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Python Dictionaries: A Data Compression Perspective What is a Python Dictionary? A dictionary is a fundamental data structure in Python. It stores data in key-value pairs. Keys must be immutable (e.g., strings, numbers, tuples). Values can be of any data type. Dictionaries are unordered (before Python 3.7) and mutable. Dictionaries and Data Compression Dictionaries facilitate efficient data representation. They can be used to build symbol tables for encoding/decoding in compression algorithms. Representing frequent data with shorter keys saves space. Key-value pairs can map original data to compressed representations. Example: Huffman Coding with Dictionaries Create a dictionary mapping characters to their Huffman codes. { 'A': '00', 'B': '01', 'C': '10', 'D': '11'} Use this dictionary to encode a string. Decode using the same dictionary, reversing the mapping. Example: Run-Length Encoding (R...

Data Compression: Mastering Type Conversion in Python What is Type Conversion? Type conversion, also known as type casting, is the process of changing a variable's data type from one to another. Python supports both implicit (automatic) and explicit (manual) type conversion. Implicit Type Conversion Python automatically converts data types in certain situations to prevent errors. Example: Adding an integer to a float results in a float. Explicit Type Conversion We use built-in functions like `int()`, `float()`, `str()`, `bool()` etc. to explicitly change data types. Example: Converting a string "10" to an integer using `int("10")`. Example: Data Compression Context Imagine you're storing compressed file sizes (originally floats) in a database designed for integers. Explicit type conversion (using `int()`) would truncate the decimal part, losing precision but saving space. This is a type of lossy compression. Converting from a larger data ...

Understanding Local and Global Variables in Python: A Data Compression Perspective What are Local Variables? Local variables are declared inside a function. Their scope is limited to that function. They are created when the function is called and destroyed when the function exits. This localized nature can be relevant in optimizing data structures within a function, aiding compression strategies. Improper use can lead to unnecessary data duplication if not handled carefully in recursive functions or complex data structures. What are Global Variables? Global variables are declared outside any function. Their scope extends throughout the entire program. They are accessible from any function within the program. Overuse can negatively impact data compression efforts by increasing memory usage unnecessarily, especially in large applications. Careful management is crucial for maintaining modularity and data integrity in complex systems, a key factor in efficient compress...

Decoding the Magic of LZW Compression: A Data Compression Deep Dive What is LZW Compression? Lempel-Ziv-Welch (LZW) is a lossless data compression algorithm. It works by replacing repeating sequences of data with shorter codes. It's widely used in GIF image format and other applications. Highly effective for data with repeating patterns. How LZW Compression Works: A Step-by-Step Guide Starts with a dictionary containing single characters. Reads the input data character by character. Concatenates characters to form strings. When a string is not found, it's added to the dictionary with a new code. The code for the longest matching string is written to the output. This process continues until the entire input is processed. LZW Compression Example: Initial Dictionary: {'A': 1, 'B': 2, 'C': 3} Input String: "ABABCABABCACC" Processing: - 'A' is encoded as 1. - 'AB' is encoded as 4 (added to dictio...

Decoding the Mystery of Golomb Codes: A Data Compression Deep Dive What is Golomb Coding? A unary code combined with a fixed-length code. Used for compressing data where small integers are more frequent than large ones. Ideal for data with geometric distributions. Parameter 'm' determines the code's structure. How Golomb Code Works Divides the input integer 'n' by 'm' (the code parameter). Represents the quotient using unary coding. Represents the remainder using a fixed-length binary code (length log₂m). Example: Golomb Code with m = 3 Let's encode the integer 7. Divide 7 by 3: 7 ÷ 3 = 2 remainder 1. Quotient (2) in unary: 110. Remainder (1) in binary (log₂3 ≈ 2, so we'll use 2 bits): 01. Complete Golomb code for 7 (with m=3): 11001. Decoding Golomb Codes Read the unary part to obtain the quotient. Read the fixed-length binary part to obtain the remainder. Calculate: (quotient * m) + remainder. Golomb Code Advantages Effic...

Decoding Arithmetic Codes: A Step-by-Step Guide Understanding the Input Encoded data: The arithmetic code tag (a single floating-point number). Probability model: The probability distribution of symbols used during encoding. This is crucial for decoding. Must be identical to the encoder's model. Symbol alphabet: The set of all possible symbols. Decoding Algorithm Initialize lower bound (L) to 0.0 and upper bound (U) to 1.0. Obtain the encoded value. Iterate through the following steps until a symbol is decoded: * Calculate the range size (U - L). * For each symbol in the alphabet: * Calculate the cumulative probability (C) up to that symbol. * If the encoded value falls within the interval [L + C * range size, L + (C + P) * range size), where P is the symbol probability, then decode the symbol. * Update the lower and upper bounds: * L = L + C * range size * U = L + (C + P) * range size Repeat step 3 until the entire enc...