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Added Burrows-Wheeler transform algorithm. (#1029)
* Added doctest and more explanation about Dijkstra execution. * tests were not passing with python2 due to missing __init__.py file at number_theory folder * Removed the dot at the beginning of the imported modules names because 'python3 -m doctest -v data_structures/hashing/*.py' and 'python3 -m doctest -v data_structures/stacks/*.py' were failing not finding hash_table.py and stack.py modules. * Moved global code to main scope and added doctest for project euler problems 1 to 14. * Added test case for negative input. * Changed N variable to do not use end of line scape because in case there is a space after it the script will break making it much more error prone. * Added problems description and doctests to the ones that were missing. Limited line length to 79 and executed python black over all scripts. * Changed the way files are loaded to support pytest call. * Added __init__.py to problems to make them modules and allow pytest execution. * Added project_euler folder to test units execution * Changed 'os.path.split(os.path.realpath(__file__))' to 'os.path.dirname()' * Added Burrows-Wheeler transform algorithm. * Added changes suggested by cclauss
This commit is contained in:
Bruno Simas Hadlich
cclauss
parent
f64b602938
commit
e662a5aaef
176
compression/burrows_wheeler.py
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176
compression/burrows_wheeler.py
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"""
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https://en.wikipedia.org/wiki/Burrows%E2%80%93Wheeler_transform
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The Burrows–Wheeler transform (BWT, also called block-sorting compression)
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rearranges a character string into runs of similar characters. This is useful
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for compression, since it tends to be easy to compress a string that has runs
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of repeated characters by techniques such as move-to-front transform and
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run-length encoding. More importantly, the transformation is reversible,
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without needing to store any additional data except the position of the first
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original character. The BWT is thus a "free" method of improving the efficiency
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of text compression algorithms, costing only some extra computation.
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"""
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from typing import List, Dict
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def all_rotations(s: str) -> List[str]:
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"""
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:param s: The string that will be rotated len(s) times.
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:return: A list with the rotations.
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:raises TypeError: If s is not an instance of str.
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Examples:
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>>> all_rotations("^BANANA|") # doctest: +NORMALIZE_WHITESPACE
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['^BANANA|', 'BANANA|^', 'ANANA|^B', 'NANA|^BA', 'ANA|^BAN', 'NA|^BANA',
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'A|^BANAN', '|^BANANA']
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>>> all_rotations("a_asa_da_casa") # doctest: +NORMALIZE_WHITESPACE
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['a_asa_da_casa', '_asa_da_casaa', 'asa_da_casaa_', 'sa_da_casaa_a',
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'a_da_casaa_as', '_da_casaa_asa', 'da_casaa_asa_', 'a_casaa_asa_d',
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'_casaa_asa_da', 'casaa_asa_da_', 'asaa_asa_da_c', 'saa_asa_da_ca',
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'aa_asa_da_cas']
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>>> all_rotations("panamabanana") # doctest: +NORMALIZE_WHITESPACE
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['panamabanana', 'anamabananap', 'namabananapa', 'amabananapan',
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'mabananapana', 'abananapanam', 'bananapanama', 'ananapanamab',
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'nanapanamaba', 'anapanamaban', 'napanamabana', 'apanamabanan']
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>>> all_rotations(5)
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Traceback (most recent call last):
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...
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TypeError: The parameter s type must be str.
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"""
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if not isinstance(s, str):
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raise TypeError("The parameter s type must be str.")
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return [s[i:] + s[:i] for i in range(len(s))]
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def bwt_transform(s: str) -> Dict:
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"""
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:param s: The string that will be used at bwt algorithm
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:return: the string composed of the last char of each row of the ordered
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rotations and the index of the original string at ordered rotations list
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:raises TypeError: If the s parameter type is not str
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:raises ValueError: If the s parameter is empty
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Examples:
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>>> bwt_transform("^BANANA")
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{'bwt_string': 'BNN^AAA', 'idx_original_string': 6}
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>>> bwt_transform("a_asa_da_casa")
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{'bwt_string': 'aaaadss_c__aa', 'idx_original_string': 3}
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>>> bwt_transform("panamabanana")
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{'bwt_string': 'mnpbnnaaaaaa', 'idx_original_string': 11}
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>>> bwt_transform(4)
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Traceback (most recent call last):
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...
