1 // Core Part about Regular Expression Matching |
1 // Core Part about Regular Expression Matching |
2 //============================================= |
2 //============================================= |
3 |
3 |
4 object CW8c { |
4 object M3 { |
5 |
5 |
6 // Regular Expressions |
6 // Regular Expressions |
7 abstract class Rexp |
7 abstract class Rexp |
8 case object ZERO extends Rexp |
8 case object ZERO extends Rexp |
9 case object ONE extends Rexp |
9 case object ONE extends Rexp |
10 case class CHAR(c: Char) extends Rexp |
10 case class CHAR(c: Char) extends Rexp |
11 case class ALT(r1: Rexp, r2: Rexp) extends Rexp |
11 case class ALTs(rs: List[Rexp]) extends Rexp // alternatives |
12 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp |
12 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp // sequence |
13 case class STAR(r: Rexp) extends Rexp |
13 case class STAR(r: Rexp) extends Rexp // star |
14 |
14 |
15 // some convenience for typing in regular expressions |
15 // some convenience for typing in regular expressions |
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16 |
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17 |
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18 //the usual binary choice can be defined in terms of ALTs |
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19 def ALT(r1: Rexp, r2: Rexp) = ALTs(List(r1, r2)) |
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20 |
16 |
21 |
17 import scala.language.implicitConversions |
22 import scala.language.implicitConversions |
18 import scala.language.reflectiveCalls |
23 import scala.language.reflectiveCalls |
19 |
24 |
20 |
25 |
61 |
66 |
62 def der (c: Char, r: Rexp) : Rexp = r match { |
67 def der (c: Char, r: Rexp) : Rexp = r match { |
63 case ZERO => ZERO |
68 case ZERO => ZERO |
64 case ONE => ZERO |
69 case ONE => ZERO |
65 case CHAR(d) => if (c == d) ONE else ZERO |
70 case CHAR(d) => if (c == d) ONE else ZERO |
66 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
71 case ALTs(rs) => ALTs(rs.map(der(c, _))) |
67 case SEQ(r1, r2) => |
72 case SEQ(r1, r2) => |
68 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
73 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
69 else SEQ(der(c, r1), r2) |
74 else SEQ(der(c, r1), r2) |
70 case STAR(r1) => SEQ(der(c, r1), STAR(r1)) |
75 case STAR(r1) => SEQ(der(c, r1), STAR(r1)) |
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76 } |
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77 |
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78 |
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79 |
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80 def flts(rs: List[Rexp]) : List[Rexp] = rs match { |
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81 case Nil => Nil |
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82 case ZERO::tl => flts(tl) |
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83 case ALTs(rs1)::rs2 => rs1 ::: flts(rs2) |
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84 case r::rs => r :: flts(rs) |
71 } |
85 } |
72 |
86 |
73 // (3) Complete the simp function according to |
87 // (3) Complete the simp function according to |
74 // the specification given in the coursework; this |
88 // the specification given in the coursework; this |
75 // function simplifies a regular expression from |
89 // function simplifies a regular expression from |
76 // the inside out, like you would simplify arithmetic |
90 // the inside out, like you would simplify arithmetic |
77 // expressions; however it does not simplify inside |
91 // expressions; however it does not simplify inside |
78 // STAR-regular expressions. |
92 // STAR-regular expressions. |
79 |
93 |
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94 |
80 def simp(r: Rexp) : Rexp = r match { |
