Feat/needleman wunsch

[Sanchana05]

Describe your change:
[x] Add an algorithm?
[ ] Fix a bug or typo in an existing algorithm?
[ ] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
[ ] Documentation change?

Checklist:
[x] I have read CONTRIBUTING.md.
[x] This pull request is all my own work -- I have not plagiarized.
[x] I know that pull requests will not be merged if they fail the automated tests.
[x] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
[x] All new Python files are placed inside an existing directory.
[x] All filenames are in all lowercase characters with no spaces or dashes.
[x] All functions and variable names follow Python naming conventions.
[x] All function parameters and return values are annotated with Python type hints.
[x] All functions have doctests that pass the automated testing.
[x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
[ ] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: "Fixes #ISSUE-NUMBER".

Description:
Added the Needleman-Wunsch algorithm for optimal global sequence alignment to the bioinformatics directory.

Changes:

Implemented needleman_wunsch DP matrix filling and traceback.

Added comprehensive docstrings, including matching/mismatch/gap penalty logic.

Included passing doctests for validation.

Strictly adhered to pure Python (no external dependencies).

Added type hinting for all functions.

[cclauss]

@priya-sundaram-dev this pull request or

• feat(dynamic_programming): add Needleman-Wunsch global sequence align… #15294

[priya-sundaram-dev]

Thanks for the ping @cclauss — they're duplicates (both add dynamic_programming/needleman_wunsch.py), so only one should land.

I pulled both branches and checked them:

	#14440 (this PR)	#15294
Lines	554	187
Doctests	pass	pass (7)
Compiles	✓	✓
Scope	algorithm + scoring/traceback/print helpers + a __main__ demo that re-runs doctests and pretty-prints matrices	single needleman_wunsch() with the alignment returned as a tuple

Both are correct, but #15294 is the better fit for this repo: it's the focused ~190-line module with a clean docstring, type hints and 7 doctests (including the Wikipedia GCATGCG/GATTACA case), and no display/__main__ scaffolding. #14440 does a lot of genuinely nice teaching work, but the extra matrix-printing helpers and the manual doctest-runner in __main__ are the kind of scaffolding we usually trim.

My suggestion: merge #15294, and it'd be great to invite @Sanchana05 to fold in the one thing #14440 has that #15294 doesn't — a couple of extra worked examples as doctests — so the effort here isn't lost. Happy to help review whichever one you take forward.