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1 // Part 1 about Regular Expression Matching |
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2 //========================================== |
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3 |
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4 object CW8a { |
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5 |
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6 abstract class Rexp |
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7 case object ZERO extends Rexp |
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8 case object ONE extends Rexp |
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9 case class CHAR(c: Char) extends Rexp |
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10 case class ALT(r1: Rexp, r2: Rexp) extends Rexp |
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11 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp |
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12 case class STAR(r: Rexp) extends Rexp |
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13 |
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14 // some convenience for typing in regular expressions |
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15 |
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16 import scala.language.implicitConversions |
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17 import scala.language.reflectiveCalls |
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18 |
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19 |
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20 def charlist2rexp(s: List[Char]): Rexp = s match { |
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21 case Nil => ONE |
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22 case c::Nil => CHAR(c) |
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23 case c::s => SEQ(CHAR(c), charlist2rexp(s)) |
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24 } |
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25 implicit def string2rexp(s: String): Rexp = charlist2rexp(s.toList) |
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26 |
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27 implicit def RexpOps (r: Rexp) = new { |
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28 def | (s: Rexp) = ALT(r, s) |
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29 def % = STAR(r) |
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30 def ~ (s: Rexp) = SEQ(r, s) |
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31 } |
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32 |
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33 implicit def stringOps (s: String) = new { |
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34 def | (r: Rexp) = ALT(s, r) |
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35 def | (r: String) = ALT(s, r) |
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36 def % = STAR(s) |
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37 def ~ (r: Rexp) = SEQ(s, r) |
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38 def ~ (r: String) = SEQ(s, r) |
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39 } |
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40 |
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41 // (1a) Complete the function nullable according to |
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42 // the definition given in the coursework; this |
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43 // function checks whether a regular expression |
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44 // can match 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 ZERO => false |
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48 case ONE => true |
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49 case CHAR(_) => false |
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50 case ALT(r1, r2) => nullable(r1) || nullable(r2) |
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51 case SEQ(r1, r2) => nullable(r1) && nullable(r2) |
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52 case STAR(_) => true |
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53 } |
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54 |
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55 // (1b) Complete the function der according to |
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56 // the definition given in the coursework; this |
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57 // function calculates the derivative of a |
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58 // regular expression w.r.t. a character |
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59 |
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60 def der (c: Char, r: Rexp) : Rexp = r match { |
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61 case ZERO => ZERO |
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62 case ONE => ZERO |
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63 case CHAR(d) => if (c == d) ONE else ZERO |
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64 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
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65 case SEQ(r1, r2) => |
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66 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
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67 else SEQ(der(c, r1), r2) |
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68 case STAR(r1) => SEQ(der(c, r1), STAR(r1)) |
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69 } |
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70 |
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71 // (1c) Complete the function der according to |
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72 // the specification given in the coursework; this |
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73 // function simplifies a regular expression; |
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74 // however it does not simplify inside STAR-regular |
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75 // expressions |
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76 |
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77 def simp(r: Rexp) : Rexp = r match { |
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78 case ALT(r1, r2) => (simp(r1), simp(r2)) match { |
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79 case (ZERO, r2s) => r2s |
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80 case (r1s, ZERO) => r1s |
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81 case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s) |
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82 } |
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83 case SEQ(r1, r2) => (simp(r1), simp(r2)) match { |
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84 case (ZERO, _) => ZERO |
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85 case (_, ZERO) => ZERO |
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86 case (ONE, r2s) => r2s |
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87 case (r1s, ONE) => r1s |
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88 case (r1s, r2s) => SEQ(r1s, r2s) |
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89 } |
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90 case r => r |
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91 } |
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92 |
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93 // (1d) Complete the two functions below; the first |
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94 // calculates the derivative w.r.t. a string; the second |
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95 // is the regular expression matcher taking a regular |
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96 // expression and a string and checks whether the |
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97 // string matches the regular expression |
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98 |
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99 def ders (s: List[Char], r: Rexp) : Rexp = s match { |
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100 case Nil => r |
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101 case c::s => ders(s, simp(der(c, r))) |
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102 } |
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103 |
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104 // main matcher function |
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105 def matcher(r: Rexp, s: String): Boolean = nullable(ders(s.toList, r)) |
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106 |
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107 // (1e) Complete the size function for regular |
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108 // expressions according to the specification |
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109 // given in the coursework. |
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110 |
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111 def size(r: Rexp): Int = r match { |
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112 case ZERO => 1 |
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113 case ONE => 1 |
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114 case CHAR(_) => 1 |
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115 case ALT(r1, r2) => 1 + size(r1) + size (r2) |
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116 case SEQ(r1, r2) => 1 + size(r1) + size (r2) |
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117 case STAR(r1) => 1 + size(r1) |
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118 } |
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119 |
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120 |
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121 |
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122 // some testing data |
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123 /* |
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124 matcher(("a" ~ "b") ~ "c", "abc") // => true |
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125 matcher(("a" ~ "b") ~ "c", "ab") // => false |
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126 |
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127 // the supposedly 'evil' regular expression (a*)* b |
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128 val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b')) |
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129 |
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130 matcher(EVIL, "a" * 1000 ++ "b") // => true |
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131 matcher(EVIL, "a" * 1000) // => false |
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132 |
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133 // size without simplifications |
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134 size(der('a', der('a', EVIL))) // => 28 |
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135 size(der('a', der('a', der('a', EVIL)))) // => 58 |
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136 |
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137 // size with simplification |
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138 size(simp(der('a', der('a', EVIL)))) // => 8 |
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139 size(simp(der('a', der('a', der('a', EVIL))))) // => 8 |
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140 |
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141 // Java needs around 30 seconds for matching 28 a's with EVIL. |
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142 // |
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143 // Lets see how long it takes to match strings with |
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144 // 0.5 Million a's...it should be in the range of some |
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145 // seconds. |
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146 |
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147 def time_needed[T](i: Int, code: => T) = { |
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148 val start = System.nanoTime() |
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149 for (j <- 1 to i) code |
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150 val end = System.nanoTime() |
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151 (end - start)/(i * 1.0e9) |
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152 } |
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153 |
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154 for (i <- 0 to 5000000 by 500000) { |
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155 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i)))) |
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156 } |
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157 */ |
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158 |
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159 } |