47 |
15 |
48 sortOn(identity, List(99,99,99,98,10,-3,2)) |
16 sortOn(identity, List(99,99,99,98,10,-3,2)) |
49 sortOn(n => - n, List(99,99,99,98,10,-3,2)) |
17 sortOn(n => - n, List(99,99,99,98,10,-3,2)) |
50 |
18 |
51 |
19 |
52 |
|
53 |
|
54 // Recursion Again ;o) |
20 // Recursion Again ;o) |
55 //==================== |
21 //==================== |
56 |
22 |
57 |
23 |
58 // A Web Crawler / Email Harvester |
24 // another well-known example: Towers of Hanoi |
59 //================================= |
25 //============================================= |
60 // |
|
61 // the idea is to look for links using the |
|
62 // regular expression "https?://[^"]*" and for |
|
63 // email addresses using yet another regex. |
|
64 |
|
65 import io.Source |
|
66 import scala.util._ |
|
67 |
|
68 // gets the first 10K of a web-page |
|
69 def get_page(url: String) : String = { |
|
70 Try(Source.fromURL(url)("ISO-8859-1").take(10000).mkString). |
|
71 getOrElse { println(s" Problem with: $url"); ""} |
|
72 } |
|
73 |
|
74 // regex for URLs and emails |
|
75 val http_pattern = """"https?://[^"]*"""".r |
|
76 val email_pattern = """([a-z0-9_\.-]+)@([\da-z\.-]+)\.([a-z\.]{2,6})""".r |
|
77 |
|
78 // val s = "foo bla christian@kcl.ac.uk 1234567" |
|
79 // email_pattern.findAllIn(s).toList |
|
80 |
|
81 // drops the first and last character from a string |
|
82 def unquote(s: String) = s.drop(1).dropRight(1) |
|
83 |
|
84 def get_all_URLs(page: String): Set[String] = |
|
85 http_pattern.findAllIn(page).map(unquote).toSet |
|
86 |
|
87 // a naive version of crawl - searches until a given depth, |
|
88 // visits pages potentially more than once |
|
89 def crawl(url: String, n: Int) : Unit = { |
|
90 if (n == 0) () |
|
91 else { |
|
92 println(s" Visiting: $n $url") |
|
93 val page = get_page(url) |
|
94 for (u <- get_all_URLs(page)) crawl(u, n - 1) |
|
95 } |
|
96 } |
|
97 |
|
98 // some starting URLs for the crawler |
|
99 val startURL = """https://nms.kcl.ac.uk/christian.urban/""" |
|
100 |
|
101 crawl(startURL, 2) |
|
102 |
|
103 for (x <- List(1,2,3,4,5,6)) println(x) |
|
104 |
|
105 // a primitive email harvester |
|
106 def emails(url: String, n: Int) : Set[String] = { |
|
107 if (n == 0) Set() |
|
108 else { |
|
109 println(s" Visiting: $n $url") |
|
110 val page = get_page(url) |
|
111 val new_emails = email_pattern.findAllIn(page).toSet |
|
112 new_emails ++ (for (u <- get_all_URLs(page).par) yield emails(u, n - 1)).flatten |
|
113 } |
|
114 } |
|
115 |
|
116 emails(startURL, 3) |
|
117 |
|
118 |
|
119 // if we want to explore the internet "deeper", then we |
|
120 // first have to parallelise the request of webpages: |
|
121 // |
|
122 // scala -cp scala-parallel-collections_2.13-0.2.0.jar |
|
123 // import scala.collection.parallel.CollectionConverters._ |
|
124 |
|
125 |
|
126 |
|
127 // another well-known example |
|
128 //============================ |
|
129 |
26 |
130 def move(from: Char, to: Char) = |
27 def move(from: Char, to: Char) = |
131 println(s"Move disc from $from to $to!") |
28 println(s"Move disc from $from to $to!") |
132 |
29 |
133 def hanoi(n: Int, from: Char, via: Char, to: Char) : Unit = { |
30 def hanoi(n: Int, from: Char, via: Char, to: Char) : Unit = { |
141 |
38 |
142 hanoi(4, 'A', 'B', 'C') |
39 hanoi(4, 'A', 'B', 'C') |
143 |
40 |
144 |
41 |
145 |
42 |
146 // Jumping Towers |
|
147 //================ |
|
148 |
|
149 |
|
150 // the first n prefixes of xs |
|
151 // for 1 => include xs |
|
152 |
|
153 def moves(xs: List[Int], n: Int) : List[List[Int]] = (xs, n) match { |
|
154 case (Nil, _) => Nil |
|
155 case (_, 0) => Nil |
|
156 case (y::ys, n) => xs :: moves(ys, n - 1) |
|
157 } |
|
158 |
|
159 |
|
160 moves(List(5,1,0), 1) |
|
161 moves(List(5,1,0), 2) |
|
162 moves(List(5,1,0), 5) |
|
163 |
|
164 // checks whether a jump tour exists at all |
|
165 |
|
166 def search(xs: List[Int]) : Boolean = xs match { |
