* [pre-commit.ci] pre-commit autoupdate

updates:
- [github.com/astral-sh/ruff-pre-commit: v0.15.15 → v0.15.20](astral-sh/ruff-pre-commit@v0.15.15...v0.15.20)
- [github.com/tox-dev/pyproject-fmt: v2.23.0 → v2.25.1](tox-dev/pyproject-fmt@v2.23.0...v2.25.1)

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

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Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

Bumps [actions/setup-python](https://github.com/actions/setup-python) from 6 to 7.
- [Release notes](https://github.com/actions/setup-python/releases)
- [Commits](actions/setup-python@v6...v7)

---
updated-dependencies:
- dependency-name: actions/setup-python
  dependency-version: '7'
  dependency-type: direct:production
  update-type: version-update:semver-major
...

Signed-off-by: dependabot[bot] <support@github.com>
Co-authored-by: dependabot[bot] <49699333+dependabot[bot]@users.noreply.github.com>

* docs: expand bubble sort docstrings with algorithm explanation

Add a concise description of how bubble sort works (repeated
adjacent comparisons/swaps until a pass makes no swaps) and note
time/space complexity for both the iterative and recursive
implementations. No behavior changes; all existing doctests pass.

* Fix Ruff 0.16 lint failures

* S310

---------

Co-authored-by: Christian Clauss <cclauss@me.com>

* Fix invalid Python 2 syntax in except clause

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update ruff-pre-commit version to v0.16.1

* Fix indentation in test_cancer_data function

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

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Co-authored-by: Christian Clauss <cclauss@me.com>

…hms#14936)

* fix: raise ValueError in encode() for non-lowercase input

encode() previously accepted uppercase letters, digits, and other
non-lowercase characters silently, producing incorrect/out-of-range
values (e.g. negative numbers for uppercase letters) instead of
failing. Add input validation using str.islower() and str.isalpha()
to raise a ValueError when the input isn't purely lowercase a-z.
Added a doctest covering the new error case.

* resolved doctest

* Fix Ruff 0.16 lint failures

* Enhance encode function error handling examples

Update error handling in encode function to include examples for mixed case and invalid characters.

* Fix indentation in test_cancer_data function

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

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Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

updates:
- [github.com/codespell-project/codespell: v2.4.2 → v2.4.3](codespell-project/codespell@v2.4.2...v2.4.3)
- [github.com/tox-dev/pyproject-fmt: v2.25.1 → v2.26.0](tox-dev/pyproject-fmt@v2.25.1...v2.26.0)

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

…5070)

* fix: sub-interval midpoint formula in ternary search

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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The docstring incorrectly referenced Sylvester's sequence (a copy-paste
error from maths/sylvester_sequence.py) and used param names that did
not match the actual function signature.

Fixes TheAlgorithms#15013

Co-authored-by: kumarsatyam9378-art <kumarsatyam9378@gmail.com>

* Clean up the audio_filters directory

- Restore equal_loudness_filter.py: replace the third-party 'yulewalker'
  dependency with a dependency-free 'yulewalk' implementation (numpy + scipy
  only, both already project dependencies) so the filter works again.
- Fix two bugs in iir_filter.set_coefficients: the a0-omitted branch never
  triggered, and the b_coeffs length error reported len(a_coeffs).
- Add doctests covering valid and erroneous inputs (coefficient-length errors,
  yulewalk input validation).
- Add Wikipedia URLs to the docstrings that were missing them.
- Add two new RBJ Audio EQ Cookbook filters: make_notch and make_bandpass_peak.
- Rewrite audio_filters/README.md to document every file and filter.

* audio_filters: clarify make_notch, document biquad notation, tighten set_coefficients guard

- Add a shared notation guide to butterworth_filter so the single-letter
  RBJ-cookbook names (w0/alpha/a0..a2/b0..b2) are self-explanatory across
  every filter instead of diverging in one function.
- Comment make_notch's feed-forward/feed-back sections in plain English.
- set_coefficients only fills the optional a_0 when exactly one coefficient
  is missing, so genuinely too-short inputs raise with their real length
  (new regression doctest).

* Clean up the networking_flow directory

- Add networking_flow/README.md covering max-flow / min-cut, with a
  file-by-file table and guidance on which algorithm to use.
- minimum_cut.py: add a module docstring with a Wikipedia URL, type
  hints, and corner-case doctests; work on a copy so the input graph is
  no longer mutated.
- Add dinic.py: Dinic's algorithm (BFS level graph + DFS blocking flow),
  adjacency-list based so it handles parallel edges and sparse graphs.
- Add push_relabel.py: the Goldberg-Tarjan push-relabel (preflow) method
  with highest-label selection.

Both new algorithms are fully type-hinted, documented with a Wikipedia
reference, and validated by doctests; their output was cross-checked
against ford_fulkerson.py on thousands of random graphs.

* Address review: drop __future__ import, use descriptive names, apply README wording

* Clean up the fractals directory

Add a directory README plus two new, fully doctested fractal generators.

