[FIX] Rewrite Armstrong Number algorithm to follow contribution guide…

[shiwans-k-yadav]

Rewritten Armstrong Number algorithm in modern C++ style.

• Added beginner-friendly comments explaining each step.
• Added interactive input for users to test their own numbers.
• Added automated self-tests to verify correctness.
• Educational and self-explanatory, following contribution guidelines.

Checklist :
✅Added description of change
✅Added file name matches File name guidelines (armstrong_number.cpp)
✅Added tests and example, test must pass
✅Added documentation so that the program is self-explanatory and educational
✅Relevant documentation/comments is changed or added
✅PR title follows semantic commit guidelines
✅Search previous suggestions before making a new one
✅I acknowledge that all my contributions will be made under the project's license

Notes:
This implementation improves readability and educational value compared to previous versions, while keeping automated tests intact.

[shiwans-k-yadav]

Hi! 👋

This PR is part of my Hacktoberfest contributions for the Armstrong Number algorithm.
All tests pass locally and the code is educational and self-explanatory.

I understand there are workflow approvals and code owner reviews required.
Since these might take some time, feel free to review whenever possible.
Thank you for maintaining this awesome repository! 🙏