feat(algorithms, greedy): largest palindromic number

[BrianLusina]

Describe your change:

Adds algorithm for finding largest palindromic number from a given number string with digits from 0 to 9

• 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

• New Features

  • Added "Largest Palindromic Number" problem with two alternative implementations.

• Bug Fixes

  • Removed unreachable dead code from an existing stock algorithm.

• Documentation

  • Added a detailed problem README with algorithm outline, edge cases, and complexity notes.
  • Updated directory index to include the new problem.

• Tests

  • Added parameterized test suite validating both implementations.

_{✏️ Tip: You can customize this high-level summary in your review settings.}

[coderabbitai]

Caution

Review failed

The pull request is closed.

📝 Walkthrough

Walkthrough

Adds a new "Largest Palindromic Number" solution with two implementations, README, and tests to the greedy algorithms; removes an unreachable return in the buy/sell stock DP module; updates DIRECTORY.md to include the new subsection.

Changes

Cohort / File(s)	Summary
Largest Palindromic Number Implementation algorithms/greedy/largest_palindromic_number/__init__.py	Adds largest_palindromic_number() and largest_palindromic_number_v2() to build the largest palindrome from digit counts, handling leading-zero and all-zero edge cases.
Documentation algorithms/greedy/largest_palindromic_number/README.md, DIRECTORY.md	New README documenting problem, algorithm, examples, complexity; DIRECTORY.md updated to include the new subsection under greedy.
Tests algorithms/greedy/largest_palindromic_number/test_largest_palindromic_number.py	New parameterized unittest suite validating both implementations against multiple cases.
Cleanup algorithms/dynamic_programming/buy_sell_stock/__init__.py	Removed an unreachable return 0 (dead code) from max_profit_two_pointers.

Sequence Diagram(s)

(Skipped — changes are algorithmic within modules and do not introduce multi-component control flow.)

Estimated code review effort

🎯 4 (Complex) | ⏱️ ~45 minutes

Poem

🐰 I counted digits, hopped with glee,

Pairs and a center, symmetrical spree.
From nine down, I stitched a mirror true,
A largest palindrome, born anew —
Hooray for hops that code can do! ✨

🚥 Pre-merge checks | ✅ 2 | ❌ 1

❌ Failed checks (1 warning)

Check name	Status	Explanation	Resolution
Docstring Coverage	⚠️ Warning	Docstring coverage is 0.00% which is insufficient. The required threshold is 80.00%.	Write docstrings for the functions missing them to satisfy the coverage threshold.

✅ Passed checks (2 passed)

Check name	Status	Explanation
Title check	✅ Passed	The title clearly describes the main change: adding a new greedy algorithm for finding the largest palindromic number.
Description check	✅ Passed	The description provides a clear summary of the change and includes a completed checklist covering all required contribution guidelines.

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

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[coderabbitai]

Actionable comments posted: 3

🤖 Fix all issues with AI agents

In `@algorithms/greedy/largest_palindromic_number/__init__.py`:
- Around line 46-65: The middle-digit selection loop currently iterates digits
with "for digit in range(9, 0, -1)" which skips '0' and causes wrong results for
inputs where 0 is the only odd-count digit; update the loop to include 0 (e.g.,
range(9, -1, -1) or otherwise fall back to checking digit '0') so that
digit_counter['0'] can be chosen as result when appropriate, and remember to
decrement digit_counter[digit_str] when you pick '0' just like for other digits;
keep the subsequent symmetric-pair logic (the number loop that divides counts by
two and builds temp/result) unchanged and ensure final return still uses
result.strip("0") or "0".

In `@algorithms/greedy/largest_palindromic_number/README.md`:
- Line 63: Update the time complexity sentence in the README.md (the line
stating "The time complexity of the solution is O(n), where n is the length of
the nums string.") to replace "nums string" with "num string" so it reads
"...where n is the length of the num string."

In `@DIRECTORY.md`:
- Around line 144-145: The markdown list indentation is inconsistent for the
"Largest Palindromic Number" entry and its test link; update the second bullet
(the line starting with "[Test Largest Palindromic
Number](https://github.com/.../test_largest_palindromic_number.py)") to the
correct nesting level by indenting it to match the configured list nesting (use
the same number of spaces as other sub-items, e.g., two spaces) so the "Largest
Palindromic Number" header and its test link have consistent indentation and
satisfy MD007.

🧹 Nitpick comments (1)

algorithms/greedy/largest_palindromic_number/test_largest_palindromic_number.py (1)

8-16: Add regression case for odd‑zero middle.

Include a case like ("11000", "10001") so both implementations are guarded against skipping 0 as the middle digit.

✅ Test case addition

 LARGEST_PALINDROMIC_NUMBER_TEST_CASES = [
     ("2012", "212"),
     ("000001", "1"),
     ("111222333", "3213123"),
     ("000000", "0"),
     ("123456789123456789", "987654321123456789"),
     ("444947137", "7449447"),
     ("00009", "9"),
+    ("11000", "10001"),
 ]