Pythagorean triples: Difference between revisions
Content added Content deleted
m (→using single evenness for determinacy: elided a word from the output section.) |
m (→{{header|Haskell}}: Applied Ormolu, preferred <> to ++) |
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(\(_, a, b, c) -> a + b + c <= n) |
(\(_, a, b, c) -> a + b + c <= n) |
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[ (prim a b c, a, b, c) |
[ (prim a b c, a, b, c) |
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| a <- xs |
| a <- xs, |
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b <- drop a xs, |
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c <- drop b xs, |
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a ^ 2 + b ^ 2 == c ^ 2 |
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] |
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where |
where |
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xs = [1 .. n] |
xs = [1 .. n] |
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main = |
main = |
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putStrLn $ |
putStrLn $ |
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"Up to 100 there are " |
"Up to 100 there are " |
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show (length xs) |
<> show (length xs) |
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" triples, of which " |
<> " triples, of which " |
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show (length $ filter (\(x, _, _, _) -> x) xs) |
<> show (length $ filter (\(x, _, _, _) -> x) xs) |
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<> " are primitive." |
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where |
where |
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xs = pytr 100</lang> |
xs = pytr 100</lang> |
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Or equivalently (desugaring the list comprehension down to nested concatMaps, and pruning back the search space a little): |
Or equivalently (desugaring the list comprehension down to nested concatMaps, and pruning back the search space a little): |
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<lang haskell> |
<lang haskell>------------------- PYTHAGOREAN TRIPLES ------------------ |
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pythagoreanTriplesBelow :: Int -> [[Int]] |
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pythagoreanTriplesBelow n = |
pythagoreanTriplesBelow n = |
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| ⚫ | |||
| ⚫ | |||
( \x -> |
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concatMap |
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concatMap |
(\y -> concatMap (go x y) [y + 1 .. m]) |
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[x + 1 .. m] |
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) |
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| ⚫ | |||
[1 .. m] |
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where |
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if x + y + z <= n && x ^ 2 + y ^ 2 == z ^ 2 |
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| ⚫ | |||
then [[x, y, z]] |
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go x y z |
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else []) |
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| x + y + z <= n && x ^ 2 + y ^ 2 == z ^ 2 = |
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[[x, y, z]] |
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| otherwise = [] |
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--------------------------- TEST ------------------------- |
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main :: IO () |
main :: IO () |
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main = |
main = |
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mapM_ |
mapM_ |
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(print . length) |
(print . length) |
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([id, filter (\[x, y, _] -> gcd x y == 1)] |
( [id, filter (\[x, y, _] -> gcd x y == 1)] |
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<*> [pythagoreanTriplesBelow 100] |
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)</lang> |
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{{Out}} |
{{Out}} |
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<pre>17 |
<pre>17 |
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map |
map |
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(map (sum . zipWith (*) t)) |
(map (sum . zipWith (*) t)) |
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[ [[1, -2, 2], [2, -1, 2], [2, -2, 3]] |
[ [[1, -2, 2], [2, -1, 2], [2, -2, 3]], |
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[[1, 2, 2], [2, 1, 2], [2, 2, 3]], |
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[[-1, 2, 2], [-2, 1, 2], [-2, 2, 3]] |
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] |
] |
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main = |
main = |
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mapM_ |
mapM_ |
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((putStrLn . (\n -> show n |
((putStrLn . (\n -> show n <> " " <> show (triangleCount n))) . (10 ^)) |
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[1 .. 7]</lang> |
[1 .. 7]</lang> |
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{{out}} |
{{out}} |
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