2 |
2 |
3 abstract class Rexp { |
3 abstract class Rexp { |
4 def simp : Rexp = this |
4 def simp : Rexp = this |
5 } |
5 } |
6 |
6 |
7 case object NULL extends Rexp |
7 case object ZERO extends Rexp |
8 case object EMPTY extends Rexp |
8 case object ONE extends Rexp |
9 case class CHAR(c: Char) extends Rexp |
9 case class CHAR(c: Char) extends Rexp |
10 case class ALT(r1: Rexp, r2: Rexp) extends Rexp { |
10 case class ALT(r1: Rexp, r2: Rexp) extends Rexp { |
11 override def simp = (r1.simp, r2.simp) match { |
11 override def simp = (r1.simp, r2.simp) match { |
12 case (NULL, r) => r |
12 case (ZERO, r) => r |
13 case (r, NULL) => r |
13 case (r, ZERO) => r |
14 case (r, EMPTY) => if (nullable(r)) r else ALT(r, EMPTY) |
14 case (r, ONE) => if (nullable(r)) r else ALT(r, ONE) |
15 case (EMPTY, r) => if (nullable(r)) r else ALT(r, EMPTY) |
15 case (ONE, r) => if (nullable(r)) r else ALT(r, ONE) |
16 case (r1, r2) => if (r1 == r2) r1 else ALT(r1, r2) |
16 case (r1, r2) => if (r1 == r2) r1 else ALT(r1, r2) |
17 } |
17 } |
18 } |
18 } |
19 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp { |
19 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp { |
20 override def simp = (r1.simp, r2.simp) match { |
20 override def simp = (r1.simp, r2.simp) match { |
21 case (NULL, _) => NULL |
21 case (ZERO, _) => ZERO |
22 case (_, NULL) => NULL |
22 case (_, ZERO) => ZERO |
23 case (EMPTY, r) => r |
23 case (ONE, r) => r |
24 case (r, EMPTY) => r |
24 case (r, ONE) => r |
25 case (r1, r2) => SEQ(r1, r2) |
25 case (r1, r2) => SEQ(r1, r2) |
26 } |
26 } |
27 } |
27 } |
28 case class STAR(r: Rexp) extends Rexp { |
28 case class STAR(r: Rexp) extends Rexp { |
29 override def simp = r.simp match { |
29 override def simp = r.simp match { |
30 case NULL => EMPTY |
30 case ZERO => ONE |
31 case EMPTY => EMPTY |
31 case ONE => ONE |
32 case r => STAR(r) |
32 case r => STAR(r) |
33 } |
33 } |
34 } |
34 } |
35 case class NTIMES(r: Rexp, n: Int) extends Rexp { |
35 case class NTIMES(r: Rexp, n: Int) extends Rexp { |
36 override def simp = if (n == 0) EMPTY else |
36 override def simp = if (n == 0) ONE else |
37 r.simp match { |
37 r.simp match { |
38 case NULL => NULL |
38 case ZERO => ZERO |
39 case EMPTY => EMPTY |
39 case ONE => ONE |
40 case r => NTIMES(r, n) |
40 case r => NTIMES(r, n) |
41 } |
41 } |
42 } |
42 } |
43 |
43 |
44 // some convenience for typing in regular expressions |
44 // some convenience for typing in regular expressions |
45 def charlist2rexp(s : List[Char]) : Rexp = s match { |
45 def charlist2rexp(s : List[Char]) : Rexp = s match { |
46 case Nil => EMPTY |
46 case Nil => ONE |
47 case c::Nil => CHAR(c) |
47 case c::Nil => CHAR(c) |
48 case c::s => SEQ(CHAR(c), charlist2rexp(s)) |
48 case c::s => SEQ(CHAR(c), charlist2rexp(s)) |
49 } |
49 } |
50 implicit def string2rexp(s : String) : Rexp = charlist2rexp(s.toList) |
50 implicit def string2rexp(s : String) : Rexp = charlist2rexp(s.toList) |
51 |
51 |
52 |
52 |
53 // nullable function: tests whether the regular |
53 // nullable function: tests whether the regular |
54 // expression can recognise the empty string |
54 // expression can recognise the empty string |
55 def nullable (r: Rexp) : Boolean = r match { |
55 def nullable (r: Rexp) : Boolean = r match { |
56 case NULL => false |
56 case ZERO => false |
57 case EMPTY => true |
57 case ONE => true |
58 case CHAR(_) => false |
58 case CHAR(_) => false |
59 case ALT(r1, r2) => nullable(r1) || nullable(r2) |
