7 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp |
7 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp |
8 case class STAR(r: Rexp) extends Rexp |
8 case class STAR(r: Rexp) extends Rexp |
9 case class NTIMES(r: Rexp, n: Int) extends Rexp |
9 case class NTIMES(r: Rexp, n: Int) extends Rexp |
10 case class UPNTIMES(r: Rexp, n: Int) extends Rexp |
10 case class UPNTIMES(r: Rexp, n: Int) extends Rexp |
11 |
11 |
12 // nullable function: tests whether the regular |
12 // the nullable function: tests whether the regular |
13 // expression can recognise the empty string |
13 // expression can recognise the empty string |
14 def nullable (r: Rexp) : Boolean = r match { |
14 def nullable (r: Rexp) : Boolean = r match { |
15 case ZERO => false |
15 case ZERO => false |
16 case ONE => true |
16 case ONE => true |
17 case CHAR(_) => false |
17 case CHAR(_) => false |
20 case STAR(_) => true |
20 case STAR(_) => true |
21 case NTIMES(r, i) => if (i == 0) true else nullable(r) |
21 case NTIMES(r, i) => if (i == 0) true else nullable(r) |
22 case UPNTIMES(r: Rexp, n: Int) => true |
22 case UPNTIMES(r: Rexp, n: Int) => true |
23 } |
23 } |
24 |
24 |
25 // derivative of a regular expression w.r.t. a character |
25 // the derivative of a regular expression w.r.t. a character |
26 def der (c: Char, r: Rexp) : Rexp = r match { |
26 def der (c: Char, r: Rexp) : Rexp = r match { |
27 case ZERO => ZERO |
27 case ZERO => ZERO |
28 case ONE => ZERO |
28 case ONE => ZERO |
29 case CHAR(d) => if (c == d) ONE else ZERO |
29 case CHAR(d) => if (c == d) ONE else ZERO |
30 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
30 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
56 } |
56 } |
57 case r => r |
57 case r => r |
58 } |
58 } |
59 |
59 |
60 |
60 |
61 // derivative w.r.t. a string (iterates der) |
61 // the derivative w.r.t. a string (iterates der) |
62 def ders (s: List[Char], r: Rexp) : Rexp = s match { |
62 def ders (s: List[Char], r: Rexp) : Rexp = s match { |
63 case Nil => r |
63 case Nil => r |
64 case c::s => ders(s, simp(der(c, r))) |
64 case c::s => ders(s, simp(der(c, r))) |
65 } |
65 } |
66 |
66 |
67 |
67 |
68 // main matcher function |
68 // the main matcher function |
69 def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r)) |
69 def matches(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r)) |
70 |
70 |
71 //one or zero |
71 // one or zero |
72 def OPT(r: Rexp) = ALT(r, ONE) |
72 def OPT(r: Rexp) = ALT(r, ONE) |
73 |
73 |
74 //evil regular expressions |
74 // evil regular expressions |
75 def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n)) |
75 def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n)) |
76 val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b')) |
76 val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b')) |
77 val EVIL3 = SEQ(STAR(ALT(CHAR('a'), SEQ(CHAR('a'),CHAR('a')))), CHAR('b')) |
77 val EVIL3 = SEQ(STAR(ALT(CHAR('a'), SEQ(CHAR('a'),CHAR('a')))), CHAR('b')) |
78 |
78 |
79 def time_needed[T](i: Int, code: => T) = { |
79 def time_needed[T](i: Int, code: => T) = { |
80 val start = System.nanoTime() |
80 val start = System.nanoTime() |
81 for (j <- 1 to i) code |
81 for (j <- 1 to i) code |
82 val end = System.nanoTime() |
82 val end = System.nanoTime() |
83 (end - start)/(i * 1.0e9) |
83 "%.5f".format((end - start) / (i * 1.0e9)) |
84 } |
84 } |
85 |
85 |
86 |
86 |
87 //test: (a?{n}) (a{n}) |
87 // test: (a?{n}) (a{n}) |
88 for (i <- 1 to 8001 by 1000) { |
88 for (i <- 0 to 8000 by 1000) { |
89 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i)))) |
89 println(s"$i: ${time_needed(2, matches(EVIL1(i), "a" * i))}") |
90 } |
90 } |
91 |
91 |
92 for (i <- 1 to 8001 by 1000) { |
92 // test: (a*)* b |
93 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i)))) |
93 for (i <- 0 to 6000000 by 500000) { |
94 } |
94 println(s"$i: ${time_needed(2, matches(EVIL2, "a" * i))}") |
95 |
|
96 //test: (a*)* b |
|
97 for (i <- 1 to 6000001 by 500000) { |
|
98 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i)))) |
|
99 } |
|
100 |
|
101 for (i <- 1 to 6000001 by 500000) { |
|
102 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i)))) |
|
103 } |
95 } |
104 |
96 |
105 |
97 |
106 val r0 = simp(der('a', EVIL3)) |
98 val r0 = simp(der('a', EVIL3)) |
107 val r1 = simp(der('a', r0)) |
99 val r1 = simp(der('a', r0)) |