|
167 case Nil => true |
|
168 case x::xs => |
|
169 if (xs.length < x) true |
|
170 else moves(xs, x).exists(search(_)) |
|
171 } |
|
172 |
|
173 |
|
174 search(List(5,3,2,5,1,1)) |
|
175 search(List(3,5,1,0,0,0,1)) |
|
176 search(List(3,5,1,0,0,0,0,1)) |
|
177 search(List(3,5,1,0,0,0,1,1)) |
|
178 search(List(3,5,1)) |
|
179 search(List(5,1,1)) |
|
180 search(Nil) |
|
181 search(List(1)) |
|
182 search(List(5,1,1)) |
|
183 search(List(3,5,1,0,0,0,0,0,0,0,0,1)) |
|
184 |
|
185 // generates *all* jump tours |
|
186 // if we are only interested in the shortest one, we could |
|
187 // shortcircut the calculation and only return List(x) in |
|
188 // case where xs.length < x, because no tour can be shorter |
|
189 // than 1 |
|
190 // |
|
191 |
|
192 def jumps(xs: List[Int]) : List[List[Int]] = xs match { |
|
193 case Nil => Nil |
|
194 case x::xs => { |
|
195 val children = moves(xs, x) |
|
196 val results = children.map(cs => jumps(cs).map(x :: _)).flatten |
|
197 if (xs.length < x) List(x)::results else results |
|
198 } |
|
199 } |
|
200 |
|
201 jumps(List(5,3,2,5,1,1)).minBy(_.length) |
|
202 jumps(List(3,5,1,2,1,2,1)) |
|
203 jumps(List(3,5,1,2,3,4,1)) |
|
204 jumps(List(3,5,1,0,0,0,1)) |
|
205 jumps(List(3,5,1)) |
|
206 jumps(List(5,1,1)) |
|
207 jumps(Nil) |
|
208 jumps(List(1)) |
|
209 jumps(List(5,1,2)) |
|
210 moves(List(1,2), 5) |
|
211 jumps(List(1,5,1,2)) |
|
212 jumps(List(3,5,1,0,0,0,0,0,0,0,0,1)) |
|
213 |
|
214 jumps(List(5,3,2,5,1,1)).minBy(_.length) |
|
215 jumps(List(1,3,5,8,9,2,6,7,6,8,9)).minBy(_.length) |
|
216 jumps(List(1,3,6,1,0,9)).minBy(_.length) |
|
217 jumps(List(2,3,1,1,2,4,2,0,1,1)).minBy(_.length) |
|
218 |
|
219 |
|
220 |
|
221 |
|
222 |
|
223 |
|
224 // User-defined Datatypes |
43 // User-defined Datatypes |
225 //======================== |
44 //======================== |
226 |
45 |
227 abstract class Tree |
46 abstract class Tree |
228 case class Leaf(x: Int) extends Tree |
47 case class Leaf(x: Int) extends Tree |
229 case class Node(s: String, left: Tree, right: Tree) extends Tree |
48 case class Node(s: String, left: Tree, right: Tree) extends Tree |
230 |
49 |
231 List(Leaf(20), Node("foo", Leaf(1), Leaf(2))) |
50 val lf = Leaf(20) |
232 |
51 val tr = Node("foo", Leaf(10), Leaf(23)) |
233 sealed abstract class Colour |
52 |
|
53 val lst : List[Tree] = List(lf, tr) |
|
54 |
|
55 |
|
56 abstract class Colour |
234 case object Red extends Colour |
57 case object Red extends Colour |
235 case object Green extends Colour |
58 case object Green extends Colour |
236 case object Blue extends Colour |
59 case object Blue extends Colour |
237 case object Yellow extends Colour |
60 case object Yellow extends Colour |
238 |
61 |
295 RomanNumeral2Int(List(I,X)) // 9 |
119 RomanNumeral2Int(List(I,X)) // 9 |
296 RomanNumeral2Int(List(M,C,M,L,X,X,I,X)) // 1979 |
120 RomanNumeral2Int(List(M,C,M,L,X,X,I,X)) // 1979 |
297 RomanNumeral2Int(List(M,M,X,V,I,I)) // 2017 |
121 RomanNumeral2Int(List(M,M,X,V,I,I)) // 2017 |
298 |
122 |
299 |
123 |
|
124 // expressions (essentially trees) |
|
125 |
|
126 abstract class Exp |
|
127 case class N(n: Int) extends Exp // for numbers |
|
128 case class Plus(e1: Exp, e2: Exp) extends Exp |
|
129 case class Times(e1: Exp, e2: Exp) extends Exp |
|
130 |
|
131 def string(e: Exp) : String = e match { |
|
132 case N(n) => s"$n" |
|
133 case Plus(e1, e2) => s"(${string(e1)} + ${string(e2)})" |
|
134 case Times(e1, e2) => s"(${string(e1)} * ${string(e2)})" |
|
135 } |
|
136 |
|
137 val e = Plus(N(9), Times(N(3), N(4))) |
|
138 e.toString |
|
139 println(string(e)) |
|
140 |
|
141 def eval(e: Exp) : Int = e match { |
|
142 case N(n) => n |
|
143 case Plus(e1, e2) => eval(e1) + eval(e2) |
|
144 case Times(e1, e2) => eval(e1) * eval(e2) |
|
145 } |
|
146 |
|
147 println(eval(e)) |
|
148 |
|
149 // simplification rules: |
|
150 // e + 0, 0 + e => e |
|