59 case ALT(r1, r2) => nullable(r1) || nullable(r2) |
60 case SEQ(r1, r2) => nullable(r1) && nullable(r2) |
60 case SEQ(r1, r2) => nullable(r1) && nullable(r2) |
61 case STAR(_) => true |
61 case STAR(_) => true |
62 case NTIMES(r, i) => if (i == 0) true else nullable(r) |
62 case NTIMES(r, i) => if (i == 0) true else nullable(r) |
63 } |
63 } |
64 |
64 |
65 // derivative of a regular expression w.r.t. a character |
65 // derivative of a regular expression w.r.t. a character |
66 def der (c: Char, r: Rexp) : Rexp = r match { |
66 def der (c: Char, r: Rexp) : Rexp = r match { |
67 case NULL => NULL |
67 case ZERO => ZERO |
68 case EMPTY => NULL |
68 case ONE => ZERO |
69 case CHAR(d) => if (c == d) EMPTY else NULL |
69 case CHAR(d) => if (c == d) ONE else ZERO |
70 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
70 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
71 case SEQ(r1, r2) => |
71 case SEQ(r1, r2) => |
72 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
72 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
73 else SEQ(der(c, r1), r2) |
73 else SEQ(der(c, r1), r2) |
74 case STAR(r) => SEQ(der(c, r), STAR(r)) |
74 case STAR(r) => SEQ(der(c, r), STAR(r)) |
75 case NTIMES(r, i) => |
75 case NTIMES(r, i) => |
76 if (i == 0) NULL else SEQ(der(c, r), NTIMES(r, i - 1)) |
76 if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1)) |
77 } |
77 } |
78 |
78 |
79 // derivative w.r.t. a string (iterates der) |
79 // derivative w.r.t. a string (iterates der) |
80 @tailrec |
80 @tailrec |
81 def ders (s: List[Char], r: Rexp) : Rexp = s match { |
81 def ders (s: List[Char], r: Rexp) : Rexp = s match { |
82 case Nil => r |
82 case Nil => r |
83 case c::s => ders(s, der(c, r).simp) |
83 case c::s => ders(s, der(c, r).simp) |
84 } |
84 } |
85 |
85 |
|
86 |
|
87 def ders2 (s: List[Char], r: Rexp) : Rexp = (s, r) match { |
|
88 case (Nil, r) => r |
|
89 case (s, ZERO) => ZERO |
|
90 case (s, ONE) => if (s == Nil) ONE else ZERO |
|
91 case (s, CHAR(c)) => if (s == List(c)) ONE else |
|
92 if (s == Nil) CHAR(c) else ZERO |
|
93 case (s, ALT(r1, r2)) => ALT(ders2(s, r2), ders2(s, r2)) |
|
94 case (c::s, r) => ders2(s, der(c, r).simp) |
|
95 } |
|
96 |
86 // main matcher function |
97 // main matcher function |
87 def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r)) |
98 def matcher(r: Rexp, s: String) : Boolean = nullable(ders2(s.toList, r)) |
88 |
99 |
89 |
100 |
90 //one or zero |
101 //one or zero |
91 def OPT(r: Rexp) = ALT(r, EMPTY) |
102 def OPT(r: Rexp) = ALT(r, ONE) |
92 |
103 |
93 def EVIL(n: Int) = SEQ(NTIMES(OPT("a"), n), NTIMES("a", n)) |
104 def EVIL(n: Int) = SEQ(NTIMES(OPT("a"), n), NTIMES("a", n)) |
94 |
105 |
95 def time_needed[T](i: Int, code: => T) = { |
106 def time_needed[T](i: Int, code: => T) = { |
96 val start = System.nanoTime() |
107 val start = System.nanoTime() |
97 for (j <- 1 to i) code |
108 for (j <- 1 to i) code |
98 val end = System.nanoTime() |
109 val end = System.nanoTime() |
99 (end - start)/(i * 1.0e9) |
110 (end - start)/(i * 1.0e9) |
100 } |
111 } |
101 |
112 |
|
113 val i = 5000000 |
|
114 println(i + " " + "%.5f".format(time_needed(10, matcher(EVIL(i), "a" * i)))) |
102 |
115 |
103 for (i <- 1 to 12001 by 500) { |
116 for (i <- 1 to 800001 by 10000) { |
104 println(i + " " + "%.5f".format(time_needed(1, matcher(EVIL(i), "a" * i)))) |
117 println(i + " " + "%.5f".format(time_needed(10, matcher(EVIL(i), "a" * i)))) |
105 } |
118 } |
106 |
119 |
107 |
120 |