1 |
1 |
2 abstract class Rexp { |
2 abstract class Rexp |
3 def simp : Rexp = this |
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4 } |
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5 |
3 |
6 case object NULL extends Rexp |
4 case object NULL extends Rexp |
7 case object EMPTY extends Rexp |
5 case object EMPTY extends Rexp |
8 case class CHAR(c: Char) extends Rexp |
6 case class CHAR(c: Char) extends Rexp |
9 case class ALT(r1: Rexp, r2: Rexp) extends Rexp { |
7 case class ALT(r1: Rexp, r2: Rexp) extends Rexp |
10 override def simp = (r1.simp, r2.simp) match { |
8 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp |
11 case (NULL, r) => r |
9 case class STAR(r: Rexp) extends Rexp |
12 case (r, NULL) => r |
10 case class NTIMES(r: Rexp, n: Int) extends Rexp |
13 case (r, EMPTY) => if (nullable(r)) r else ALT(r, EMPTY) |
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14 case (EMPTY, r) => if (nullable(r)) r else ALT(r, EMPTY) |
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15 case (r1, r2) => if (r1 == r2) r1 else ALT(r1, r2) |
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16 } |
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17 } |
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18 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp { |
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19 override def simp = (r1.simp, r2.simp) match { |
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20 case (NULL, _) => NULL |
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21 case (_, NULL) => NULL |
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22 case (EMPTY, r) => r |
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23 case (r, EMPTY) => r |
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24 case (r1, r2) => SEQ(r1, r2) |
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25 } |
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26 } |
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27 case class STAR(r: Rexp) extends Rexp { |
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28 override def simp = r.simp match { |
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29 case NULL => EMPTY |
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30 case EMPTY => EMPTY |
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31 case r => STAR(r) |
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32 } |
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33 } |
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34 |
11 |
35 // some convenience for typing in regular expressions |
12 // some convenience for typing in regular expressions |
36 def charlist2rexp(s : List[Char]) : Rexp = s match { |
13 def charlist2rexp(s : List[Char]) : Rexp = s match { |
37 case Nil => EMPTY |
14 case Nil => EMPTY |
38 case c::Nil => CHAR(c) |
15 case c::Nil => CHAR(c) |
60 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
38 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
61 case SEQ(r1, r2) => |
39 case SEQ(r1, r2) => |
62 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
40 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
63 else SEQ(der(c, r1), r2) |
41 else SEQ(der(c, r1), r2) |
64 case STAR(r) => SEQ(der(c, r), STAR(r)) |
42 case STAR(r) => SEQ(der(c, r), STAR(r)) |
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43 case NTIMES(r, i) => |
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44 if (i == 0) NULL else SEQ(der(c, r), NTIMES(r, i - 1)) |
65 } |
45 } |
66 |
46 |
67 // derivative w.r.t. a string (iterates der) |
47 // derivative w.r.t. a string (iterates der) |
68 def ders (s: List[Char], r: Rexp) : Rexp = s match { |
48 def ders (s: List[Char], r: Rexp) : Rexp = s match { |
69 case Nil => r |
49 case Nil => r |
70 case c::s => ders(s, der(c, r).simp) |
50 case c::s => ders(s, der(c, r)) |
71 } |
51 } |
72 |
52 |
73 // main matcher function |
53 // main matcher function |
74 def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r)) |
54 def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r)) |
75 |
55 |
76 |
56 |
77 //one or zero |
57 //one or zero |
78 def OPT(r: Rexp) = ALT(r, EMPTY) |
58 def OPT(r: Rexp) = ALT(r, EMPTY) |
79 |
59 |
80 //n-times |
60 def EVIL(n: Int) = SEQ(NTIMES(OPT("a"), n), NTIMES("a", n)) |
81 def NTIMES(r: Rexp, n: Int) : Rexp = n match { |
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82 case 0 => EMPTY |
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83 case 1 => r |
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84 case n => SEQ(r, NTIMES(r, n - 1)) |
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85 } |
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86 |
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87 def RTEST(n: Int) = SEQ(NTIMES(OPT("a"), n), NTIMES("a", n)) |
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88 |
61 |
89 def time_needed[T](i: Int, code: => T) = { |
62 def time_needed[T](i: Int, code: => T) = { |
90 val start = System.nanoTime() |
63 val start = System.nanoTime() |
91 for (j <- 1 to i) code |
64 for (j <- 1 to i) code |
92 val end = System.nanoTime() |
65 val end = System.nanoTime() |
93 (end - start)/(i * 1.0e9) |
66 (end - start)/(i * 1.0e9) |
94 } |
67 } |
95 |
68 |
96 for (i <- 1 to 100) { |
69 for (i <- 1 to 100) { |
97 println(i + ": " + "%.5f".format(time_needed(1, matcher(RTEST(i), "a" * i)))) |
70 println(i + ": " + "%.5f".format(time_needed(1, matcher(EVIL(i), "a" * i)))) |
98 } |
71 } |
99 |
72 |
100 |
73 |
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74 for (i <- 1 to 1000 by 50) { |
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75 println(i + " " + "%.5f".format(time_needed(1, matcher(EVIL(i), "a" * i)))) |
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76 } |
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77 |
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78 |