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TypeError: The parameter s type must be str.
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>>> bwt_transform('')
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Traceback (most recent call last):
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...
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ValueError: The parameter s must not be empty.
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"""
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if not isinstance(s, str):
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raise TypeError("The parameter s type must be str.")
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if not s:
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raise ValueError("The parameter s must not be empty.")
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rotations = all_rotations(s)
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rotations.sort() # sort the list of rotations in alphabetically order
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# make a string composed of the last char of each rotation
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return {
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"bwt_string": "".join([word[-1] for word in rotations]),
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"idx_original_string": rotations.index(s),
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}
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def reverse_bwt(bwt_string: str, idx_original_string: int) -> str:
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"""
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:param bwt_string: The string returned from bwt algorithm execution
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:param idx_original_string: A 0-based index of the string that was used to
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generate bwt_string at ordered rotations list
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:return: The string used to generate bwt_string when bwt was executed
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:raises TypeError: If the bwt_string parameter type is not str
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:raises ValueError: If the bwt_string parameter is empty
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:raises TypeError: If the idx_original_string type is not int or if not
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possible to cast it to int
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:raises ValueError: If the idx_original_string value is lower than 0 or
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greater than len(bwt_string) - 1
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>>> reverse_bwt("BNN^AAA", 6)
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'^BANANA'
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>>> reverse_bwt("aaaadss_c__aa", 3)
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'a_asa_da_casa'
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>>> reverse_bwt("mnpbnnaaaaaa", 11)
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'panamabanana'
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>>> reverse_bwt(4, 11)
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Traceback (most recent call last):
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...
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TypeError: The parameter bwt_string type must be str.
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>>> reverse_bwt("", 11)
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Traceback (most recent call last):
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...
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ValueError: The parameter bwt_string must not be empty.
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>>> reverse_bwt("mnpbnnaaaaaa", "asd") # doctest: +NORMALIZE_WHITESPACE
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Traceback (most recent call last):
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...
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TypeError: The parameter idx_original_string type must be int or passive
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of cast to int.
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>>> reverse_bwt("mnpbnnaaaaaa", -1)
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Traceback (most recent call last):
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...
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ValueError: The parameter idx_original_string must not be lower than 0.
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>>> reverse_bwt("mnpbnnaaaaaa", 12) # doctest: +NORMALIZE_WHITESPACE
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Traceback (most recent call last):
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...
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ValueError: The parameter idx_original_string must be lower than
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len(bwt_string).
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>>> reverse_bwt("mnpbnnaaaaaa", 11.0)
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'panamabanana'
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>>> reverse_bwt("mnpbnnaaaaaa", 11.4)
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'panamabanana'
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"""
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if not isinstance(bwt_string, str):
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raise TypeError("The parameter bwt_string type must be str.")
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if not bwt_string:
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raise ValueError("The parameter bwt_string must not be empty.")
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try:
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idx_original_string = int(idx_original_string)
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except ValueError:
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raise TypeError(
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(
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"The parameter idx_original_string type must be int or passive"
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" of cast to int."
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)
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)
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if idx_original_string < 0:
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raise ValueError(
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"The parameter idx_original_string must not be lower than 0."
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)
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if idx_original_string >= len(bwt_string):
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raise ValueError(
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(
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"The parameter idx_original_string must be lower than"
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" len(bwt_string)."
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)
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)
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ordered_rotations = [""] * len(bwt_string)
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for x in range(len(bwt_string)):
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for i in range(len(bwt_string)):
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ordered_rotations[i] = bwt_string[i] + ordered_rotations[i]
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ordered_rotations.sort()
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return ordered_rotations[idx_original_string]
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if __name__ == "__main__":
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entry_msg = "Provide a string that I will generate its BWT transform: "
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s = input(entry_msg).strip()
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result = bwt_transform(s)
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bwt_output_msg = "Burrows Wheeler tranform for string '{}' results in '{}'"
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print(bwt_output_msg.format(s, result["bwt_string"]))
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original_string = reverse_bwt(
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result["bwt_string"], result["idx_original_string"]
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)
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fmt = (
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"Reversing Burrows Wheeler tranform for entry '{}' we get original"
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" string '{}'"
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)
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print(fmt.format(result["bwt_string"], original_string))
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