95 def simp(r: Rexp) : Rexp = r match { |
81 case ALT(r1, r2) => (simp(r1), simp(r2)) match { |
96 case ALTs(rs) => (flts(rs.map(simp)).distinct) match { |
82 case (ZERO, r2s) => r2s |
97 case Nil => ZERO |
83 case (r1s, ZERO) => r1s |
98 case r::Nil => r |
84 case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s) |
99 case rs => ALTs(rs) |
85 } |
100 } |
86 case SEQ(r1, r2) => (simp(r1), simp(r2)) match { |
101 case SEQ(r1, r2) => (simp(r1), simp(r2)) match { |
87 case (ZERO, _) => ZERO |
102 case (ZERO, _) => ZERO |
88 case (_, ZERO) => ZERO |
103 case (_, ZERO) => ZERO |
89 case (ONE, r2s) => r2s |
104 case (ONE, r2s) => r2s |
130 //matcher(("a" ~ "b") ~ "c", "ab") // => false |
145 //matcher(("a" ~ "b") ~ "c", "ab") // => false |
131 |
146 |
132 // the supposedly 'evil' regular expression (a*)* b |
147 // the supposedly 'evil' regular expression (a*)* b |
133 val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b')) |
148 val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b')) |
134 |
149 |
135 //matcher(EVIL, "a" * 1000 ++ "b") // => true |
150 //println(matcher(EVIL, "a" * 1000 ++ "b")) // => true |
136 //matcher(EVIL, "a" * 1000) // => false |
151 //println(matcher(EVIL, "a" * 1000)) // => false |
137 |
152 |
138 // size without simplifications |
153 // size without simplifications |
139 //size(der('a', der('a', EVIL))) // => 28 |
154 //println(size(der('a', der('a', EVIL)))) // => 28 |
140 //size(der('a', der('a', der('a', EVIL)))) // => 58 |
155 //println(size(der('a', der('a', der('a', EVIL))))) // => 58 |
141 |
156 |
142 // size with simplification |
157 // size with simplification |
143 //size(simp(der('a', der('a', EVIL)))) // => 8 |
158 //println(simp(der('a', der('a', EVIL)))) |
144 //size(simp(der('a', der('a', der('a', EVIL))))) // => 8 |
159 //println(simp(der('a', der('a', der('a', EVIL))))) |
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160 |
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161 //println(size(simp(der('a', der('a', EVIL))))) // => 8 |
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162 //println(size(simp(der('a', der('a', der('a', EVIL)))))) // => 8 |
145 |
163 |
146 // Python needs around 30 seconds for matching 28 a's with EVIL. |
164 // Python needs around 30 seconds for matching 28 a's with EVIL. |
147 // Java 9 and later increase this to an "astonishing" 40000 a's in |
165 // Java 9 and later increase this to an "astonishing" 40000 a's in |
148 // around 30 seconds. |
166 // around 30 seconds. |
149 // |
167 // |
153 |
171 |
154 def time_needed[T](i: Int, code: => T) = { |
172 def time_needed[T](i: Int, code: => T) = { |
155 val start = System.nanoTime() |
173 val start = System.nanoTime() |
156 for (j <- 1 to i) code |
174 for (j <- 1 to i) code |
157 val end = System.nanoTime() |
175 val end = System.nanoTime() |
158 (end - start)/(i * 1.0e9) |
176 "%.5f".format((end - start)/(i * 1.0e9)) |
159 } |
177 } |
160 |
178 |
161 //for (i <- 0 to 5000000 by 500000) { |
179 //for (i <- 0 to 5000000 by 500000) { |
162 // println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i))) + " secs.") |
180 // println(s"$i ${time_needed(2, matcher(EVIL, "a" * i))} secs.") |
163 //} |
181 //} |
164 |
182 |
165 // another "power" test case |
183 // another "power" test case |
166 //simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(100).next) == ONE |
184 //simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(100).next) == ONE |
167 |
185 |
168 // the Iterator produces the rexp |
186 // the Iterator produces the rexp |
169 // |
187 // |
170 // SEQ(SEQ(SEQ(..., ONE | ONE) , ONE | ONE), ONE | ONE) |
188 // SEQ(SEQ(SEQ(..., ONE | ONE) , ONE | ONE), ONE | ONE) |
171 // |
189 // |
172 // where SEQ is nested 100 times. |
190 // where SEQ is nested 50 times. |
173 |
191 |
174 |
192 |
175 |
193 |
176 } |
194 } |