dynamic_programming.narcissistic_number
=======================================

.. py:module:: dynamic_programming.narcissistic_number

.. autoapi-nested-parse::

   Find all narcissistic numbers up to a given limit using dynamic programming.

   A narcissistic number (also known as an Armstrong number or plus perfect number)
   is a number that is the sum of its own digits each raised to the power of the
   number of digits.

   For example, 153 is a narcissistic number because 153 = 1^3 + 5^3 + 3^3.

   This implementation uses dynamic programming with memoization to efficiently
   compute digit powers and find all narcissistic numbers up to a specified limit.

   The DP optimization caches digit^power calculations. When searching through many
   numbers, the same digit power calculations occur repeatedly (e.g., 153, 351, 135
   all need 1^3, 5^3, 3^3). Memoization avoids these redundant calculations.

   Examples of narcissistic numbers:
       Single digit: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
       Three digit: 153, 370, 371, 407
       Four digit: 1634, 8208, 9474
       Five digit: 54748, 92727, 93084

   Reference: https://en.wikipedia.org/wiki/Narcissistic_number



Attributes
----------

.. autoapisummary::

   dynamic_programming.narcissistic_number.narcissistic_numbers


Functions
---------

.. autoapisummary::

   dynamic_programming.narcissistic_number.find_narcissistic_numbers


Module Contents
---------------

.. py:function:: find_narcissistic_numbers(limit: int) -> list[int]

   Find all narcissistic numbers up to the given limit using dynamic programming.

   This function uses memoization to cache digit power calculations, avoiding
   redundant computations across different numbers with the same digit count.

   Args:
       limit: The upper bound for searching narcissistic numbers (exclusive)

   Returns:
       list[int]: A sorted list of all narcissistic numbers below the limit

   Examples:
       >>> find_narcissistic_numbers(10)
       [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
       >>> find_narcissistic_numbers(160)
       [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153]
       >>> find_narcissistic_numbers(400)
       [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371]
       >>> 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]
       >>> find_narcissistic_numbers(1)
       [0]
       >>> find_narcissistic_numbers(0)
       []


.. py:data:: narcissistic_numbers
   :value: []