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1 // Part 1 about Regular Expression Matching |
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2 //========================================== |
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3 |
2 abstract class Rexp |
4 abstract class Rexp |
3 case object ZERO extends Rexp |
5 case object ZERO extends Rexp |
4 case object ONE extends Rexp |
6 case object ONE extends Rexp |
5 case class CHAR(c: Char) extends Rexp |
7 case class CHAR(c: Char) extends Rexp |
6 case class ALT(r1: Rexp, r2: Rexp) extends Rexp |
8 case class ALT(r1: Rexp, r2: Rexp) extends Rexp // alternative |
7 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp |
9 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp // sequence |
8 case class STAR(r: Rexp) extends Rexp |
10 case class STAR(r: Rexp) extends Rexp // star |
9 |
11 |
10 // nullable function: tests whether the regular |
12 |
11 // expression can recognise the empty string |
13 // some convenience for typing in regular expressions |
12 def nullable (r: Rexp) : Boolean = r match { |
14 |
13 case ZERO => false |
15 import scala.language.implicitConversions |
14 case ONE => true |
16 import scala.language.reflectiveCalls |
15 case CHAR(_) => false |
17 |
16 case ALT(r1, r2) => nullable(r1) || nullable(r2) |
18 def charlist2rexp(s: List[Char]): Rexp = s match { |
17 case SEQ(r1, r2) => nullable(r1) && nullable(r2) |
19 case Nil => ONE |
18 case STAR(_) => true |
20 case c::Nil => CHAR(c) |
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21 case c::s => SEQ(CHAR(c), charlist2rexp(s)) |
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22 } |
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23 implicit def string2rexp(s: String): Rexp = charlist2rexp(s.toList) |
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24 |
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25 implicit def RexpOps (r: Rexp) = new { |
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26 def | (s: Rexp) = ALT(r, s) |
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27 def % = STAR(r) |
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28 def ~ (s: Rexp) = SEQ(r, s) |
19 } |
29 } |
20 |
30 |
21 // derivative of a regular expression w.r.t. a character |
31 implicit def stringOps (s: String) = new { |
22 def der (c: Char, r: Rexp) : Rexp = r match { |
32 def | (r: Rexp) = ALT(s, r) |
23 case ZERO => ZERO |
33 def | (r: String) = ALT(s, r) |
24 case ONE => ZERO |
34 def % = STAR(s) |
25 case CHAR(d) => if (c == d) ONE else ZERO |
35 def ~ (r: Rexp) = SEQ(s, r) |
26 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
36 def ~ (r: String) = SEQ(s, r) |
27 case SEQ(r1, r2) => |
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28 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
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29 else SEQ(der(c, r1), r2) |
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30 case STAR(r1) => SEQ(der(c, r1), STAR(r1)) |
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31 } |
37 } |
32 |
38 |
33 def simp(r: Rexp) : Rexp = r match { |
39 // (1a) Complete the function nullable according to |
34 case ALT(r1, r2) => (simp(r1), simp(r2)) match { |
40 // the definition given in the coursework; this |
35 case (ZERO, r2s) => r2s |
41 // function checks whether a regular expression |
36 case (r1s, ZERO) => r1s |
42 // can match the empty string |
37 case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s) |
43 |
38 } |
44 def nullable (r: Rexp) : Boolean = ... |
39 case SEQ(r1, r2) => (simp(r1), simp(r2)) match { |
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40 case (ZERO, _) => ZERO |
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41 case (_, ZERO) => ZERO |
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42 case (ONE, r2s) => r2s |
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43 case (r1s, ONE) => r1s |
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44 case (r1s, r2s) => SEQ(r1s, r2s) |
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45 } |
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46 case r => r |
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47 } |
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48 |
45 |
49 |
46 |
50 // derivative w.r.t. a string (iterates der) |
47 // (1b) Complete the function der according to |
51 def ders (s: List[Char], r: Rexp) : Rexp = s match { |
48 // the definition given in the coursework; this |
52 case Nil => r |
49 // function calculates the derivative of a |
53 case c::s => ders(s, simp(der(c, r))) |
50 // regular expression w.r.t. a character |
54 } |
51 |
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52 def der (c: Char, r: Rexp) : Rexp = ... |
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53 |
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54 // (1c) Complete the function der according to |
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55 // the specification given in the coursework; this |
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56 // function simplifies a regular expression; |
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57 // however it does not simplify inside STAR-regular |
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58 // expressions |
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59 |
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60 def simp(r: Rexp) : Rexp = ... |
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61 |
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62 // (1d) Complete the two functions below; the first |
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63 // calculates the derivative w.r.t. a string; the second |
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64 // is the regular expression matcher taking a regular |
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65 // expression and a string and checks whether the |
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66 // string matches the regular expression |
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67 |
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68 def ders (s: List[Char], r: Rexp) : Rexp = ... |
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69 |
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70 def matcher(r: Rexp, s: String): Boolean = ... |
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71 |
56 |
72 |
57 // main matcher function |
73 // (1e) Complete the function below: it searches (from the left to |
58 def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r)) |
74 // right) in string s1 all the non-empty substrings that match the |
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75 // regular expression -- these substrings are assumed to be |
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76 // the longest substrings matched by the regular expression and |
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77 // assumed to be non-overlapping. All these substrings in s1 are replaced |
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78 // by s2. |
59 |
79 |
60 //one or zero |
80 def replace(r: Rexp, s1: String, s2: String): String = ... |
61 def OPT(r: Rexp) = ALT(r, ONE) |
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62 |
81 |
63 //evil regular expressions |
82 |
64 def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n)) |
83 |
65 val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b')) |
84 // some testing data |
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85 // the supposedly 'evil' regular expression (a*)* b |
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86 /* |
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87 val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b')) |
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88 println(matcher(EVIL, "a" * 1000 ++ "b")) |
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89 println(matcher(EVIL, "a" * 1000)) |
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90 |
67 |
91 |
68 def time_needed[T](i: Int, code: => T) = { |
92 def time_needed[T](i: Int, code: => T) = { |
69 val start = System.nanoTime() |
93 val start = System.nanoTime() |
70 for (j <- 1 to i) code |
94 for (j <- 1 to i) code |
71 val end = System.nanoTime() |
95 val end = System.nanoTime() |
72 (end - start)/(i * 1.0e9) |
96 (end - start)/(i * 1.0e9) |
73 } |
97 } |
74 |
98 |
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99 for (i <- 1 to 5000001 by 500000) { |
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100 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i)))) |
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101 } |
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102 */ |
75 |
103 |
76 //test: (a?{n}) (a{n}) |
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77 for (i <- 1 to 8001 by 1000) { |
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78 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i)))) |
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79 } |
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80 |
104 |
81 for (i <- 1 to 8001 by 1000) { |
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82 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i)))) |
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83 } |
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84 |
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85 //test: (a*)* b |
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86 for (i <- 1 to 7000001 by 500000) { |
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87 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i)))) |
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88 } |
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89 |
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90 for (i <- 1 to 7000001 by 500000) { |
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91 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i)))) |
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92 } |
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93 |
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