37 def % = STAR(s) |
37 def % = STAR(s) |
38 def ~ (r: Rexp) = SEQ(s, r) |
38 def ~ (r: Rexp) = SEQ(s, r) |
39 def ~ (r: String) = SEQ(s, r) |
39 def ~ (r: String) = SEQ(s, r) |
40 } |
40 } |
41 |
41 |
42 // (1) Complete the function nullable according to |
42 // (5) Complete the function nullable according to |
43 // the definition given in the coursework; this |
43 // the definition given in the coursework; this |
44 // function checks whether a regular expression |
44 // function checks whether a regular expression |
45 // can match the empty string and Returns a boolean |
45 // can match the empty string and Returns a boolean |
46 // accordingly. |
46 // accordingly. |
47 |
47 |
48 def nullable (r: Rexp) : Boolean = r match { |
48 def nullable (r: Rexp) : Boolean = { |
49 case ZERO => false |
49 r match { |
50 case ONE => true |
50 case ZERO => false |
51 case CHAR(_) => false |
51 case ONE => true |
52 case ALT(r1, r2) => nullable(r1) || nullable(r2) |
52 case CHAR(c) => false |
53 case SEQ(r1, r2) => nullable(r1) && nullable(r2) |
53 case ALT(r1, r2) => (nullable(r1) || nullable(r2)) |
54 case STAR(_) => true |
54 case SEQ(r1, r2) => (nullable(r1) && nullable(r2)) |
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55 case STAR(r) => true |
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56 } |
55 } |
57 } |
56 |
58 |
57 // (2) Complete the function der according to |
59 // (6) Complete the function der according to |
58 // the definition given in the coursework; this |
60 // the definition given in the coursework; this |
59 // function calculates the derivative of a |
61 // function calculates the derivative of a |
60 // regular expression w.r.t. a character. |
62 // regular expression w.r.t. a character. |
61 |
63 |
62 def der (c: Char, r: Rexp) : Rexp = r match { |
64 def der (c: Char, r: Rexp) : Rexp = { |
63 case ZERO => ZERO |
65 r match { |
64 case ONE => ZERO |
66 case ZERO => ZERO |
65 case CHAR(d) => if (c == d) ONE else ZERO |
67 case ONE => ZERO |
66 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
68 case CHAR(d) => if(d == c) ONE else ZERO |
67 case SEQ(r1, r2) => |
69 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
68 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
70 case SEQ(r1, r2) => if(nullable(r1)) { |
69 else SEQ(der(c, r1), r2) |
71 (ALT(SEQ(der(c, r1), r2), der(c, r2))) |
70 case STAR(r1) => SEQ(der(c, r1), STAR(r1)) |
72 } else { |
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73 SEQ(der(c, r1), r2) |
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74 } |
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75 case STAR(r) => SEQ(der(c, r), STAR(r)) |
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76 } |
71 } |
77 } |
72 |
78 |
73 // (3) Complete the simp function according to |
79 |
|
80 // (7) Complete the simp function according to |
74 // the specification given in the coursework; this |
81 // the specification given in the coursework; this |
75 // function simplifies a regular expression from |
82 // function simplifies a regular expression from |
76 // the inside out, like you would simplify arithmetic |
83 // the inside out, like you would simplify arithmetic |
77 // expressions; however it does not simplify inside |
84 // expressions; however it does not simplify inside |
78 // STAR-regular expressions. |
85 // STAR-regular expressions. |
79 |
86 |
80 def simp(r: Rexp) : Rexp = r match { |
87 def simp(r: Rexp) : Rexp = { |
81 case ALT(r1, r2) => (simp(r1), simp(r2)) match { |
88 r match { |
82 case (ZERO, r2s) => r2s |
89 case STAR(r) => STAR(r) // does not process r star |
83 case (r1s, ZERO) => r1s |
90 case SEQ(r1, r2) => { |
84 case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s) |
91 val x = (simp(r1), simp(r2)) |
85 } |
92 if(x._1 == ZERO) ZERO else |
86 case SEQ(r1, r2) => (simp(r1), simp(r2)) match { |
93 if(x._2 == ZERO) ZERO else |
87 case (ZERO, _) => ZERO |
94 if(x._1 == ONE) simp(x._2) else |
88 case (_, ZERO) => ZERO |
95 if(x._2 == ONE) simp(x._1) else |
89 case (ONE, r2s) => r2s |
96 if(x._1 == x._2) simp(x._2) else |
90 case (r1s, ONE) => r1s |
97 SEQ(simp(x._1), simp(x._2)) |
91 case (r1s, r2s) => SEQ(r1s, r2s) |
98 } |
92 } |
99 case ALT(r1, r2) => { |
93 case r => r |
100 val x = (simp(r1), simp(r2)) |
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101 if(x._1 == ZERO) simp(x._2) else |
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102 if(x._2 == ZERO) simp(x._1) else |
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103 if(x._1 == x._2) simp(x._2) else |
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104 ALT(simp(x._1), simp(x._2)) |
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105 } |
|
106 case r => r // if single regex, return it |
|
107 } |
94 } |
108 } |
95 |
109 |
96 |
110 |
97 // (4) Complete the two functions below; the first |
111 // (8) Complete the two functions below; the first |
98 // calculates the derivative w.r.t. a string; the second |
112 // calculates the derivative w.r.t. a string; the second |
99 // is the regular expression matcher taking a regular |
113 // is the regular expression matcher taking a regular |
