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1 // Version with simplification during derivatives; |
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2 // this keeps the regular expressions small, which |
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3 // is good for run-time |
1 |
4 |
2 abstract class Rexp |
5 abstract class Rexp |
3 case object ZERO extends Rexp |
6 case object ZERO extends Rexp |
4 case object ONE extends Rexp |
7 case object ONE extends Rexp |
5 case class CHAR(c: Char) extends Rexp |
8 case class CHAR(c: Char) extends Rexp |
30 case SEQ(r1, r2) => |
33 case SEQ(r1, r2) => |
31 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
34 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
32 else SEQ(der(c, r1), r2) |
35 else SEQ(der(c, r1), r2) |
33 case STAR(r1) => SEQ(der(c, r1), STAR(r1)) |
36 case STAR(r1) => SEQ(der(c, r1), STAR(r1)) |
34 case NTIMES(r, i) => |
37 case NTIMES(r, i) => |
35 if (i == 0) ZERO else der(c, SEQ(r, NTIMES(r, i - 1))) |
38 if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1)) |
36 } |
39 } |
37 |
40 |
38 def simp(r: Rexp) : Rexp = r match { |
41 def simp(r: Rexp) : Rexp = r match { |
39 case ALT(r1, r2) => (simp(r1), simp(r2)) match { |
42 case ALT(r1, r2) => (simp(r1), simp(r2)) match { |
40 case (ZERO, r2s) => r2s |
43 case (ZERO, r2s) => r2s |
61 |
64 |
62 // main matcher function |
65 // main matcher function |
63 def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r)) |
66 def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r)) |
64 |
67 |
65 |
68 |
66 var regex = NTIMES(CHAR('a'),5) |
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67 println(matcher(regex,"aaaaa")) |
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68 |
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69 //one or zero |
69 //one or zero |
70 def OPT(r: Rexp) = ALT(r, ONE) |
70 def OPT(r: Rexp) = ALT(r, ONE) |
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71 |
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72 |
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73 // Test Cases |
71 |
74 |
72 //evil regular expressions |
75 //evil regular expressions |
73 def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n)) |
76 def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n)) |
74 val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b')) |
77 val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b')) |
75 |
78 |
81 (end - start)/(i * 1.0e9) |
84 (end - start)/(i * 1.0e9) |
82 } |
85 } |
83 |
86 |
84 |
87 |
85 //test: (a?{n}) (a{n}) |
88 //test: (a?{n}) (a{n}) |
86 for (i <- 1 to 9001 by 10) { |
89 for (i <- 1 to 11001 by 1000) { |
87 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i)))) |
90 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i)))) |
88 } |
91 } |
89 |
92 |
90 for (i <- 1 to 9001 by 1000) { |
93 for (i <- 1 to 11001 by 1000) { |
91 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i)))) |
94 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i)))) |
92 } |
95 } |
93 |
96 |
94 //test: (a*)* b |
97 //test: (a*)* b |
95 for (i <- 1 to 7000001 by 500000) { |
98 for (i <- 1 to 6000001 by 500000) { |
96 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i)))) |
99 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i)))) |
97 } |
100 } |
98 |
101 |
99 for (i <- 1 to 7000001 by 500000) { |
102 for (i <- 1 to 6000001 by 500000) { |
100 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i)))) |
103 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i)))) |
101 } |
104 } |
102 |
105 |
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106 |
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107 |
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108 // size of a regular expressions - for testing purposes |
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109 def size(r: Rexp) : Int = r match { |
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110 case ZERO => 1 |
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111 case ONE => 1 |
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112 case CHAR(_) => 1 |
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113 case ALT(r1, r2) => 1 + size(r1) + size(r2) |
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114 case SEQ(r1, r2) => 1 + size(r1) + size(r2) |
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115 case STAR(r) => 1 + size(r) |
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116 case NTIMES(r, _) => 1 + size(r) |
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117 } |
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118 |
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119 |
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120 // now the size of the derivatives grows |
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121 // much, much slower |
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122 |
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123 size(ders("".toList, EVIL2)) // 5 |
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124 size(ders("a".toList, EVIL2)) // 8 |
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125 size(ders("aa".toList, EVIL2)) // 8 |
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126 size(ders("aaa".toList, EVIL2)) // 8 |
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127 size(ders("aaaa".toList, EVIL2)) // 8 |
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128 size(ders("aaaaa".toList, EVIL2)) // 8 |