project_euler.problem_124.sol1
==============================

.. py:module:: project_euler.problem_124.sol1

.. autoapi-nested-parse::

   Project Euler Problem 124: https://projecteuler.net/problem=124

   Ordered Radicals



Functions
---------

.. autoapisummary::

   project_euler.problem_124.sol1.generate_n
   project_euler.problem_124.sol1.generate_primes
   project_euler.problem_124.sol1.generate_rads
   project_euler.problem_124.sol1.solution


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

.. py:function:: generate_n(factors: list[int], n_max: int, n: int, res: set[int])

   Generates all numbers n that can be constructed out of 'factors', with any
   multiplicity, but that do no exceed 'n_max'.

   >>> generate_n([2], 10, 1, set())


.. py:function:: generate_primes(n: int) -> list[int]

   Calculates the list of primes up to and including n.

   >>> generate_primes(6)
   [2, 3, 5]


.. py:function:: generate_rads(factors_all: list[int], n_max: int, n: int, res: dict, factors_prev: list[int])

   Generates all rads and associated factors, e.g., rad = factor_1 * ... * factor_k.
   Output is stored in 'res' dict argument.

   >>> generate_rads([2], 10, 1, {}, [])


.. py:function:: solution(n_max: int = 100000, k: int = 10000) -> int

   Loops over sorted 'rads' and generates all numbers 'n' for rad.
   Keeps track of total number of n, and when k falls inside some rad,
   it sorts all 'n' for it and picks up associated n.

   >>> solution(10, 6)
   9
   >>> solution(10, 9)
   7