Merge branch 'master' into fix-invalid-parameter-default

Author: kadubhumika

.devcontainer/README.md

@@ -13,14 +13,15 @@ This is **Devcontainer** configuration to provide a consistent development envir
 
 ## Usage
 
-1. Install [**Docker** ](https://www.docker.com/get-started/) and [**Visual Studio Code**](https://code.visualstudio.com/)
+1. Install [**Docker**](https://www.docker.com/get-started/) and [**Visual Studio Code**](https://code.visualstudio.com/)
 2. Install the **Remote - Containers** extension in VS Code
 
     - Do `CTRL+P`, paste this command and press `Enter`
 
         ```shell
         ext install ms-vscode-remote.remote-containers
         ```
+
 3. Open this repository in VS Code
 4. When prompted, click **"Reopen in Container"**
 5. Wait for the environment to build and initialize

.github/dependabot.yml

@@ -6,3 +6,5 @@ updates:
     directory: "/"
     schedule:
       interval: "daily"
+    cooldown:
+      default-days: 7

.github/pull_request_template.md

@@ -1,21 +1,20 @@
-### Describe your change:
-
-
+### Describe your change
 
 * [ ] 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:
+### Checklist
+
 * [ ] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/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.
+* [ ] 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](https://docs.python.org/3/library/typing.html).
 * [ ] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing.
 * [ ] 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](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".
+* [ ] If this pull request resolves one or more open issues, then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

.github/skills/code-review/SKILL.md

@@ -33,6 +33,32 @@ suggest the fix — never just "rejected".
 - [ ] Descriptive variable and function names (no single letters where a word helps).
 - [ ] Code is formatted and lint-clean (`ruff`, `pre-commit`).
 
+> **Optional hint:** When a PR hand-writes a simple class that is mostly a
+> bundle of fields (a manual `__init__` plus `__repr__`/`__eq__`), it is worth
+> **suggesting** `from typing import NamedTuple` or
+> `from dataclasses import dataclass` where they would simplify the code. These
+> are underutilized tools that our contributors would benefit from using where
+> they make sense. Offer it as an optional improvement, not a blocker — do not
+> request changes solely because a class was written the longhand way.
+
+#### When a PR fails `ruff check`
+
+Don't just report the failure — try the mechanical fixes and recommend the one
+that works, in this order:
+
+1. Run `ruff check --fix file_path.py`. If that makes the file pass, recommend
+   that solution — these are the fixes `ruff` considers **safe**.
+2. If it still fails, run `ruff check --fix --unsafe-fixes file_path.py`. If that
+   makes the file pass **and** the resulting diff is genuinely safe (it preserves
+   behavior — review it, don't trust it blindly), recommend that solution and note
+   that it required `--unsafe-fixes`.
+3. If neither passes, or the unsafe fix would change behavior, describe the
+   remaining rule violations and the manual change the author needs to make.
+
+Always quote the exact rule code(s) `ruff` reports (e.g., `ruff rule UP047`,
+`ruff rule RUF100`) so the author can run those commands to read the rules being
+flagged. Also, paste the concrete command you ran.
+
 ### 3. Other Requirements for Submissions
 
 - [ ] At least one **Wikipedia (or equivalent) URL** documenting the algorithm.
@@ -43,7 +69,7 @@ suggest the fix — never just "rejected".
 
 Emit exactly these headings so reviews are comparable and easy to automate:
 
-```
+```text
 ### Is this an algorithm? — <yes/no + one-line why>
 ### Duplicate / prior-art check — <#NNNN | none found>
 ### Coding style — <pass | issues: …>

