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@samklr samklr/Huffm.scala
Created Nov 6, 2012

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Huff
package patmat
import common._
import scala.collection.immutable._
/**
* 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 Fork(_,_,_,w) => w
case Leaf(_,w) => w
}
def chars(tree: CodeTree): List[Char] = tree match {
case Fork(_,_,cs,_) => cs
case Leaf(c,_) => List(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 incr(acc:Map[Char, Int], c:Char) = {
val count = (acc get c).getOrElse(0) + 1
acc + ((c, count))
}
(Map[Char,Int]() /: chars)(incr).iterator.toList
}
/**
* 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] = {
freqs.sortWith((f1,f2) => f1._2 < f2._2).map((f) => Leaf (f._1, f._2))
}
/**
* 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, f: List[CodeTree]=>List[CodeTree])(trees: List[CodeTree]): List[CodeTree] = {
if (p(trees)) trees
else until(p, f)( f(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)
}
/**
* 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, _, _) => 1 :: lookup(right)(c)
}
text flatMap lookup(tree)
}
// Part 4b: Encoding using code table
type Code = (Char, List[Bit])
type CodeTable = List[Code]
/**
* 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))
}
object Main extends App {
import Huffman._
val t1 = Fork(Fork(Leaf('a',2), Leaf('b',3), List('a','b'), 5), Leaf('d',4), List('a','b','d'), 9)
val enc1 = encode(t1)(string2Chars("abd"))
println( enc1 )
println( quickEncode(t1)(string2Chars("abd")) )
println( decodedSecret )
}
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