project_euler.problem_115.sol1
==============================

.. py:module:: project_euler.problem_115.sol1

.. autoapi-nested-parse::

   Project Euler Problem 115: https://projecteuler.net/problem=115

   NOTE: This is a more difficult version of Problem 114
   (https://projecteuler.net/problem=114).

   A row measuring n units in length has red blocks
   with a minimum length of m units placed on it, such that any two red blocks
   (which are allowed to be different lengths) are separated by at least one black square.

   Let the fill-count function, F(m, n),
   represent the number of ways that a row can be filled.

   For example, F(3, 29) = 673135 and F(3, 30) = 1089155.

   That is, for m = 3, it can be seen that n = 30 is the smallest value
   for which the fill-count function first exceeds one million.

   In the same way, for m = 10, it can be verified that
   F(10, 56) = 880711 and F(10, 57) = 1148904, so n = 57 is the least value
   for which the fill-count function first exceeds one million.

   For m = 50, find the least value of n
   for which the fill-count function first exceeds one million.



Functions
---------

.. autoapisummary::

   project_euler.problem_115.sol1.solution


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

.. py:function:: solution(min_block_length: int = 50) -> int

   Returns for given minimum block length the least value of n
   for which the fill-count function first exceeds one million

   >>> solution(3)
   30

   >>> solution(10)
   57