Add LZ77 compression algorithm (#8059)

* - add "lz77_compressor" class with compress and decompress methods using LZ77 compression algorithm

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* - use "list" instead "List", formatting

* - fix spelling

* - add Python type hints

* - add 'Token' class to represent triplet (offset, length, indicator)

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* - add test, hange type rom List to list

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* - remove extra import

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* - better test

* - edit comments

* - add return types

* - add tests for __str__ and __repr__

* Update lz77.py

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Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <[email protected]>

Author: 3 people

Diff for: compression/lz77.py

@@ -0,0 +1,227 @@
+"""
+LZ77 compression algorithm
+- lossless data compression published in papers by Abraham Lempel and Jacob Ziv in 1977
+- also known as LZ1 or sliding-window compression
+- form the basis for many variations including LZW, LZSS, LZMA and others
+
+It uses a “sliding window” method. Within the sliding window we have:
+  - search buffer
+  - look ahead buffer
+len(sliding_window) = len(search_buffer) + len(look_ahead_buffer)
+
+LZ77 manages a dictionary that uses triples composed of:
+    - Offset into search buffer, it's the distance between the start of a phrase and
+      the beginning of a file.
+    - Length of the match, it's the number of characters that make up a phrase.
+    - The indicator is represented by a character that is going to be encoded next.
+
+As a file is parsed, the dictionary is dynamically updated to reflect the compressed
+data contents and size.
+
+Examples:
+"cabracadabrarrarrad" <-> [(0, 0, 'c'), (0, 0, 'a'), (0, 0, 'b'), (0, 0, 'r'),
+                           (3, 1, 'c'), (2, 1, 'd'), (7, 4, 'r'), (3, 5, 'd')]
+"ababcbababaa" <-> [(0, 0, 'a'), (0, 0, 'b'), (2, 2, 'c'), (4, 3, 'a'), (2, 2, 'a')]
+"aacaacabcabaaac" <-> [(0, 0, 'a'), (1, 1, 'c'), (3, 4, 'b'), (3, 3, 'a'), (1, 2, 'c')]
+
+Sources:
+en.wikipedia.org/wiki/LZ77_and_LZ78
+"""
+
+
+from dataclasses import dataclass
+
+__version__ = "0.1"
+__author__ = "Lucia Harcekova"
+
+
+@dataclass
+class Token:
+    """
+    Dataclass representing triplet called token consisting of length, offset
+    and indicator. This triplet is used during LZ77 compression.
+    """
+
+    offset: int
+    length: int
+    indicator: str
+
+    def __repr__(self) -> str:
+        """
+        >>> token = Token(1, 2, "c")
+        >>> repr(token)
+        '(1, 2, c)'
+        >>> str(token)
+        '(1, 2, c)'
+        """
+        return f"({self.offset}, {self.length}, {self.indicator})"
+
+
+class LZ77Compressor:
+    """
+    Class containing compress and decompress methods using LZ77 compression algorithm.
+    """
+
+    def __init__(self, window_size: int = 13, lookahead_buffer_size: int = 6) -> None:
+        self.window_size = window_size
+        self.lookahead_buffer_size = lookahead_buffer_size
+        self.search_buffer_size = self.window_size - self.lookahead_buffer_size
+
+    def compress(self, text: str) -> list[Token]:
+        """
+        Compress the given string text using LZ77 compression algorithm.
+
+        Args:
+            text: string to be compressed
+
+        Returns:
+            output: the compressed text as a list of Tokens
+
+        >>> lz77_compressor = LZ77Compressor()
+        >>> str(lz77_compressor.compress("ababcbababaa"))
+        '[(0, 0, a), (0, 0, b), (2, 2, c), (4, 3, a), (2, 2, a)]'
+        >>> str(lz77_compressor.compress("aacaacabcabaaac"))
+        '[(0, 0, a), (1, 1, c), (3, 4, b), (3, 3, a), (1, 2, c)]'
+        """
+
+        output = []
+        search_buffer = ""
+
+        # while there are still characters in text to compress
+        while text:
+
+            # find the next encoding phrase
+            # - triplet with offset, length, indicator (the next encoding character)
+            token = self._find_encoding_token(text, search_buffer)
+
+            # update the search buffer:
+            # - add new characters from text into it
+            # - check if size exceed the max search buffer size, if so, drop the
+            #   oldest elements
+            search_buffer += text[: token.length + 1]
+            if len(search_buffer) > self.search_buffer_size:
+                search_buffer = search_buffer[-self.search_buffer_size :]
+
+            # update the text
