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- package forcomp
- object Anagrams {
- /** A word is simply a `String`. */
- type Word = String
- /** A sentence is a `List` of words. */
- type Sentence = List[Word]
- /** `Occurrences` is a `List` of pairs of characters and positive integers saying
- * how often the character appears.
- * This list is sorted alphabetically w.r.t. to the character in each pair.
- * All characters in the occurrence list are lowercase.
- *
- * Any list of pairs of lowercase characters and their frequency which is not sorted
- * is **not** an occurrence list.
- *
- * Note: If the frequency of some character is zero, then that character should not be
- * in the list.
- */
- type Occurrences = List[(Char, Int)]
- /** The dictionary is simply a sequence of words.
- * It is predefined and obtained as a sequence using the utility method `loadDictionary`.
- */
- val dictionary: List[Word] = loadDictionary
- /** Converts the word into its character occurence list.
- *
- * Note: the uppercase and lowercase version of the character are treated as the
- * same character, and are represented as a lowercase character in the occurrence list.
- */
- def wordOccurrences(w: Word): Occurrences = {
- val lowerCaseWord = w.toLowerCase.toList
- def occurencesOfCharInString(char: Char): Int = {
- lowerCaseWord.count((charInWord: Char) => char == charInWord)
- }
- val charactersForOccurence: Map[Int, List[Char]] = lowerCaseWord.groupBy((char: Char) => occurencesOfCharInString(char))
- val occurences: Occurrences = charactersForOccurence.map(tuple => tuple._2.map(char => (char, tuple._1))).flatten.toSet.toList
- occurences.sortWith((left, right) => left._1 < right._1)
- }
- /** Converts a sentence into its character occurrence list. */
- def sentenceOccurrences(s: Sentence): Occurrences = {
- val mergedSentence: String = s.mkString("")
- wordOccurrences(mergedSentence)
- }
- /** The `dictionaryByOccurrences` is a `Map` from different occurrences to a sequence of all
- * the words that have that occurrence count.
- * This map serves as an easy way to obtain all the anagrams of a word given its occurrence list.
- *
- * For example, the word "eat" has the following character occurrence list:
- *
- * `List(('a', 1), ('e', 1), ('t', 1))`
- *
- * Incidentally, so do the words "ate" and "tea".
- *
- * This means that the `dictionaryByOccurrences` map will contain an entry:
- *
- * List(('a', 1), ('e', 1), ('t', 1)) -> Seq("ate", "eat", "tea")
- *
- */
- lazy val dictionaryByOccurrences: Map[Occurrences, List[Word]] = dictionary.groupBy(word => wordOccurrences(word))
- /** Returns all the anagrams of a given word. */
- def wordAnagrams(word: Word): List[Word] = {
- val occurencesForGivenWord: Occurrences = wordOccurrences(word)
- dictionaryByOccurrences.get(occurencesForGivenWord).get
- }
- /** Returns the list of all subsets of the occurrence list.
- * This includes the occurrence itself, i.e. `List(('k', 1), ('o', 1))`
- * is a subset of `List(('k', 1), ('o', 1))`.
- * It also include the empty subset `List()`.
- *
- * Example: the subsets of the occurrence list `List(('a', 2), ('b', 2))` are:
- *
- * List(
- * List(),
- * List(('a', 1)),
- * List(('a', 2)),
- * List(('b', 1)),
- * List(('a', 1), ('b', 1)),
- * List(('a', 2), ('b', 1)),
- * List(('b', 2)),
- * List(('a', 1), ('b', 2)),
- * List(('a', 2), ('b', 2))
- * )
- *
- * Note that the order of the occurrence list subsets does not matter -- the subsets
- * in the example above could have been displayed in some other order.
- */
- def combinations(occurrences: Occurrences): List[Occurrences] = {
- val result = for {
- o1 <- occurrences
- o2 <- occurrences
- if o1._1 < o2._1
- i1 <- 0 to o1._2
- i2 <- 0 to o2._2
- } yield ((o1._1, i1) ::(o2._1, i2) :: Nil).filter((p: (Char, Int)) => p._2 > 0)
- result ::: List(List())
- }
- /** Subtracts occurrence list `y` from occurrence list `x`.
- *
- * The precondition is that the occurrence list `y` is a subset of
- * the occurrence list `x` -- any character appearing in `y` must
- * appear in `x`, and its frequency in `y` must be smaller or equal
- * than its frequency in `x`.
- *
- * Note: the resulting value is an occurrence - meaning it is sorted
- * and has no zero-entries.
- */
- def subtract(x: Occurrences, y: Occurrences): Occurrences = {
- val mapY = y.toMap
- val (toSubstract, ready) = x.partition(tuple => mapY.contains(tuple._1))
- (toSubstract.map(t => (t._1, t._2 - mapY(t._1))) ::: ready).filter(p => p._2 > 0).sortWith( (l,r) => l._1 < r._1)
- }
- /** Returns a list of all anagram sentences of the given sentence.
- *
- * An anagram of a sentence is formed by taking the occurrences of all the characters of
- * all the words in the sentence, and producing all possible combinations of words with those characters,
- * such that the words have to be from the dictionary.
- *
- * The number of words in the sentence and its anagrams does not have to correspond.
- * For example, the sentence `List("I", "love", "you")` is an anagram of the sentence `List("You", "olive")`.
- *
- * Also, two sentences with the same words but in a different order are considered two different anagrams.
- * For example, sentences `List("You", "olive")` and `List("olive", "you")` are different anagrams of
- * `List("I", "love", "you")`.
- *
- * Here is a full example of a sentence `List("Yes", "man")` and its anagrams for our dictionary:
- *
- * List(
- * List(en, as, my),
- * List(en, my, as),
- * List(man, yes),
- * List(men, say),
- * List(as, en, my),
- * List(as, my, en),
- * List(sane, my),
- * List(Sean, my),
- * List(my, en, as),
- * List(my, as, en),
- * List(my, sane),
- * List(my, Sean),
- * List(say, men),
- * List(yes, man)
- * )
- *
- * The different sentences do not have to be output in the order shown above - any order is fine as long as
- * all the anagrams are there. Every returned word has to exist in the dictionary.
- *
- * Note: in case that the words of the sentence are in the dictionary, then the sentence is the anagram of itself,
- * so it has to be returned in this list.
- *
- * Note: There is only one anagram of an empty sentence.
- */
- def sentenceAnagrams(sentence: Sentence): List[Sentence] = {
- def iter(occ: Occurrences): List[Sentence] = occ match {
- case Nil => List(List())
- case occ =>
- for {
- subOcc <- combinations(occ)
- word <- dictionaryByOccurrences getOrElse (subOcc, List())
- sentence <- iter(subtract(occ, subOcc))
- } yield word :: sentence
- }
- iter(sentenceOccurrences(sentence))
- }
- }
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