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Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: John Law <johnlaw.po@gmail.com>
65 lines
2.0 KiB
Python
65 lines
2.0 KiB
Python
"""
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Project Euler Problem 116: https://projecteuler.net/problem=116
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A row of five grey square tiles is to have a number of its tiles
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replaced with coloured oblong tiles chosen
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from red (length two), green (length three), or blue (length four).
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If red tiles are chosen there are exactly seven ways this can be done.
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|red,red|grey|grey|grey| |grey|red,red|grey|grey|
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|grey|grey|red,red|grey| |grey|grey|grey|red,red|
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|red,red|red,red|grey| |red,red|grey|red,red|
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|grey|red,red|red,red|
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If green tiles are chosen there are three ways.
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|green,green,green|grey|grey| |grey|green,green,green|grey|
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|grey|grey|green,green,green|
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And if blue tiles are chosen there are two ways.
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|blue,blue,blue,blue|grey| |grey|blue,blue,blue,blue|
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Assuming that colours cannot be mixed there are 7 + 3 + 2 = 12 ways
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of replacing the grey tiles in a row measuring five units in length.
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How many different ways can the grey tiles in a row measuring fifty units in length
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be replaced if colours cannot be mixed and at least one coloured tile must be used?
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NOTE: This is related to Problem 117 (https://projecteuler.net/problem=117).
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"""
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def solution(length: int = 50) -> int:
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"""
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Returns the number of different ways can the grey tiles in a row
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of the given length be replaced if colours cannot be mixed
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and at least one coloured tile must be used
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>>> solution(5)
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12
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"""
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different_colour_ways_number = [[0] * 3 for _ in range(length + 1)]
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for row_length in range(length + 1):
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for tile_length in range(2, 5):
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for tile_start in range(row_length - tile_length + 1):
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different_colour_ways_number[row_length][tile_length - 2] += (
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different_colour_ways_number[row_length - tile_start - tile_length][
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tile_length - 2
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]
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+ 1
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)
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return sum(different_colour_ways_number[length])
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if __name__ == "__main__":
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print(f"{solution() = }")
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