feat(math): add two negabinary numbers

[BrianLusina]

Describe your change:

Add two negabinary numbers

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Documentation change?

Checklist:

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized.
• I know that pull requests will not be merged if they fail the automated tests.
• This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• All new Python files are placed inside an existing directory.
• All filenames are in all lowercase characters with no spaces or dashes.
• All functions and variable names follow Python naming conventions.
• All function parameters and return values are annotated with Python type hints.
• All functions have doctests that pass the automated testing.
• All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
• If this pull request resolves one or more open issues then the commit message contains Fixes: #{$ISSUE_NO}.

Summary by CodeRabbit

Release Notes

• New Features

  • Added support for solving negabinary (base −2) number addition problems with alternative implementations.

• Documentation

  • Expanded repository index with multiple new algorithm and data-structure problem categories including Dynamic Programming, graphs, hash tables, and matrices.
  • Added comprehensive documentation with examples for new problems.

• Tests

  • Introduced parameterised unit tests for new functionality.

[coderabbitai]

📝 Walkthrough

Walkthrough

Adds a new pymath/adding_two_negabinary_numbers module with two implementations of negabinary (base -2) addition (add_negabinary and add_negabinary_2), a problem README, and parameterised unit tests. Updates DIRECTORY.md to add index entries across multiple categories and remove three misclassified entries.

Changes

Negabinary Addition Module

Layer / File(s)	Summary
Negabinary addition implementations and README pymath/adding_two_negabinary_numbers/__init__.py, pymath/adding_two_negabinary_numbers/README.md	Two public functions added: add_negabinary uses dual-index iteration with explicit carry rewrite rules, and add_negabinary_2 reverses inputs and normalises via modulo arithmetic. README documents the problem, three examples, constraints, and topic tags.
Parameterised unit tests pymath/adding_two_negabinary_numbers/test_add_two_negabinary_numbers.py	AddTwoNegabinaryNumbersTestCase defines shared test data and two parameterised test methods, one for each implementation, asserting equality against expected outputs.

Directory Index Corrections and Additions

Layer / File(s)

Summary

Directory index additions, removals, and reclassifications DIRECTORY.md

Adds entries for Cherry Pickup, Number Of Connected Components, Custom Sort String, Game Of Life, Frequency Of The Most Frequent Element, Russian Doll Envelopes, Replace Words (Trie), Issubsequence, Acounts Merge, Sum Of All Subset Xor Totals, Nested Iterator, Sparse Vector, Adding Two Negabinary Numbers, and a Utils test link. Removes three misclassified entries (Puzzles/Arrays Maxlen Contiguous Binary Subarray, Pystrings Is Subsequence test link, Tests/Puzzles Replace Words test link).

Estimated code review effort

🎯 2 (Simple) | ⏱️ ~10 minutes

Suggested labels

enhancement, Documentation

Poem

🐇 In base minus two, I carry and flip,
Each negabinary bit makes a trip.
Two approaches to sum what seems quite arcane,
With tests to confirm it's not all in vain.
The directory grows, all tidy and neat —
This rabbit's proud work is now complete! ✨

🚥 Pre-merge checks | ✅ 4 | ❌ 1

❌ Failed checks (1 inconclusive)

Check name	Status	Explanation	Resolution
Description check	❓ Inconclusive	The description covers the main change and includes all critical checklist items completed, though it marks multiple unrelated checkboxes as completed.	Clarify the description by only checking boxes that genuinely apply (only the first checkbox about adding an algorithm should be marked). Review whether doctests are actually present in the implementation.

✅ Passed checks (4 passed)

Check name	Status	Explanation
Title check	✅ Passed	The title clearly and concisely describes the main feature addition: implementing an algorithm to add two negabinary numbers.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.
Linked Issues check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check	✅ Passed	Check skipped because no linked issues were found for this pull request.

_{✏️ Tip: You can configure your own custom pre-merge checks in the settings.}

✨ Finishing Touches

📝 Generate docstrings

• Create stacked PR
• Commit on current branch

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Commit unit tests in branch feat/math-add-two-negabinary-numbers

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[coderabbitai]

Actionable comments posted: 1

🤖 Prompt for all review comments with AI agents

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

Inline comments:
In `@pymath/adding_two_negabinary_numbers/README.md`:
- Around line 5-7: The README.md file in the
pymath/adding_two_negabinary_numbers directory has grammar and punctuation
issues in lines 5-7 that create ambiguity in the input format description. Fix
the redundant and awkwardly-phrased "format:  as an array" construct on line 5
by removing the colon and extra space, and correct the confusing "array, format"
phrase on line 7 by removing the comma. The sentences should flow more naturally
while clearly describing that the input numbers are provided as arrays of 0s and
1s from most significant to least significant bit.

🪄 Autofix (Beta)

Fix all unresolved CodeRabbit comments on this PR:

• Push a commit to this branch (recommended)
• Create a new PR with the fixes

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ℹ️ Review info

⚙️ Run configuration

Configuration used: Organization UI

Review profile: CHILL

Plan: Pro

Run ID: 1bf1b73e-9af3-4035-93a7-cf085cf885e4

📥 Commits

Reviewing files that changed from the base of the PR and between 63bc9eb and e377c4c.

📒 Files selected for processing (4)

• DIRECTORY.md
• pymath/adding_two_negabinary_numbers/README.md
• pymath/adding_two_negabinary_numbers/__init__.py
• pymath/adding_two_negabinary_numbers/test_add_two_negabinary_numbers.py