Add Digital Root algorithm to maths

[MeiSiristhebest]

Description

Adds the Digital Root algorithm (maths/digital_root.py).

The digital root (repeated digital sum) of a non-negative integer is the single-digit value obtained by iteratively summing its decimal digits until only one digit remains. It complements the existing maths/sum_of_digits.py (single-pass digit sum) and is a classic number-theory / arithmetic routine.

Reference

• https://en.wikipedia.org/wiki/Digital_root

Verification (local CI, matching repo config: Python 3.14, ruff, mypy, pytest)

• ruff format --check : passed
• ruff check : passed
• mypy : passed (no issues)
• pytest --doctest-modules : 1 passed (doctests cover 0, single digit, multi-digit, negative input, and a large number)

Checklist

• Single algorithm per file, snake_case filename
• Type hints + docstring + doctests present
• Wikipedia reference linked
• No duplicate of an existing implementation
• DIRECTORY.md is auto-generated by the directory_writer workflow on push (not manually edited)

[algorithms-keeper]

Click here to look at the relevant links ⬇️

🔗 Relevant Links

Repository:

• Contributing guidelines
• Project Euler solution guidelines

Python:

• Formatted string literals (f-strings)
• Type hints
• doctest
• unittest
• pytest

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[algorithms-keeper]

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