Huffman

package patmat

import common._
import scala.collection.parallel.RemainsIterator

/**
 * 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 {
    case Leaf(_, n)       => n
    case Fork(_, _, _, w) => w
  }

  def chars(tree: CodeTree): List[Char] = tree match {
    case Leaf(x, _)       => List(x)
    case Fork(_, _, c, _) => c
  }

  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)] = {

    def getPair(list: List[(Char, Int)], char: Char): (Char, Int) = {
      if (list.isEmpty) null
      else if (list.head._1 == char) list.head
      else getPair(list.tail, char)
    }

    def collect(list: List[Char], result: List[(Char, Int)]): List[(Char, Int)] = {
      if (list.isEmpty) result
      else {
        getPair(result, list.head) match {
          case (theChar, theInt) => collect(list.tail, (list.head, theInt + 1) ::
            result.filterNot(p => p._1 == theChar))
          case _ => collect(list.tail, (list.head, 1) :: result)
        }
      }
    }
    collect(chars, List.empty)
  }

  /**
   * 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] = {

    def order(input: List[(Char, Int)], result: List[Leaf]): List[Leaf] = {
      if (input.isEmpty) result.sortWith(_.weight < _.weight)
      else input.head match {
        case (char, weight) => order(input.tail, Leaf(char, weight) :: result)
      }
    }
    order(freqs, List.empty)
  }

  /**
   * Checks whether the list `trees` contains only one single code tree.
   */
  def singleton(trees: List[CodeTree]): Boolean = trees.size == 1

  /**
   * 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] = trees match {
    case left :: right :: cs => (makeCodeTree(left, right) :: cs)
      .sortWith((t1, t2) => weight(t1) < weight(t2))
    case _ => trees
  }

  /**
   * 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(p: List[CodeTree] => Boolean, q: List[CodeTree] => List[CodeTree])(trees: List[CodeTree]): List[CodeTree] =
    if (p(trees)) trees
    else until(p, q)(q(trees))

  /**
   * 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 =
    until(singleton, combine)(makeOrderedLeafList(times(chars))).head

  // 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] =
    {
      //      def traverse(remaining: CodeTree, bits: List[Bit]): List[Char] =
      //        remaining match {
      //          case Leaf(c, _) if (bits.isEmpty) => List(c)
      //          case Leaf(c, _) => c :: traverse(tree, bits)
      //          case Fork(left, right, _, _) if (bits.head == 0) => traverse(left, bits.tail)
      //          case Fork(left, right, _, _) => traverse(right, bits.tail)
      //        }
      //      traverse(tree, bits)
      //    }

      val finalTree = tree

      tree match {

        case Leaf(c, _) if (bits.isEmpty)         => List(c)
        case Leaf(c, _)                           => c :: decode(finalTree, bits)
        case Fork(l, r, _, _) if (bits.head == 0) => decode(l, bits.tail)
        case Fork(l, r, _, _)                     => decode(r, bits.tail)
      }
    }
  /**
   * 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] = decode(frenchCode, secret)

  // 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] = {

    def lookup(tree: CodeTree)(c: Char): List[Bit] = tree match {
      case Leaf(_, _) => List()
      case Fork(left, right, _, _) if chars(left).contains(c) => 0 :: lookup(left)(c)
      case Fork(left, right, _, _) if chars(right).contains(c) => 1 :: lookup(right)(c)
    }
    text flatMap lookup(tree)
  }

  // Part 4b: Encoding using code table

  type CodeTable = List[(Char, List[Bit])]
  type Code = (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] =
    table.filter((code) => code._1 == char).head._2

  /**
   * 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 = tree match {

    case Leaf(c, w)               => List((c, List()))
    case Fork(left, right, cs, w) => mergeCodeTables(convert(left), convert(right))
  }

  /**
   * 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 = {

    def prepend(b: Bit)(code: Code): Code =
      (code._1, b :: code._2)
    a.map(prepend(0)) ::: b.map(prepend(1))
  }

  /**
   * 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] =
    text flatMap codeBits(convert(tree))
}