.github/skills/new-pull-request/SKILL.md

@@ -0,0 +1,75 @@
+# Skill: New pull request for TheAlgorithms/Python
+
+Create a new pull request using the rules already written in
+[`CONTRIBUTING.md`](../../../CONTRIBUTING.md). The goal is that creating a new
+pull request (human or AI) can run the same way every time, and that produces a
+clear, kind, tested, type-hinted, mergeable contribution.
+
+## How to run this skill
+
+Make sure that the local `master` branch is synced with `upstream/master` before
+creating a new pull request.
+
+Create a new clearly named branch for the pull request. Pull request changes must
+not be made or submitted on the `master` branch.
+
+Never hand-edit or revert the `uv.lock` file. If you add a legitimate
+dependency, let the `uv-lock` pre-commit hook regenerate it — do not touch it by
+hand. A hand-modified `uv.lock` makes the `algorithms-keeper` bot close the pull
+request as invalid, and even a repo maintainer cannot undo that.
+
+Always check at least one Markdown checkbox in the pull request description (the "Describe your change" section), or the
+`algorithms-keeper` bot will close the pull request as invalid — and it does
+this *before* a human reads the PR, so a genuinely good change gets closed for a
+formatting reason. This applies to **every** pull request, including CI, docs,
+and tooling changes that are not algorithms: tick the boxes that genuinely apply
+so the body is never submitted with all boxes empty. Any repo maintainer can
+undo this if you @mention them on the closed pull request, but re-opening is
+often unreliable, so it is far better to get it right the first time.
+
+### 1. Before contributing / Is this an algorithm?
+
+- [ ] The change adds, fixes, or documents **one algorithm** — not multiple, and
+      not both code and doctest changes in the same PR.
+- [ ] It is a genuine algorithm or data structure (see the *What is an Algorithm?*
+      section), not a script, snippet, how-to-use for an existing API, or exercise
+      dump.
+- [ ] It is **not already in the repository** (search the existing directories).
+- [ ] **No earlier open PR** already does the same thing — link it if one exists.
+- [ ] Properly attributed — no plagiarism; prior sources credited.
+
+### 2. Coding Style
+
+- [ ] `from __future__ import annotations` is not needed because this repo only uses
+      the latest version of CPython.
+- [ ] File and directory names are lowercase, use underscores, and land inside an
+      existing directory.
+- [ ] Public functions/classes have **type hints**.
+- [ ] Public functions have **doctests that actually pass**.
+- [ ] Descriptive variable and function names (no single letters where a word helps).
+- [ ] For a simple class that is mostly a bundle of fields, **consider**
+      `from typing import NamedTuple` or `from dataclasses import dataclass`
+      instead of a hand-written `__init__`/`__repr__`/`__eq__`. These are
+      underutilized tools that make simple classes shorter and clearer — use
+      them where they genuinely simplify the code, not everywhere.
+- [ ] Code is formatted and lint-clean (`ruff`, `pre-commit`).
+- [ ] `DIRECTORY.md` and `README.md` are **not hand-edited** — the
+      `algorithms-keeper` bot regenerates them automatically after merge.
+
+### 3. Other Requirements for Submissions
+
+- [ ] At least one **Wikipedia (or equivalent) URL** documenting the algorithm.
+- [ ] Docstring explains what the function does and its parameters/returns.
+- [ ] No unnecessary third-party dependencies.
+
+## Before you click "Create pull request"
+
+This is the final gate. Do not open the pull request until every item here is true:
+
+- [ ] At least one Markdown checkbox in the PR description is checked. **Verify
+      this by re-reading the rendered body** — if every box is still `- [ ]`, the
+      `algorithms-keeper` bot will auto-close the PR before any human sees it.
+      Check the boxes that genuinely apply to this change; never submit an
+      all-empty checklist, even for a CI, docs, or tooling PR.
+- [ ] The branch is not `master`, and `master` is synced with `upstream/master`.
+- [ ] `uv.lock` was not hand-edited.

