project_euler.problem_164.sol1
==============================

.. py:module:: project_euler.problem_164.sol1

.. autoapi-nested-parse::

   Project Euler Problem 164: https://projecteuler.net/problem=164

   Three Consecutive Digital Sum Limit

   How many 20 digit numbers n (without any leading zero) exist such that no three
   consecutive digits of n have a sum greater than 9?

   Brute-force recursive solution with caching of intermediate results.



Functions
---------

.. autoapisummary::

   project_euler.problem_164.sol1.solution
   project_euler.problem_164.sol1.solve


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

.. py:function:: solution(n_digits: int = 20) -> int

   Solves the problem for n_digits number of digits.

   >>> solution(2)
   45
   >>> solution(10)
   21838806


.. py:function:: solve(digit: int, prev1: int, prev2: int, sum_max: int, first: bool, cache: dict[str, int]) -> int

   Solve for remaining 'digit' digits, with previous 'prev1' digit, and
   previous-previous 'prev2' digit, total sum of 'sum_max'.
   Pass around 'cache' to store/reuse intermediate results.

   >>> solve(digit=1, prev1=0, prev2=0, sum_max=9, first=True, cache={})
   9
   >>> solve(digit=1, prev1=0, prev2=0, sum_max=9, first=False, cache={})
   10