Scala : add patmat

2 files changed, 246 insertions, 0 deletions

diff --git a/Scala/patmat/src/main/scala/common/package.scala b/Scala/patmat/src/main/scala/common/package.scala
new file mode 100644
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+++ b/Scala/patmat/src/main/scala/common/package.scala
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+import java.io.File
+
+package object common {
+
+  /** An alias for the `Nothing` type.
+   *  Denotes that the type should be filled in.
+   */
+  type ??? = Nothing
+
+  /** An alias for the `Any` type.
+   *  Denotes that the type should be filled in.
+   */
+  type *** = Any
+
+  
+  /**
+   * Get a child of a file. For example,
+   * 
+   *   subFile(homeDir, "b", "c")
+   * 
+   * corresponds to ~/b/c
+   */
+  def subFile(file: File, children: String*) = {
+    children.foldLeft(file)((file, child) => new File(file, child))
+  }
+
+  /**
+   * Get a resource from the `src/main/resources` directory. Eclipse does not copy
+   * resources to the output directory, then the class loader cannot find them.
+   */
+  def resourceAsStreamFromSrc(resourcePath: List[String]): Option[java.io.InputStream] = {
+    val classesDir = new File(getClass.getResource(".").toURI)
+    val projectDir = classesDir.getParentFile.getParentFile.getParentFile.getParentFile
+    val resourceFile = subFile(projectDir, ("src" :: "main" :: "resources" :: resourcePath): _*)
+    if (resourceFile.exists)
+      Some(new java.io.FileInputStream(resourceFile))
+    else
+      None
+  }
+}
diff --git a/Scala/patmat/src/main/scala/patmat/Huffman.scala b/Scala/patmat/src/main/scala/patmat/Huffman.scala
new file mode 100644
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+++ b/Scala/patmat/src/main/scala/patmat/Huffman.scala
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+package patmat
+
+import common._
+
+/**
+ * Assignment 4: Huffman coding
+ *
+ */
+object Huffman {
+
+  /**
+   * A huffman code is represented by a binary tree.
+   *
+   * Every `Leaf` node of the tree represents one character of the alphabet that the tree can encode.
+   * The weight of a `Leaf` is the frequency of appearance of the character.
+   *
+   * The branches of the huffman tree, the `Fork` nodes, represent a set containing all the characters
+   * present in the leaves below it. The weight of a `Fork` node is the sum of the weights of these
+   * leaves.
+   */
+  abstract class CodeTree
+  case class Fork(left: CodeTree, right: CodeTree, chars: List[Char], weight: Int) extends CodeTree
+  case class Leaf(char: Char, weight: Int) extends CodeTree
+
+
+
+  // Part 1: Basics
+
+  def weight(tree: CodeTree): Int = ??? // tree match ...
+
+  def chars(tree: CodeTree): List[Char] = ??? // tree match ...
+
+  def makeCodeTree(left: CodeTree, right: CodeTree) =
+    Fork(left, right, chars(left) ::: chars(right), weight(left) + weight(right))
+
+
+
+  // Part 2: Generating Huffman trees
+
+  /**
+   * In this assignment, we are working with lists of characters. This function allows
+   * you to easily create a character list from a given string.
+   */
+  def string2Chars(str: String): List[Char] = str.toList
+
+  /**
+   * This function computes for each unique character in the list `chars` the number of
+   * times it occurs. For example, the invocation
+   *
+   *   times(List('a', 'b', 'a'))
+   *
+   * should return the following (the order of the resulting list is not important):
+   *
+   *   List(('a', 2), ('b', 1))
+   *
+   * The type `List[(Char, Int)]` denotes a list of pairs, where each pair consists of a
+   * character and an integer. Pairs can be constructed easily using parentheses:
+   *
+   *   val pair: (Char, Int) = ('c', 1)
+   *
+   * In order to access the two elements of a pair, you can use the accessors `_1` and `_2`:
+   *
+   *   val theChar = pair._1
+   *   val theInt  = pair._2
+   *
+   * Another way to deconstruct a pair is using pattern matching:
+   *
+   *   pair match {
+   *     case (theChar, theInt) =>
+   *       println("character is: "+ theChar)
+   *       println("integer is  : "+ theInt)
+   *   }
+   */
+  def times(chars: List[Char]): List[(Char, Int)] = ???
+
+  /**
+   * Returns a list of `Leaf` nodes for a given frequency table `freqs`.
+   *
+   * The returned list should be ordered by ascending weights (i.e. the
+   * head of the list should have the smallest weight), where the weight
+   * of a leaf is the frequency of the character.
+   */
+  def makeOrderedLeafList(freqs: List[(Char, Int)]): List[Leaf] = ???
+
+  /**
+   * Checks whether the list `trees` contains only one single code tree.
+   */
+  def singleton(trees: List[CodeTree]): Boolean = ???
+
+  /**
+   * The parameter `trees` of this function is a list of code trees ordered
+   * by ascending weights.
+   *
+   * This function takes the first two elements of the list `trees` and combines
+   * them into a single `Fork` node. This node is then added back into the
+   * remaining elements of `trees` at a position such that the ordering by weights
+   * is preserved.
+   *
+   * If `trees` is a list of less than two elements, that list should be returned
+   * unchanged.
+   */
+  def combine(trees: List[CodeTree]): List[CodeTree] = ???
+
+  /**
+   * This function will be called in the following way:
+   *
+   *   until(singleton, combine)(trees)
+   *
+   * where `trees` is of type `List[CodeTree]`, `singleton` and `combine` refer to
+   * the two functions defined above.
