project_euler.problem_115.sol1

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

solution(→ int)

Returns for given minimum block length the least value of n

Module Contents

project_euler.problem_115.sol1.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