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54 lines
1.5 KiB
Python
54 lines
1.5 KiB
Python
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"""
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Project Euler Problem 117: https://projecteuler.net/problem=117
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Using a combination of grey square tiles and oblong tiles chosen from:
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red tiles (measuring two units), green tiles (measuring three units),
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and blue tiles (measuring four units),
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it is possible to tile a row measuring five units in length
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in exactly fifteen different ways.
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|grey|grey|grey|grey|grey| |red,red|grey|grey|grey|
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|grey|red,red|grey|grey| |grey|grey|red,red|grey|
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|grey|grey|grey|red,red| |red,red|red,red|grey|
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|red,red|grey|red,red| |grey|red,red|red,red|
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|green,green,green|grey|grey| |grey|green,green,green|grey|
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|grey|grey|green,green,green| |red,red|green,green,green|
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|green,green,green|red,red| |blue,blue,blue,blue|grey|
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|grey|blue,blue,blue,blue|
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How many ways can a row measuring fifty units in length be tiled?
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NOTE: This is related to Problem 116 (https://projecteuler.net/problem=116).
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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 ways can a row of the given length be tiled
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>>> solution(5)
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15
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"""
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ways_number = [1] * (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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ways_number[row_length] += ways_number[
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row_length - tile_start - tile_length
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]
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return ways_number[length]
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if __name__ == "__main__":
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print(f"{solution() = }")
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