100 // expression and a string and checks whether the |
114 // expression and a string and checks whether the |
101 // string matches the regular expression. |
115 // string matches the regular expression |
102 |
116 |
103 def ders (s: List[Char], r: Rexp) : Rexp = s match { |
117 def ders (s: List[Char], r: Rexp) : Rexp = { |
104 case Nil => r |
118 s match { |
105 case c::s => ders(s, simp(der(c, r))) |
119 case Nil => r |
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120 case c :: cs => ders(cs, simp(der(c,r))) |
|
121 } |
106 } |
122 } |
107 |
123 |
108 // main matcher function |
124 def matcher(r: Rexp, s: String): Boolean = { |
109 def matcher(r: Rexp, s: String) = nullable(ders(s.toList, r)) |
125 val listOfCharacters = s.toList |
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126 val result = ders(listOfCharacters, r) |
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127 nullable(result) |
|
128 } |
110 |
129 |
111 // (5) Complete the size function for regular |
130 |
|
131 // (9) Complete the size function for regular |
112 // expressions according to the specification |
132 // expressions according to the specification |
113 // given in the coursework. |
133 // given in the coursework. |
114 |
134 |
115 |
135 def size(r: Rexp): Int = { |
116 def size(r: Rexp): Int = r match { |
136 r match { |
117 case ZERO => 1 |
137 case ZERO => 1 |
118 case ONE => 1 |
138 case ONE => 1 |
119 case CHAR(_) => 1 |
139 case CHAR(c) => 1 |
120 case ALT(r1, r2) => 1 + size(r1) + size (r2) |
140 case ALT(r1, r2) => 1 + size(r1) + size(r2) |
121 case SEQ(r1, r2) => 1 + size(r1) + size (r2) |
141 case SEQ(r1, r2) => 1 + size(r1) + size(r2) |
122 case STAR(r1) => 1 + size(r1) |
142 case STAR(r) => 1 + size(r) |
|
143 } |
123 } |
144 } |
124 |
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125 |
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126 |
145 |
127 // some testing data |
146 // some testing data |
128 |
147 |
129 //matcher(("a" ~ "b") ~ "c", "abc") // => true |
148 /* |
130 //matcher(("a" ~ "b") ~ "c", "ab") // => false |
149 matcher(("a" ~ "b") ~ "c", "abc") // => true |
|
150 matcher(("a" ~ "b") ~ "c", "ab") // => false |
131 |
151 |
132 // the supposedly 'evil' regular expression (a*)* b |
152 // the supposedly 'evil' regular expression (a*)* b |
133 val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b')) |
153 // val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b')) |
134 |
154 |
135 //matcher(EVIL, "a" * 1000 ++ "b") // => true |
155 matcher(EVIL, "a" * 1000 ++ "b") // => true |
136 //matcher(EVIL, "a" * 1000) // => false |
156 matcher(EVIL, "a" * 1000) // => false |
137 |
157 |
138 // size without simplifications |
158 // size without simplifications |
139 //size(der('a', der('a', EVIL))) // => 28 |
159 size(der('a', der('a', EVIL))) // => 28 |
140 //size(der('a', der('a', der('a', EVIL)))) // => 58 |
160 size(der('a', der('a', der('a', EVIL)))) // => 58 |
141 |
161 |
142 // size with simplification |
162 // size with simplification |
143 //size(simp(der('a', der('a', EVIL)))) // => 8 |
163 size(simp(der('a', der('a', EVIL)))) // => 8 |
144 //size(simp(der('a', der('a', der('a', EVIL))))) // => 8 |
164 size(simp(der('a', der('a', der('a', EVIL))))) // => 8 |
145 |
165 |
146 // Python needs around 30 seconds for matching 28 a's with EVIL. |
166 // Python needs around 30 seconds for matching 28 a's with EVIL. |
147 // Java 9 and later increase this to an "astonishing" 40000 a's in |
167 // Java 9 and later increase this to an "astonishing" 40000 a's in |
148 // around 30 seconds. |
168 // 30 seconds. |
149 // |
169 // |
150 // Lets see how long it takes to match strings with |
170 // Lets see how long it really takes to match strings with |
151 // 5 Million a's...it should be in the range of a |
171 // 5 Million a's...it should be in the range of a couple |
152 // couple of seconds. |
172 // of seconds. |
153 |
173 |
154 def time_needed[T](i: Int, code: => T) = { |
174 def time_needed[T](i: Int, code: => T) = { |
155 val start = System.nanoTime() |
175 val start = System.nanoTime() |
156 for (j <- 1 to i) code |
176 for (j <- 1 to i) code |
157 val end = System.nanoTime() |
177 val end = System.nanoTime() |
158 (end - start)/(i * 1.0e9) |
178 (end - start)/(i * 1.0e9) |
159 } |
179 } |
160 |
180 |
161 //for (i <- 0 to 5000000 by 500000) { |
181 for (i <- 0 to 5000000 by 500000) { |
162 // println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i))) + " secs.") |
182 println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i)))) |
163 //} |
183 } |
164 |
184 |
165 // another "power" test case |
185 // another "power" test case |
166 //simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(100).next) == ONE |
186 simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(50).next) == ONE |
167 |
187 |
168 // the Iterator produces the rexp |
188 // the Iterator produces the rexp |
169 // |
189 // |
170 // SEQ(SEQ(SEQ(..., ONE | ONE) , ONE | ONE), ONE | ONE) |
190 // SEQ(SEQ(SEQ(..., ONE | ONE) , ONE | ONE), ONE | ONE) |
171 // |
191 // |
172 // where SEQ is nested 100 times. |
192 // where SEQ is nested 50 times. |
173 |
|
174 |
193 |
|
194 */ |
175 |
195 |
176 } |
196 } |