- README.md: overview table of every fractal, how to run them, and further
  reading. Distinguishes the visual (turtle/matplotlib) demos from the
  pure-computation ones that run under doctest in CI.
- sierpinski_carpet.py: integer-arithmetic Sierpinski carpet. is_filled(),
  generate_carpet() and count_filled_cells() are all doctested; no display
  needed.
- barnsley_fern.py: the Barnsley fern iterated function system. transform(),
  choose_transformation() and generate_fern() are doctested and made
  deterministic via an optional seed; matplotlib plotting is optional and
  guarded behind __main__.

* fractals: inline demo code under __main__ (address keeper-bot doctest note)

…ithms#15110)

…-commit hook (TheAlgorithms#15111)

- Add astral-sh/uv-pre-commit (uv-lock) so uv.lock stays in sync with
  pyproject.toml automatically instead of relying on manual relocks.
- Replace 'python-version: 3.14' with 'python-version-file: pyproject.toml'
  in every workflow that uses actions/setup-python (build, project_euler,
  sphinx, directory_writer), making requires-python the single source of
  truth for the interpreter version.

…5112)

The uv-lock hook (added in TheAlgorithms#15111) resolves dependencies against PyPI, but
pre-commit.ci runs hooks in a sandbox with no network access, so it fails on
every PR with a DNS lookup error. Skip it on pre-commit.ci via the ci.skip
key; the hook still runs locally and in the uv-lock CI job.

…TheAlgorithms#15114)

`machine_learning/automatic_differentiation.py` was the only module
importing `Self` from `typing_extensions`, behind a `# noqa: UP035`.
Since the repo requires Python >=3.14, `typing.Self` (added in 3.11)
is always available, so import it from the stdlib and drop the noqa.

### 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](https://github.com/TheAlgorithms/Python/blob/master/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. If not, please split into separate PRs.
* [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.

…d_learning) (TheAlgorithms#15118)

* ci: un-ignore local_weighted_learning doctests in build.yml

machine_learning/local_weighted_learning/local_weighted_learning.py only
imports numpy and matplotlib (both already project dependencies) and its
5 doctests pass headlessly. Removing it from the pytest --ignore list so
the module is covered by CI again.

* fix(local_weighted_learning): use a well-conditioned bandwidth in doctests

The doctests used tau=0.6 on data with feature values ~17-25, so the
Gaussian weights underflowed to ~0 (e.g. 8e-118, 1e-177). That made
X\u1d40WX numerically singular (cond ~5.6e18), so its inverse - and the
resulting predictions - were nondeterministic across numpy/BLAS builds.
That is why the module was on the pytest --ignore list; on the CI numpy
the first prediction came out 0.0 instead of the documented 1.07.

Switch the doctests to tau=5 (cond ~2e2), matching the bandwidth the
module's own main() already uses, and round the outputs so they are
stable across platforms. Deterministic now; removed from --ignore.

* Add Suffix Automaton algorithm in strings

* Use descriptive variable names for algorithms-keeper

* Refactor State class to use dataclass and update count_occurrences time complexity in SuffixAutomaton

* Apply suggestion from @cclauss

---------

Co-authored-by: Christian Clauss <cclauss@me.com>

…ithms#15120)

* quantum: modernize QFT to Qiskit 2.x + re-enable its test

quantum/q_fourier_transform.py used the Aer and execute symbols that were
removed from qiskit in the 1.0 API break, so it could never run and was on
the pytest --ignore list. Port it to the current API:

- Drop 'from qiskit import Aer, execute'. Build the circuit unchanged, then
  simulate with the pure-Python BasicSimulator via transpile() + backend.run(),
  so no compiled qiskit-aer backend is needed (qiskit-aer has no Python 3.14
  wheels yet; BasicSimulator ships inside qiskit core).
- Seed the run (seed_simulator=42) and rewrite the doctest to assert the
  reproducible, shot-noise-independent facts (the four outcomes appear and the
  counts sum to the shot total) instead of exact per-state counts, which random
  sampling can never hit.
- Add 'qiskit>=2' to project dependencies and drop the quantum ignore + the
  stale '# TODO: TheAlgorithms#8818 Re-enable quantum tests' comment in build.yml.

Draft until CI confirms qiskit installs and imports on the repo's Python 3.14.

* Update quantum/q_fourier_transform.py

---------

Co-authored-by: Christian Clauss <cclauss@me.com>

* Add uv-pre-commit

* updating DIRECTORY.md

---------

Co-authored-by: cclauss <cclauss@users.noreply.github.com>

…hms#15121)

* docs: add AGENTS.md with contribution rules for AI agents

Adds a model-neutral AGENTS.md at the repo root summarizing the
conventions that most often trip up automated contributors, most
importantly that algorithms-keeper closes any PR without a checked
box in the 'Describe your change' section. Complements CONTRIBUTING.md.

* docs: use uvx/uv commands in AGENTS.md (this repo uses uv, not requirements.txt)