.github/skills/review-open-issue/SKILL.md

@@ -0,0 +1,110 @@
+# Skill: Review an open issue for TheAlgorithms/Python
+
+Triage an open issue — most often one carrying the `bug` label — **together with
+every pull request attached to it**, and produce a verdict a maintainer can act on
+without re-doing the work. The goal is a review that any triager (human or AI) can
+run the same way every time, and that ends in an explicit list of `Closes #NNNNN`
+lines the maintainer can paste into a merge commit.
+
+This repo exists to **teach visitors to fix bugs by doing**. So the default is to
+merge adequate existing contributor work, not to open a fresh PR that races them.
+Only open your own PR when no attached PR adequately solves the issue.
+
+## How to run this skill
+
+### 1. Reproduce before you trust the report
+
+- Check out current `master` and actually **run the failing case** from the issue.
+- If it reproduces, say so and paste the minimal reproducer (inputs → observed
+  output, e.g. `nan` + a `RuntimeWarning`).
+- If you **cannot** confirm it locally — an optional dependency isn't installed,
+  the failure needs an external service, the report is too vague — **say that
+  explicitly rather than guessing.** "Not reproducible in a vanilla checkout"
+  is a real, useful verdict.
+
+### 2. Classify the issue
+
+Sort each issue into one bucket and act accordingly:
+
+- **Confirmed bug with an adequate open PR** → recommend the specific PR to merge.
+- **Confirmed bug, no adequate PR** → open a new PR yourself (see step 5).
+- **Not a bug / working-as-intended** → recommend closing, and explain why (e.g.
+  binary search returning *an* index of a duplicate is correct, not a defect).
+- **Feature request mislabeled as a bug** → recommend dropping the `bug` label; do
+  **not** close it as a bug.
+- **Too vague / needs reporter info** → comment **on the issue itself** asking for
+  the one concrete thing missing (a file path, a traceback, a reproducer), and note
+  it should be closed if no answer arrives.
+- **Environment / optional-dependency, not an algorithm defect** → note it needs
+  someone with that environment; it is not fixable in a vanilla checkout.
+
+### 3. Examine every attached PR — pick one, name the duplicates
+
+For a bug with several open PRs:
+
+- **Verify each fix's doctest values numerically** against a trusted reference
+  (`scipy`, `numpy.linalg`, `geopy`, or a brute-force check over random inputs).
+  Don't take a doctest's word for it — confirm the number.
+- Prefer the **first-in PR with the smallest correct diff** that follows repo
+  convention (doctests over new test files, `raise` over `assert`, no unrelated
+  reindentation or churn of clean doctests into floating-point noise).
+- **Reject out-of-scope "fixes"** — e.g. swapping a real divide-by-zero for a
+  `1e-15` magic constant makes results implementation-defined. Fix the issue, not
+  more.
+- Identify the byte-for-byte **duplicates** so the maintainer can close them with
+  thanks in the same action.
+
+### 4. Emit the verdict — fixed output shape
+
+Post one comment that a maintainer can act on directly. For each issue give a
+one-line rationale and the exact autoclose line. Two formatting rules matter a lot
+to human maintainers scanning the thread:
+
+- **Start every line that references an issue or PR with a Markdown list marker
+  (`-` or `* `).** GitHub-flavored Markdown only autolinks `#NNNNN` inside a list,
+  and those autolinks are colored — **purple = merged, red = closed, green = open** —
+  so the maintainer can see merge/close progress at a glance. A bare `#14813` at the
+  start of a line does not autolink.
+- **Merging a PR that closes an issue also closes the issue's other open PRs**, so
+  fold the duplicates into one autoclose statement rather than listing the winner
+  alone:
+
+  ```text
+  * #14813 — 3x3 inverse returns the transpose → merge #14821
+    (Closes #14813, Closes #14840, Closes #15045)
+  ```
+
+Recommended shape:
+
+```text
+## Confirmed bugs with an adequate open PR — merge
+* #<issue> — <one-line what/why> → merge #<pr> (Closes #<issue>, Closes #<dupe>, …)
+
+## Not a bug / not merge-ready
+* #<issue> — <feature-request → relabel | needs cleanup | needs a human call>
+
+## Summary — lines to add
+* Closes #<issue> → #<pr>
+```
+
+### 5. When you must open your own PR
+
+If no attached PR is adequate, open one — but let the contributors keep the credit
+where their work was close. Use autoclose keywords in the **commit message body**
+so the merge closes the issue *and* the superseded PRs:
+
+```text
+Fixes #12233
+Fixes #12262
+Fixes #13635
+```
+
+Follow the [`new-pull-request`](../new-pull-request/SKILL.md) skill for the
+mechanics (synced `master`, named branch, checked description box, untouched
+`uv.lock`).
+
+## Tone
+
+Be specific and kind. Name the exact PR and the exact reason, credit the
+contributor by handle, and offer runners-up detailed feedback so they learn — the
+point of the repo is that people come back and fix the next one.

.github/workflows/build.yml

@@ -10,6 +10,8 @@ jobs:
     runs-on: ubuntu-latest
     steps:
       - uses: actions/checkout@v7
+        with:
+          persist-credentials: false
       - uses: astral-sh/setup-uv@v7
         with:
           enable-cache: true

.github/workflows/devcontainer_ci.yml

@@ -15,6 +15,8 @@ jobs:
     runs-on: ubuntu-latest
     steps:
       - uses: actions/checkout@v7
+        with:
+          persist-credentials: false
       - uses: devcontainers/ci@v0.3
         with:
           push: never

.github/workflows/directory_writer.yml

@@ -9,6 +9,7 @@ jobs:
       - uses: actions/checkout@v7
         with:
           fetch-depth: 0
+          persist-credentials: false
       - uses: actions/setup-python@v7
         with:
           python-version-file: .python-version