mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-21 02:30:15 +00:00
59 lines
1.6 KiB
Python
59 lines
1.6 KiB
Python
|
"""
|
||
|
|
Project Euler Problem 114: https://projecteuler.net/problem=114
|
||
|
|
|
||
|
|
A row measuring seven units in length has red blocks with a minimum length
|
||
|
|
of three units placed on it, such that any two red blocks
|
||
|
|
(which are allowed to be different lengths) are separated by at least one grey square.
|
||
|
|
There are exactly seventeen ways of doing this.
|
||
|
|
|
||
|
|
|g|g|g|g|g|g|g| |r,r,r|g|g|g|g|
|
||
|
|
|
||
|
|
|g|r,r,r|g|g|g| |g|g|r,r,r|g|g|
|
||
|
|
|
||
|
|
|g|g|g|r,r,r|g| |g|g|g|g|r,r,r|
|
||
|
|
|
||
|
|
|r,r,r|g|r,r,r| |r,r,r,r|g|g|g|
|
||
|
|
|
||
|
|
|g|r,r,r,r|g|g| |g|g|r,r,r,r|g|
|
||
|
|
|
||
|
|
|g|g|g|r,r,r,r| |r,r,r,r,r|g|g|
|
||
|
|
|
||
|
|
|g|r,r,r,r,r|g| |g|g|r,r,r,r,r|
|
||
|
|
|
||
|
|
|r,r,r,r,r,r|g| |g|r,r,r,r,r,r|
|
||
|
|
|
||
|
|
|r,r,r,r,r,r,r|
|
||
|
|
|
||
|
|
How many ways can a row measuring fifty units in length be filled?
|
||
|
|
|
||
|
|
NOTE: Although the example above does not lend itself to the possibility,
|
||
|
|
in general it is permitted to mix block sizes. For example,
|
||
|
|
on a row measuring eight units in length you could use red (3), grey (1), and red (4).
|
||
|
|
"""
|
||
|
|
|
||
|
|
|
||
|
|
def solution(length: int = 50) -> int:
|
||
|
|
"""
|
||
|
|
Returns the number of ways a row of the given length can be filled
|
||
|
|
|
||
|
|
>>> solution(7)
|
||
|
|
17
|
||
|
|
"""
|
||
|
|
|
||
|
|
ways_number = [1] * (length + 1)
|
||
|
|
|
||
|
|
for row_length in range(3, length + 1):
|
||
|
|
for block_length in range(3, row_length + 1):
|
||
|
|
for block_start in range(row_length - block_length):
|
||
|
|
ways_number[row_length] += ways_number[
|
||
|
|
row_length - block_start - block_length - 1
|
||
|
|
]
|
||
|
|
|
||
|
|
ways_number[row_length] += 1
|
||
|
|
|
||
|
|
return ways_number[length]
|
||
|
|
|
||
|
|
|
||
|
|
if __name__ == "__main__":
|
||
|
|
print(f"{solution() = }")
|