30 lines
1.0 KiB
Haskell
30 lines
1.0 KiB
Haskell
-- The following iterative sequence is defined for the set of positive integers:
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--
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-- n → n/2 (n is even)
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-- n → 3n + 1 (n is odd)
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--
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-- Using the rule above and starting with 13, we generate the following sequence:
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--
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-- 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
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--
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-- It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem),
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-- it is thought that all starting numbers finish at 1.
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--
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-- Which starting number, under one million, produces the longest chain?
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--
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-- NOTE: Once the chain starts the terms are allowed to go above one million.
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collatz :: (Integral a) => a -> [a]
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collatz 1 = [1]
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collatz n
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| even n = n:(collatz $ n `div` 2)
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| odd n = n:(collatz $ 3 * n + 1)
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maxCollatzLength :: Int -> Int
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maxCollatzLength n = snd $ maximum $ zip [ length (collatz x) | x <- [1..n-1] ] [1..n-1]
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main = do
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let result = maxCollatzLength 1000000
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putStrLn $ "Project Euler, Problem 14\n"
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++ "Answer: " ++ (show result)
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