added coordinate_compression (#9317)

* added coordinate_compression algorithm

* added coordinate_compression & doctest

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DIRECTORY.md

@@ -174,6 +174,7 @@
 
 ## Data Compression
   * [Burrows Wheeler](data_compression/burrows_wheeler.py)
+  * [Coordinate Compression](data_compression/coordinate_compression.py)
   * [Huffman](data_compression/huffman.py)
   * [Lempel Ziv](data_compression/lempel_ziv.py)
   * [Lempel Ziv Decompress](data_compression/lempel_ziv_decompress.py)

data_compression/coordinate_compression.py

@@ -0,0 +1,132 @@
+"""
+Assumption:
+    - The values to compress are assumed to be comparable,
+      values can be sorted and compared with '<' and '>' operators.
+"""
+
+
+class CoordinateCompressor:
+    """
+    A class for coordinate compression.
+
+    This class allows you to compress and decompress a list of values.
+
+    Mapping:
+    In addition to compression and decompression, this class maintains a mapping
+    between original values and their compressed counterparts using two data
+    structures: a dictionary `coordinate_map` and a list `reverse_map`:
+    - `coordinate_map`: A dictionary that maps original values to their compressed
+      coordinates. Keys are original values, and values are compressed coordinates.
+    - `reverse_map`: A list used for reverse mapping, where each index corresponds
+      to a compressed coordinate, and the value at that index is the original value.
+
+    Example of mapping:
+    Original: 10, Compressed: 0
+    Original: 52, Compressed: 1
+    Original: 83, Compressed: 2
+    Original: 100, Compressed: 3
+
+    This mapping allows for efficient compression and decompression of values within
+    the list.
+    """
+
+    def __init__(self, arr: list[int | float | str]) -> None:
+        """
+        Initialize the CoordinateCompressor with a list.
+
+        Args:
+        arr: The list of values to be compressed.
+
+        >>> arr = [100, 10, 52, 83]
+        >>> cc = CoordinateCompressor(arr)
+        >>> cc.compress(100)
+        3
+        >>> cc.compress(52)
+        1
+        >>> cc.decompress(1)
+        52
+        """
+
+        # A dictionary to store compressed coordinates
+        self.coordinate_map: dict[int | float | str, int] = {}
+
+        # A list to store reverse mapping
+        self.reverse_map: list[int | float | str] = [-1] * len(arr)
+
+        self.arr = sorted(arr)  # The input list
+        self.n = len(arr)  # The length of the input list
+        self.compress_coordinates()
+
+    def compress_coordinates(self) -> None:
+        """
+        Compress the coordinates in the input list.
+
+        >>> arr = [100, 10, 52, 83]
+        >>> cc = CoordinateCompressor(arr)
+        >>> cc.coordinate_map[83]
+        2
+        >>> cc.coordinate_map[80]  # Value not in the original list
+        Traceback (most recent call last):
+            ...
+        KeyError: 80
+        >>> cc.reverse_map[2]
+        83
+        """
+        key = 0
+        for val in self.arr:
+            if val not in self.coordinate_map:
+                self.coordinate_map[val] = key
+                self.reverse_map[key] = val
+                key += 1
+
+    def compress(self, original: float | str) -> int:
+        """
+        Compress a single value.
+
+        Args:
+        original: The value to compress.
+
+        Returns:
+        The compressed integer, or -1 if not found in the original list.
+
+        >>> arr = [100, 10, 52, 83]
+        >>> cc = CoordinateCompressor(arr)
+        >>> cc.compress(100)
+        3
+        >>> cc.compress(7)  # Value not in the original list
+        -1
+        """
+        return self.coordinate_map.get(original, -1)
+
+    def decompress(self, num: int) -> int | float | str:
+        """
+        Decompress a single integer.
+
+        Args:
+        num: The compressed integer to decompress.
+
+        Returns:
+        The original value.
+
+        >>> arr = [100, 10, 52, 83]
+        >>> cc = CoordinateCompressor(arr)
+        >>> cc.decompress(0)
+        10
+        >>> cc.decompress(5)  # Compressed coordinate out of range
+        -1
+        """
+        return self.reverse_map[num] if 0 <= num < len(self.reverse_map) else -1
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()
+
+    arr: list[int | float | str] = [100, 10, 52, 83]
+    cc = CoordinateCompressor(arr)
+
+    for original in arr:
+        compressed = cc.compress(original)
+        decompressed = cc.decompress(compressed)
+        print(f"Original: {decompressed}, Compressed: {compressed}")