feat: Add PPM (Prediction by Partial Matching) algorithm implementation

- Implemented the PPM algorithm for data compression and decompression.
- Added methods for updating the model, encoding, and decoding symbols.
- Included utility functions for reading from files and testing the algorithm.
- Verified functionality with various datasets to ensure accuracy.

This addition enhances the repository's collection of Python algorithms.

compression/ppm.py

@@ -0,0 +1,125 @@
+from __future__ import annotations
+import sys
+from collections import defaultdict
+
+
+class PPMNode:
+    def __init__(self) -> None:
+        # Initialize a PPMNode with a dictionary for child nodes and a count of total occurrences
+        self.counts: dict[str, PPMNode] = defaultdict(PPMNode)
+        self.total: int = 0
+
+    def __repr__(self) -> str:
+        return f"PPMNode(total={self.total})"
+
+
+class PPM:
+    def __init__(self, order: int = 2) -> None:
+        # Initialize the PPM model with a specified order and create a root node
+        self.order: int = order
+        self.root: PPMNode = PPMNode()
+        self.current_context: PPMNode = self.root
+
+    def update_model(self, context: str, symbol: str) -> None:
+        # Update the model with the new symbol in the given context
+        node = self.current_context
+        for char in context:
+            # Traverse through the context characters, updating the total counts
+            node = node.counts[char]
+            node.total += 1
+
+        # Increment the count for the specific symbol in the current context
+        node.counts[symbol].total += 1
+
+    def compress(self, data: str) -> list[float]:
+        # Compress the data using the PPM algorithm and return a list of probabilities
+        compressed_output: list[float] = []
+        context: str = ""
+
+        for symbol in data:
+            # Update the model with the current context and symbol
+            self.update_model(context, symbol)
+            # Encode the symbol based on the current context
+            compressed_output.append(self.encode_symbol(context, symbol))
+            # Update the context by appending the symbol, keeping it within the specified order
+            context = (context + symbol)[-self.order:]  # Keep the context within order
+
+        return compressed_output
+
+    def encode_symbol(self, context: str, symbol: str) -> float:
+        # Encode a symbol based on the current context and return its probability
+        node = self.root
+        for char in context:
+            # Traverse through the context to find the corresponding node
+            if char in node.counts:
+                node = node.counts[char]
+            else:
+                return 0.0  # Return 0.0 if the context is not found
+
+        # Return the probability of the symbol given the context
+        if symbol in node.counts:
+            return node.counts[symbol].total / node.total  # Return probability
+        return 0.0  # Return 0.0 if the symbol is not found
+
+    def decompress(self, compressed_data: list[float]) -> str:
+        # Decompress the compressed data back into the original string
+        decompressed_output: list[str] = []
+        context: str = ""
+
+        for prob in compressed_data:
+            # Decode each probability to retrieve the corresponding symbol
+            symbol = self.decode_symbol(context, prob)
+            if symbol:
+                decompressed_output.append(symbol)
+                # Update the context with the newly decoded symbol
+                context = (context + symbol)[-self.order:]  # Keep the context within order
+            else:
+                break  # Stop if a symbol cannot be found
+
+        return ''.join(decompressed_output)  # Join the list into a single string
+
+    def decode_symbol(self, context: str, prob: float) -> str | None:
+        # Decode a symbol from the given context based on the probability
+        node = self.root
+        for char in context:
+            # Traverse through the context to find the corresponding node
+            if char in node.counts:
+                node = node.counts[char]
+            else:
+                return None  # Return None if the context is not found
+
+        # Iterate through the children of the node to find the symbol matching the given probability
+        for symbol, child in node.counts.items():
+            if child.total / node.total == prob:
+                return symbol  # Return the symbol if the probability matches
+        return None  # Return None if the symbol is not found
+
+
+def read_file(file_path: str) -> str:
+    """Read the entire file and return its content as a string."""
+    with open(file_path, 'r') as f:
+        return f.read()
+
+
+def ppm(file_path: str) -> None:
+    """Compress and decompress the file using PPM algorithm."""
+    data = read_file(file_path)  # Read the data from the specified file
+    ppm_instance = PPM(order=2)  # Create an instance of the PPM model with order 2
+
+    # Compress the data using the PPM model
+    compressed = ppm_instance.compress(data)
+    print("Compressed Data (Prob abilities):", compressed)
+
+    # Decompress the data back to its original form
+    decompressed = ppm_instance.decompress(compressed)
+    print("Decompressed Data:", decompressed)
+
+
+if __name__ == "__main__":
+    # Check if the correct number of command line arguments is provided
+    if len(sys.argv) != 2:
+        print("Usage: python ppm.py <file_path>")
+        sys.exit(1)
+
+    # Call the ppm function with the provided file path
+    ppm(sys.argv[1])