Add Burrows-Wheeler Transform algorithm

[AliAlimohammadi]

Description

Adds an implementation of the Burrows-Wheeler Transform (BWT), a block-sorting compression algorithm that rearranges strings into runs of similar characters.

The BWT is particularly useful for compression as it:

• Groups similar characters together (making run-length encoding more effective)
• Is completely reversible without storing additional data (except the index)
• Serves as preprocessing for compression algorithms like bzip2

Example

For the string "^BANANA":

• BWT produces: "BNN^AAA" with index 6
• Notice how the A's are grouped together, making it easier to compress
• The transform is fully reversible: reverse_bwt("BNN^AAA", 6) → "^BANANA"

Algorithm Overview

Forward Transform (bwt_transform):

1. Generate all rotations of the input string
2. Sort the rotations lexicographically
3. Take the last character of each sorted rotation to form the BWT string
4. Record the position of the original string in the sorted list

Reverse Transform (reverse_bwt):

1. Start with an empty table of strings
2. Iteratively prepend BWT characters and sort
3. After n iterations (where n is the string length), extract the original string at the recorded index

Time Complexity:

• Forward: O(n² log n) where n is string length
• Reverse: O(n² log n)

Space Complexity: O(n²)

Changes Made

• Added src/compression/burrows_wheeler_transform.rs
• Added module declaration and export in src/compression/mod.rs
• Includes BwtResult struct for returning transform results
• Three public functions:
  • all_rotations - generates all rotations of a string
  • bwt_transform - performs the BWT
  • reverse_bwt - reverses the BWT

Testing

All tests pass:

cargo test burrows_wheeler_transform

Test coverage includes:

• ✅ Multiple example strings (BANANA, panamabanana, etc.)
• ✅ Roundtrip tests (transform → reverse → original)
• ✅ Edge cases (single character, repeated characters)
• ✅ Error handling (empty strings, invalid indices)
• ✅ All examples from the Python implementation

Real-World Usage

The BWT is used in:

• bzip2 compression algorithm
• Bioinformatics for DNA sequence alignment (FM-index)
• Data compression as preprocessing step

References

• Burrows-Wheeler Transform - Wikipedia
• Original 1994 Paper

Checklist

• Code follows repository style guidelines
• All tests pass
• Documentation includes examples
• Functions are publicly exported
• No compiler warnings
• Roundtrip property verified in tests

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.75%. Comparing base (b6a0787) to head (872f574).

Additional details and impacted files

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+ Coverage   95.73%   95.75%   +0.02%     
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  Files         349      350       +1     
  Lines       22774    22892     +118     
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+ Hits        21802    21921     +119     
+ Misses        972      971       -1     

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[AliAlimohammadi]

@siriak, this is ready to be merged. Clippy error is a CI issue. No problem on other machines.

[Copilot]

Pull request overview

This PR adds an implementation of the Burrows-Wheeler Transform (BWT) algorithm, a block-sorting compression technique that rearranges strings into runs of similar characters to improve compressibility. The implementation includes both forward and reverse transforms with comprehensive test coverage.

Key changes:

• Implements the BWT algorithm with forward transform (bwt_transform) and reverse transform (reverse_bwt)
• Provides a utility function (all_rotations) to generate all rotations of a string
• Includes comprehensive tests for various input strings and edge cases

Reviewed changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated 6 comments.

File	Description
src/compression/burrows_wheeler_transform.rs	New file implementing the BWT algorithm with forward/reverse transforms, a BwtResult struct, and helper functions with comprehensive tests
src/compression/mod.rs	Adds module declaration and exports for the new BWT implementation
DIRECTORY.md	Adds documentation link for the new Burrows-Wheeler Transform algorithm in alphabetical order

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[siriak]

Looks good, thanks!