* Add median() function using Quickselect

* Update quick_select.py

* Update quick_select.py

* Update quick_select.py

---------

Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru>

* Add bidirectional search algorithm implementation

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

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

* Fix style and linting issues in bidirectional search

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

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

* Add doctest for main function

* Add doctest for main function

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

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

* fixed deprications

* fixed deprications

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

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

* removed unused import

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

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

* Update bidirectional_search.py

* Update bidirectional_search.py

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

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

* Update bidirectional_search.py

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

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

---------

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

* Mutable _Item

* document falsy item

* resize_down: expected test result

* resize_down: actual result

This is a problem since it causes rapid cycling

* improve comment about falsy item

Co-authored-by: Andrey <Cjkjvfnby@gmail.com>

* fix long line

* Update hash_map.py

* Update hash_map.py

---------

Co-authored-by: Andrey <Cjkjvfnby@gmail.com>
Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru>

* Add tests and cleanup sum_of_subsets algorithm.

* Update sum_of_subsets.py

* Update sum_of_subsets.py

* Update sum_of_subsets.py

* Update sum_of_subsets.py

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

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

---------

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

…eAlgorithms#12759)

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

updates:
- [github.com/astral-sh/ruff-pre-commit: v0.11.9 → v0.11.11](astral-sh/ruff-pre-commit@v0.11.9...v0.11.11)
- [github.com/tox-dev/pyproject-fmt: v2.5.1 → v2.6.0](tox-dev/pyproject-fmt@v2.5.1...v2.6.0)

* updating DIRECTORY.md

---------

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

…2772)

* maths/radix2_fft.py: Fix calculation for Python 3.14

As suggested at:
* TheAlgorithms#12729 (comment)
* TheAlgorithms#12710 (comment)

@MaximSmolskiy @KirilBangachev @skirpichev Careful review, please.  I am just implementing the suggestion, but I do not have any expertise in this area.

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

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

* Change test results

* GitHub Actions: Rename job from build to directory_writer

It is confusing to have two jobs named `build`.

---------

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

Co-authored-by: Jeonghyun Min <20122791@tafe.wa.edu.au>

* Add doctests for the boyer_moore_search algorithm.

* Update boyer_moore_search.py

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

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

* Update boyer_moore_search.py

* Update boyer_moore_search.py

---------

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