feat: add LZ77 compression algorithm

[AliAlimohammadi]

Overview

This PR adds an implementation of the LZ77 compression algorithm to the compression module.

What is LZ77?

LZ77 is a lossless data compression algorithm published by Abraham Lempel and Jacob Ziv in 1977. It uses a sliding-window approach to identify repeated patterns and forms the basis for many modern compression formats including:

• DEFLATE (used in gzip, PNG, ZIP)
• LZSS
• LZMA (7-Zip)
• LZW (GIF)

Algorithm Details

LZ77 works by maintaining a sliding window divided into:

• Search buffer: Previously seen data that can be referenced
• Look-ahead buffer: Data currently being encoded

The algorithm encodes data as triplets (tokens):

• Offset: Distance from current position to match start in search buffer
• Length: Number of matching characters
• Indicator: The next character after the match

Implementation Features

✅ Configurable window size and lookahead buffer size
✅ Token-based encoding using (offset, length, indicator) triplets
✅ Comprehensive test coverage (13+ test cases)
✅ Full rustdoc documentation with examples
✅ Zero external dependencies
✅ Efficient implementation with O(n²) worst-case complexity

API

// Create compressor with custom parameters
let compressor = LZ77Compressor::new(window_size, lookahead_buffer_size);

// Compress text to tokens
let compressed: Vec<Token> = compressor.compress("ababcbababaa");

// Decompress tokens back to text
let decompressed: String = compressor.decompress(&compressed);

Code Quality

• ✅ All tests pass (cargo test)
• ✅ Zero clippy warnings (cargo clippy -- -D warnings)
• ✅ Properly formatted (cargo fmt)
• ✅ Comprehensive documentation with examples
• ✅ Follows repository conventions

Files Modified

• src/compression/lz77.rs (new file, ~280 lines)
• src/compression/mod.rs (added module declaration and re-exports)

Testing

The implementation includes extensive tests:

• ✅ Basic compression/decompression
• ✅ Round-trip verification with multiple inputs
• ✅ Edge cases (single character, empty buffers)
• ✅ Error conditions (invalid parameters)
• ✅ All examples from the original Python implementation

Example Usage

use the_algorithms_rust::compression::{LZ77Compressor, Token};

fn main() {
    let compressor = LZ77Compressor::new(13, 6);
    
    // Compress
    let text = "cabracadabrarrarrad";
    let compressed = compressor.compress(text);
    println!("Compressed into {} tokens", compressed.len());
    
    // Decompress
    let decompressed = compressor.decompress(&compressed);
    assert_eq!(text, decompressed);
}

Compression Examples

Input: "ababcbababaa"
Compressed: [(0,0,'a'), (0,0,'b'), (2,2,'c'), (4,3,'a'), (2,2,'a')]

Input: "aacaacabcabaaac"
Compressed: [(0,0,'a'), (1,1,'c'), (3,4,'b'), (3,3,'a'), (1,2,'c')]

Input: "cabracadabrarrarrad"
Compressed: [(0,0,'c'), (0,0,'a'), (0,0,'b'), (0,0,'r'), (3,1,'c'), 
             (2,1,'d'), (7,4,'r'), (3,5,'d')]

References

• Wikipedia: LZ77 and LZ78
• Original paper: Ziv, J.; Lempel, A. (1977). "A Universal Algorithm for Sequential Data Compression"

Checklist

• Code follows project style guidelines
• All tests pass (cargo test)
• Code is properly formatted (cargo fmt)
• No clippy warnings (cargo clippy -- -D warnings)
• Documentation is complete with examples
• Module properly exported in mod.rs
• Algorithm tested with edge cases
• Doctests compile and pass

---

Note: This implementation prioritizes clarity and correctness over raw performance. While the algorithm has O(n²) worst-case complexity, it's suitable for educational purposes and moderate-sized inputs. Production implementations often use hash tables or suffix arrays for optimization.

[AliAlimohammadi]

@siriak, this is ready to be merged.

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.77%. Comparing base (ea93ffd) to head (1033ee6).

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #982      +/-   ##
==========================================
+ Coverage   95.73%   95.77%   +0.03%     
==========================================
  Files         352      353       +1     
  Lines       23166    23363     +197     
==========================================
+ Hits        22179    22375     +196     
- Misses        987      988       +1     

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[siriak]

Please resolve the conflicts

[AliAlimohammadi]

Please resolve the conflicts

Fixed.