def get_code_trie(self):
"""
Returns a Trie data structure
from the words in the code
"""
if self.__code_trie == None:
self.__code_trie = Trie(self.code_alphabet)
for word in self.code_words:
self.__code_trie.insert(word)
return self.__code_trie
def is_uniquely_decodable(self):
"""Returns boolean specifying whether or not is uniquely decodable
For the code to be uniquely decodable means that the function
code that takes a string from a the source and codifies it
is inyective.
Returns:
True if the code is uniquely decodable, False otherwise
"""
if self.__uniquely_decodable == None:
self.__C_n = [self.code_words]
trie_0 = Trie(self.code_alphabet, words=self.code_words)
while True:
new_words = set()
trie_n = Trie(self.code_alphabet, words=self.__C_n[-1])
for word_i in self.__C_n[-1]:
for new_word in trie_0.complete_word(word_i):
new_words.add(new_word)
for word_i in self.__C_n[0]:
for new_word in trie_n.complete_word(word_i):
new_words.add(new_word)
if new_words == set() or self.__repeated_C_n():
break
self.__C_n.append(new_words)
self.__C_infty = set()
for i in range(1, len(self.__C_n)):
for word in self.__C_n[i]:
self.__C_infty.add(word)
self.is_uniquely_decodable = len(self.__C_infty
& self.__C_n[0]) == 0
return self.is_uniquely_decodable
class Code:
"""
Core class for Coding and Decoding.
It has integrated core metrics to it.
To create a new Code you need to pass the rule
for the code as a dictionary.
Attributes:
arity:
An integer representing the code arity
code_alphabet:
A set containing the code alphabet
source_alphabet:
A set containing the source alphabet
"""
__code_trie = None
__source_trie = None
__uniquely_decodable = None
def __init__(self, code_dictionary):
""""
Initiates the class using a code dictionary
"""
self.code = validate_dictionary(code_dictionary)
self.code_alphabet = set()
self.source_words = set()
self.code_words = set()
self.source_alphabet = set()
self.__reverse_code = {}
coding_output = ''
source_input = ''
for key, value in self.code.items():
self.source_words.add(key)
coding_output += value
source_input += key
self.code_words.add(value)
self.__reverse_code[value] = key
for simbol in coding_output:
self.code_alphabet.add(simbol)
for simbol in source_input:
self.source_alphabet.add(simbol)
self.arity = len(self.code_alphabet)
if self.is_prefix():
self.__decoder = Encoder(self.code_alphabet, self.__reverse_code)
self.__encoder = Encoder(self.source_alphabet, self.code)
def get_arity(self):
"""Returns arity of the code
Return:
Integer value of the arity
"""
return self.arity
def is_prefix(self):
"""
Uses a Trie data structure to determine
if the code is prefix
Returns:
A boolean True if the code is prefix, False
otherwise
"""
return self.get_code_trie().is_prefix()
@staticmethod
def kraft_inequality_metric(words_length, arity):
"""
Calculates Kraft Inequality for given word lengths
Measures Kraft Inequality Metric defined as
.. math::
\sum_{i} r^{-l_i}
where r means arity, and l sub i the length of
the ith word
Also returns if an instantaneous code can be made with said words
Typical Usage:
.. highlight:: python
.. code-block:: python
>>> metric, can_be_inst = kraft_inequality_metric(words_length=[4,4,3,6],arity=2)
>>> print(metric, can_be_inst)
0.265625 True
Args:
words_length:
An list with the length of the words
arity:
Arity of the code
Returns:
metric , can_be_instantaneous.
Kraft Inequality metric.
A boolean refering to whether or not a code
with this word lenghts and arity exists.
This is dependant on the metric being less than 1
"""
if arity == None:
raise Exception('arity can not be null')
if type(arity) != int:
raise Exception('arity must be an int')
if words_length == None:
raise Exception('words_length can not be null')
metric = 0.0
epsilon = 0.00001
for l in words_length:
metric += float(arity)**float(-l)
return metric, metric - epsilon <= 1
def get_code_trie(self):
"""
Returns a Trie data structure
from the words in the code
"""
if self.__code_trie == None:
self.__code_trie = Trie(self.code_alphabet)
for word in self.code_words:
self.__code_trie.insert(word)
return self.__code_trie
def __repeated_C_n(self):
"""True if C_n has began a cycle, False otherwise"""
if len(self.__C_n) <= 3:
return False
for i in range(1, len(self.__C_n) - 1):
if self.__C_n[-1] == self.__C_n[i] and self.__C_n[
-2] == self.__C_n[i - 1]:
return True
return False
def is_uniquely_decodable(self):
"""Returns boolean specifying whether or not is uniquely decodable
For the code to be uniquely decodable means that the function
code that takes a string from a the source and codifies it
is inyective.