+            text = text[token.length + 1 :]
+
+            # append the token to output
+            output.append(token)
+
+        return output
+
+    def decompress(self, tokens: list[Token]) -> str:
+        """
+        Convert the list of tokens into an output string.
+
+        Args:
+            tokens: list containing triplets (offset, length, char)
+
+        Returns:
+            output: decompressed text
+
+        Tests:
+            >>> lz77_compressor = LZ77Compressor()
+            >>> lz77_compressor.decompress([Token(0, 0, 'c'), Token(0, 0, 'a'),
+            ... Token(0, 0, 'b'), Token(0, 0, 'r'), Token(3, 1, 'c'),
+            ... Token(2, 1, 'd'), Token(7, 4, 'r'), Token(3, 5, 'd')])
+            'cabracadabrarrarrad'
+            >>> lz77_compressor.decompress([Token(0, 0, 'a'), Token(0, 0, 'b'),
+            ... Token(2, 2, 'c'), Token(4, 3, 'a'), Token(2, 2, 'a')])
+            'ababcbababaa'
+            >>> lz77_compressor.decompress([Token(0, 0, 'a'), Token(1, 1, 'c'),
+            ... Token(3, 4, 'b'), Token(3, 3, 'a'), Token(1, 2, 'c')])
+            'aacaacabcabaaac'
+        """
+
+        output = ""
+
+        for token in tokens:
+            for _ in range(token.length):
+                output += output[-token.offset]
+            output += token.indicator
+
+        return output
+
+    def _find_encoding_token(self, text: str, search_buffer: str) -> Token:
+        """Finds the encoding token for the first character in the text.
+
+        Tests:
+            >>> lz77_compressor = LZ77Compressor()
+            >>> lz77_compressor._find_encoding_token("abrarrarrad", "abracad").offset
+            7
+            >>> lz77_compressor._find_encoding_token("adabrarrarrad", "cabrac").length
+            1
+            >>> lz77_compressor._find_encoding_token("abc", "xyz").offset
+            0
+            >>> lz77_compressor._find_encoding_token("", "xyz").offset
+            Traceback (most recent call last):
+                ...
+            ValueError: We need some text to work with.
+            >>> lz77_compressor._find_encoding_token("abc", "").offset
+            0
+        """
+
+        if not text:
+            raise ValueError("We need some text to work with.")
+
+        # Initialise result parameters to default values
+        length, offset = 0, 0
+
+        if not search_buffer:
+            return Token(offset, length, text[length])
+
+        for i, character in enumerate(search_buffer):
+            found_offset = len(search_buffer) - i
+            if character == text[0]:
+                found_length = self._match_length_from_index(text, search_buffer, 0, i)
+                # if the found length is bigger than the current or if it's equal,
+                # which means it's offset is smaller: update offset and length
+                if found_length >= length:
+                    offset, length = found_offset, found_length
+
+        return Token(offset, length, text[length])
+
+    def _match_length_from_index(
+        self, text: str, window: str, text_index: int, window_index: int
+    ) -> int:
+        """Calculate the longest possible match of text and window characters from
+        text_index in text and window_index in window.
+
+        Args:
+            text: _description_
+            window: sliding window
+            text_index: index of character in text
+            window_index: index of character in sliding window
+
+        Returns:
+            The maximum match between text and window, from given indexes.
+
+        Tests:
+            >>> lz77_compressor = LZ77Compressor(13, 6)
+            >>> lz77_compressor._match_length_from_index("rarrad", "adabrar", 0, 4)
+            5
+            >>> lz77_compressor._match_length_from_index("adabrarrarrad",
+            ...     "cabrac", 0, 1)
+            1
+        """
+        if not text or text[text_index] != window[window_index]:
+            return 0
+        return 1 + self._match_length_from_index(
+            text, window + text[text_index], text_index + 1, window_index + 1
+        )
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()
+    # Initialize compressor class
+    lz77_compressor = LZ77Compressor(window_size=13, lookahead_buffer_size=6)
+
+    # Example
+    TEXT = "cabracadabrarrarrad"
+    compressed_text = lz77_compressor.compress(TEXT)
+    print(lz77_compressor.compress("ababcbababaa"))
+    decompressed_text = lz77_compressor.decompress(compressed_text)
+    assert decompressed_text == TEXT, "The LZ77 algorithm returned the invalid result."