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28 lines
841 B
Haskell
28 lines
841 B
Haskell
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{- Find the only Pythagorean triplet, {a, b, c}, for which a + b + c = 1000.
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A Pythagorean triplet is a set of three natural numbers, a b c, for which,
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a2 + b2 = c2
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For example, 32 + 42 = 9 + 16 = 25 = 52.
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There exists exactly one Pythagorean triplet for which a + b + c = 1000.
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Find the product abc.
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-}
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import Text.Printf
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triplet sum = do
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let cs = reverse (takeWhile (<= sum - 3) [3,5..])
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let tri = head (concat (map (\x -> diffs sum x) cs))
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let (a, b, c) = tri
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a * b * c
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diffs sum c = do
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let diff = sum - c
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let range = [1..(floor ((fromIntegral diff) / 2)) + 1]
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let triangles = filter is_triangle (map (\x -> (x, diff - x, c)) range)
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triangles
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is_triangle (a, b, c) =
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a^2 + b^2 == c^2
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main = do
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printf "Pythagorean triplet product having a + b + c = 1000: %d\n" (triplet 1000 :: Integer)
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