Returns:
True if the code is uniquely decodable, False otherwise
"""
if self.__uniquely_decodable == None:
self.__C_n = [self.code_words]
trie_0 = Trie(self.code_alphabet, words=self.code_words)
while True:
new_words = set()
trie_n = Trie(self.code_alphabet, words=self.__C_n[-1])
for word_i in self.__C_n[-1]:
for new_word in trie_0.complete_word(word_i):
new_words.add(new_word)
for word_i in self.__C_n[0]:
for new_word in trie_n.complete_word(word_i):
new_words.add(new_word)
if new_words == set() or self.__repeated_C_n():
break
self.__C_n.append(new_words)
self.__C_infty = set()
for i in range(1, len(self.__C_n)):
for word in self.__C_n[i]:
self.__C_infty.add(word)
self.is_uniquely_decodable = len(self.__C_infty
& self.__C_n[0]) == 0
return self.is_uniquely_decodable
def get_C_n(self):
"""Returns C_n related to the uniquely decodable algorithm.
Returns:
List of set of words.
"""
self.is_uniquely_decodable()
return self.__C_n
def encode(self, sentence):
""""Encodes a given sentence
"""
return self.__encoder.encode_sentence(sentence)
def __encode_brute_force(self, sentence):
"""Encodes a given sentence using bruteforce
"""
encoding = ''
curr_idx = 0
sentence_length = len(sentence)
while curr_idx < sentence_length:
advance = False
for word in self.source_words:
if re.match('^' + word, sentence[curr_idx:]):
curr_idx += len(word)
encoding += self.code[word]
advance = True
break
if not advance:
raise Exception('No match found to encode {} '.format(
sentence[curr_idx:]))
return encoding
def decode(self, sentence, get_any=True):
"""Decodes a given sentence, in case
multiple outputs are possible it returns
any of them if the get_any flag is True.
Args:
sentence:
Sentence to be decoded. It must compel
with the source alphabet.
get_any:
True by default. It gives a string when
multiple answers are possible. When False
it gives the answer in a set of possible answers.
Returns:
A string with the decoded sentence
"""
if self.is_prefix():
return self.__decoder.encode_sentence(sentence)
result = self.__decode_brute_force(sentence)
if len(result) == 0:
raise Exception('No decoding possible')
if get_any:
return result.pop()
return result
def __decode_brute_force(self, sentence, curr_idx=0):
results = set()
# Base Case
if curr_idx >= len(sentence):
return ['']
for word in self.code_words:
if re.match('^' + word, sentence[curr_idx:]):
for result in self.__decode_brute_force(
sentence,
curr_idx=curr_idx + len(word),
):
results.add(self.__reverse_code[word] + result)
return results
def get_word_length(self, source):
"""Gets the average word lenght of the code
for a given Source
Args:
source:
A source of type Source
Returns:
A float with the value of the word lenght of
the code for the given source.
"""
if type(source) != Source:
raise Exception('source must be of type source')
word_length = 0.0
for word, probability in source.dictionary.items():
if word not in source.dictionary:
raise Exception('{} not part of the code source '.format(word))
word_length += probability * float(len(self.code[word]))
return word_length
@staticmethod
def make_huffman_code(source, code_alphabet={'0', '1'}):
"""Generates an optimal Huffman Code
Args:
source:
A source of type Source
code_alphabet:
Iterable with the alphabet. The items should be
of type str
Returns:
Optimal huffman code for the given source and
with arity of the given code_alphabet
"""
if type(source) != Source:
raise Exception('source must be of type source')
base_nodes = [(probability, word)
for word, probability in source.dictionary.items()]
arity = len(code_alphabet)
if arity != 2:
while len(base_nodes) % (arity - 1) != 1:
base_nodes.append((float(0), ''))
huffman = Huffman_Generator(simbols=code_alphabet,
base_nodes=base_nodes,
arity=len(code_alphabet))
return Code(huffman.make_huffman_code())
def test_complete_word():
simbols = {'0' , '2' , '1'}
t = Trie(simbols, words = {'01','21','0112','212','011'})
assert t.complete_word('01') == {'1','12'}
assert t.complete_word('21') == {'2'}
assert t.complete_word('1') == set()
def test_inserting_and_checking():
simbols = {'0' , '1' , '2'}
t = Trie(simbols)
t.insert('00')
t.insert('101')
t.insert('2')
assert not t.search('0')
assert t.search('00')
assert not t.search('10')
assert t.search('101')
assert t.search('2')
def test_words_init():
simbols = {'0' , '1' , '2'}
t = Trie(simbols, words = ['120','000','101'])
assert t.search('120')
assert not t.search('100')
def test_prefix():
simbols = {'0' , '1' , '2'}
t = Trie(simbols)
t.insert('0')
t.insert('1')
t.insert('20')
t.insert('21')
t.insert('22')
assert t.is_prefix()
t.insert('01')
assert not t.is_prefix()