaaa".toList, EVIL2)) // 116 |
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115 size(ders("aaaaa".toList, EVIL2)) // 230 |
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116 size(ders("aaaaaa".toList, EVIL2)) // 456 |
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117 |
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118 size(ders(("a" * 20).toList, EVIL2)) // 7340068 |