151 // e * 0, 0 * e => 0 |
|
152 // e * 1, 1 * e => e |
|
153 // |
|
154 // (....9 ....) |
|
155 |
|
156 def simp(e: Exp) : Exp = e match { |
|
157 case N(n) => N(n) |
|
158 case Plus(e1, e2) => (simp(e1), simp(e2)) match { |
|
159 case (N(0), e2s) => e2s |
|
160 case (e1s, N(0)) => e1s |
|
161 case (e1s, e2s) => Plus(e1s, e2s) |
|
162 } |
|
163 case Times(e1, e2) => (simp(e1), simp(e2)) match { |
|
164 case (N(0), _) => N(0) |
|
165 case (_, N(0)) => N(0) |
|
166 case (N(1), e2s) => e2s |
|
167 case (e1s, N(1)) => e1s |
|
168 case (e1s, e2s) => Times(e1s, e2s) |
|
169 } |
|
170 } |
|
171 |
|
172 |
|
173 val e2 = Times(Plus(N(0), N(1)), Plus(N(0), N(9))) |
|
174 println(string(e2)) |
|
175 println(string(simp(e2))) |
|
176 |
|
177 |
|
178 |
300 // String interpolations as patterns |
179 // String interpolations as patterns |
301 |
180 |
302 val date = "2019-11-26" |
181 val date = "2019-11-26" |
303 val s"$year-$month-$day" = date |
182 val s"$year-$month-$day" = date |
304 |
183 |
353 // for tail-recursive functions the Scala compiler |
229 // for tail-recursive functions the Scala compiler |
354 // generates loop-like code, which does not need |
230 // generates loop-like code, which does not need |
355 // to allocate stack-space in each recursive |
231 // to allocate stack-space in each recursive |
356 // call; Scala can do this only for tail-recursive |
232 // call; Scala can do this only for tail-recursive |
357 // functions |
233 // functions |
|
234 |
|
235 |
|
236 |
|
237 |
|
238 // Sudoku |
|
239 //======== |
|
240 |
|
241 |
|
242 type Pos = (Int, Int) |
|
243 val emptyValue = '.' |
|
244 val maxValue = 9 |
|
245 |
|
246 val allValues = "123456789".toList |
|
247 val indexes = (0 to 8).toList |
|
248 |
|
249 |
|
250 def empty(game: String) = game.indexOf(emptyValue) |
|
251 def isDone(game: String) = empty(game) == -1 |
|
252 def emptyPosition(game: String) : Pos = |
|
253 (empty(game) % maxValue, empty(game) / maxValue) |
|
254 |
|
255 |
|
256 def get_row(game: String, y: Int) = indexes.map(col => game(y * maxValue + col)) |
|
257 def get_col(game: String, x: Int) = indexes.map(row => game(x + row * maxValue)) |
|
258 |
|
259 def get_box(game: String, pos: Pos): List[Char] = { |
|
260 def base(p: Int): Int = (p / 3) * 3 |
|
261 val x0 = base(pos._1) |
|
262 val y0 = base(pos._2) |
|
263 for (x <- (x0 until x0 + 3).toList; |
|
264 y <- (y0 until y0 + 3).toList) yield game(x + y * maxValue) |
|
265 } |
|
266 |
|
267 |
|
268 def update(game: String, pos: Int, value: Char): String = |
|
269 game.updated(pos, value) |
|
270 |
|
271 def toAvoid(game: String, pos: Pos): List[Char] = |
|
272 (get_col(game, pos._1) ++ get_row(game, pos._2) ++ get_box(game, pos)) |
|
273 |
|
274 def candidates(game: String, pos: Pos): List[Char] = |
|
275 allValues.diff(toAvoid(game, pos)) |
|
276 |
|
277 def search(game: String): List[String] = { |
|
278 if (isDone(game)) List(game) |
|
279 else |
|
280 candidates(game, emptyPosition(game)).par. |
|
281 map(c => search(update(game, empty(game), c))).toList.flatten |
|
282 } |
|
283 |
|
284 def search1T(games: List[String]): Option[String] = games match { |
|
285 case Nil => None |
|
286 case game::rest => { |
|
287 if (isDone(game)) Some(game) |
|
288 else { |
|
289 val cs = candidates(game, emptyPosition(game)) |
|
290 search1T(cs.map(c => update(game, empty(game), c)) ::: rest) |
|
291 } |
|
292 } |
|
293 } |
|
294 |
|
295 def pretty(game: String): String = |
|
296 "\n" + (game.sliding(maxValue, maxValue).mkString(",\n")) |
|
297 |
358 |
298 |
359 // tail recursive version that searches |
299 // tail recursive version that searches |
360 // for all solutions |
300 // for all solutions |
361 |
301 |
362 def searchT(games: List[String], sols: List[String]): List[String] = games match { |
302 def searchT(games: List[String], sols: List[String]): List[String] = games match { |