Add narcissistic number finder with dynamic programming

[AliAlimohammadi]

Description

Adds a dynamic programming implementation to find all narcissistic numbers (also known as Armstrong numbers) up to a specified limit.

A narcissistic number is a number that equals the sum of its own digits each raised to the power of the number of digits. For example: 153 = 1³ + 5³ + 3³.

Implementation Details

• Uses memoization to cache digit power calculations (digit^power)
• Avoids redundant computations when checking multiple numbers
• Implements true dynamic programming with overlapping subproblems

Dynamic Programming Approach

Overlapping Subproblems: Many numbers share the same digits, so the same digit powers are computed repeatedly (e.g., 153, 351, 135 all need 1³, 5³, 3³)

Memoization: Cache stores (power, digit) -> result mappings to avoid recomputation

Optimal Substructure: The narcissistic property is built from individual digit power results

Examples

>>> find_narcissistic_numbers(10)
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

>>> find_narcissistic_numbers(1000)
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407]

>>> find_narcissistic_numbers(10000)
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474]

Type of Change

• Add an algorithm

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
• All new Python files are placed inside an existing directory (dynamic_programming/)
• Filename is in all lowercase characters with no spaces or dashes (narcissistic_number.py)
• All functions and variable names follow Python naming conventions (snake_case)
• All function parameters and return values are annotated with Python type hints
• All functions have doctests that pass the automated testing (7 tests)
• Algorithm includes a URL pointing to Wikipedia or similar explanation
• Code uses Python 3.13+ features where appropriate
• Code passes ruff check linting
• Code is formatted with black (or follows PEP 8)

References

• Narcissistic Number - Wikipedia