docs: group all 770 open PRs by algorithm directory in hacktober_2026_prep.md

[priya-sundaram-dev]

Describe your change:

As requested by @cclauss on #15081, adds a new section at the bottom of docs/hacktober_2026_prep.md grouping all 770 open pull requests by the algorithm directory they modify, in the requested format:

Total open pull requests: 770

audio_filters:
1. [ ] #14979
backtracking:
1. [ ] #10102
...

Built by examining the changed files of every open PR (GET /pulls/{n}/files) and bucketing each by its top-level algorithm directory. Each PR appears in exactly one grouping (verified: 770 assigned, 0 duplicates).

Special groupings, as specified:

• Modifies multiple algorithm directories — 53 PRs.
• Modifies no algorithm directories — 36 PRs (touch only .github/, scripts/, docs/, or root files).
• Modifies DIRECTORY.md — 1 PR.

Largest buckets: maths (105), sorts (67), machine_learning (58), data_structures (57), strings (45), searches (33). audio_filters has a single PR (#14979).

Docs-only change; no algorithm file is touched.

• 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:

• 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 include at least one URL that points to Wikipedia or another similar explanation.

[cclauss]

Please upgrade this PR to another section called "Creates a new root directory" for PRs like:

• added Process synchronization #11574 Creates an operating_system directory.
• Python os #13924 Creates an os_py directory.
• Add pytest for heap_sort #13231 Creates a tests directory.
• feat: add automated bug triage utility (#14561) #14611 Creates a triage directory.

[priya-sundaram-dev]

Done — added a Creates a new root directory section at the bottom (docs/hacktober_2026_prep.md).

To catch every one (not just the four you listed), I checked each open PR's changed files against the top-level directories on master and kept the PRs that add a file under a path that doesn't exist yet. That surfaced 13 PRs across 12 would-be root directories:

• compression — Create lz78.py #11842, Add PPM Algorithm Implementation #12392
• control_algorithms — Added the Active Disturbance Rejection Control (ADRC) Algorithm #12648
• cpu_scheduling_algorithms — Add CPU Scheduling Algorithm: FCFS #12140
• full_wave_rectifier — Added codes for finding values of elements in full wave rectifier. #9896
• half_wave_rectifier — Codes for calculating values of elements in half wave rectifier.  #9388
• haversine_calculation — Python script that performs haversine calculations #13119
• height_tree — Tree alg #13172
• operating_system — added Process synchronization #11574
• os_py — Python os #13924
• recursions — created a recursion folder  #12141
• tests — Add pytest for heap_sort #13231
• triage — feat: add automated bug triage utility (#14561) #14611

Your four are all in there. Grouped this way, the "does this new category belong in the collection?" call can be made before the line-by-line review. Happy to fold them out of the by-directory listing above if you'd rather they only appear once.

(For transparency: I'm an AI agent maintaining these tracker docs.)