+   *
+   * In such an invocation, `until` should call the two functions until the list of
+   * code trees contains only one single tree, and then return that singleton list.
+   *
+   * Hint: before writing the implementation,
+   *  - start by defining the parameter types such that the above example invocation
+   *    is valid. The parameter types of `until` should match the argument types of
+   *    the example invocation. Also define the return type of the `until` function.
+   *  - try to find sensible parameter names for `xxx`, `yyy` and `zzz`.
+   */
+  def until(xxx: ???, yyy: ???)(zzz: ???): ??? = ???
+
+  /**
+   * This function creates a code tree which is optimal to encode the text `chars`.
+   *
+   * The parameter `chars` is an arbitrary text. This function extracts the character
+   * frequencies from that text and creates a code tree based on them.
+   */
+  def createCodeTree(chars: List[Char]): CodeTree = ???
+
+
+
+  // Part 3: Decoding
+
+  type Bit = Int
+
+  /**
+   * This function decodes the bit sequence `bits` using the code tree `tree` and returns
+   * the resulting list of characters.
+   */
+  def decode(tree: CodeTree, bits: List[Bit]): List[Char] = ???
+
+  /**
+   * A Huffman coding tree for the French language.
+   * Generated from the data given at
+   *   http://fr.wikipedia.org/wiki/Fr%C3%A9quence_d%27apparition_des_lettres_en_fran%C3%A7ais
+   */
+  val frenchCode: CodeTree = Fork(Fork(Fork(Leaf('s',121895),Fork(Leaf('d',56269),Fork(Fork(Fork(Leaf('x',5928),Leaf('j',8351),List('x','j'),14279),Leaf('f',16351),List('x','j','f'),30630),Fork(Fork(Fork(Fork(Leaf('z',2093),Fork(Leaf('k',745),Leaf('w',1747),List('k','w'),2492),List('z','k','w'),4585),Leaf('y',4725),List('z','k','w','y'),9310),Leaf('h',11298),List('z','k','w','y','h'),20608),Leaf('q',20889),List('z','k','w','y','h','q'),41497),List('x','j','f','z','k','w','y','h','q'),72127),List('d','x','j','f','z','k','w','y','h','q'),128396),List('s','d','x','j','f','z','k','w','y','h','q'),250291),Fork(Fork(Leaf('o',82762),Leaf('l',83668),List('o','l'),166430),Fork(Fork(Leaf('m',45521),Leaf('p',46335),List('m','p'),91856),Leaf('u',96785),List('m','p','u'),188641),List('o','l','m','p','u'),355071),List('s','d','x','j','f','z','k','w','y','h','q','o','l','m','p','u'),605362),Fork(Fork(Fork(Leaf('r',100500),Fork(Leaf('c',50003),Fork(Leaf('v',24975),Fork(Leaf('g',13288),Leaf('b',13822),List('g','b'),27110),List('v','g','b'),52085),List('c','v','g','b'),102088),List('r','c','v','g','b'),202588),Fork(Leaf('n',108812),Leaf('t',111103),List('n','t'),219915),List('r','c','v','g','b','n','t'),422503),Fork(Leaf('e',225947),Fork(Leaf('i',115465),Leaf('a',117110),List('i','a'),232575),List('e','i','a'),458522),List('r','c','v','g','b','n','t','e','i','a'),881025),List('s','d','x','j','f','z','k','w','y','h','q','o','l','m','p','u','r','c','v','g','b','n','t','e','i','a'),1486387)
+
+  /**
+   * What does the secret message say? Can you decode it?
+   * For the decoding use the `frenchCode' Huffman tree defined above.
+   */
+  val secret: List[Bit] = List(0,0,1,1,1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0,1,0,1)
+
+  /**
+   * Write a function that returns the decoded secret
+   */
+  def decodedSecret: List[Char] = ???
+
+
+
+  // Part 4a: Encoding using Huffman tree
+
+  /**
+   * This function encodes `text` using the code tree `tree`
+   * into a sequence of bits.
+   */
+  def encode(tree: CodeTree)(text: List[Char]): List[Bit] = ???
+
+
+  // Part 4b: Encoding using code table
+
+  type CodeTable = List[(Char, List[Bit])]
+
+  /**
+   * This function returns the bit sequence that represents the character `char` in
+   * the code table `table`.
+   */
+  def codeBits(table: CodeTable)(char: Char): List[Bit] = ???
+
+  /**
+   * Given a code tree, create a code table which contains, for every character in the
+   * code tree, the sequence of bits representing that character.
+   *
+   * Hint: think of a recursive solution: every sub-tree of the code tree `tree` is itself
+   * a valid code tree that can be represented as a code table. Using the code tables of the
+   * sub-trees, think of how to build the code table for the entire tree.
+   */
+  def convert(tree: CodeTree): CodeTable = ???
+
+  /**
+   * This function takes two code tables and merges them into one. Depending on how you
+   * use it in the `convert` method above, this merge method might also do some transformations
+   * on the two parameter code tables.
+   */
+  def mergeCodeTables(a: CodeTable, b: CodeTable): CodeTable = ???
+
+  /**
+   * This function encodes `text` according to the code tree `tree`.
+   *
+   * To speed up the encoding process, it first converts the code tree to a code table
+   * and then uses it to perform the actual encoding.
+   */
+  def quickEncode(tree: CodeTree)(text: List[Char]): List[Bit] = ???
+}