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Project Euler, Problem #7, Haskell - Pastebin.com
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Project Euler, Problem #7, Haskell
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- -- By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we
- -- can see that the 6th prime is 13. What is the 10 001st prime
- -- number?
- -- Solution #1: a basic one
- main :: IO ()
- main =
- print $
- [x | x <- [1 ..], null [y | y <- [2 .. div x 2], mod x y == 0]] !! 10001
- -- 104743
- -- real 0m40,243s
- -- user 0m39,956s
- -- sys 0m0,248s
- -- #################################
- -- Solution #2: still basic, but faster
- -- The idea behind this solution is that, if a number can't be divided
- -- by any prime number smaller than itself, then this number is prime
- -- itself. The checked number "cn" is checked against the list of prime
- -- numbers "pl". If the number is prime, it's added to the list; if
- -- it's not, then it's incremented and checked again. The list is
- -- expanded as long as its size is less than 10001; when the length of
- -- the list is equal to 10001 its last item is returned.
- -- pcc (prime checker concatenator) definition #1: if an auxiliary
- -- copy of the list of primes is empty, which means that the checked
- -- number is prime, then the number is added to the main list of
- -- primes and then the number is incremented.
- pcc :: Integral t => [t] -> [t] -> t -> t
- pcc pl [] cn = lsc (pl ++ [cn]) (cn + 1)
- -- pcc definition #2: the checked number is recursively checked
- -- against numbers in an auxiliary copy of the list of prime numbers;
- -- the numbers on the list go in ascending order, so smaller, thus
- -- more likely divisors are checked first.
- pcc pl (x:xs) cn =
- if mod cn x == 0
- then pcc pl pl (cn + 1)
- else pcc pl xs cn
- -- lsc (list size checker) definition: the length of the main list is
- -- checked: if it's equal to 10001, then the last item of the main
- -- list of prime numbers is returned, otherwise incrementation, check
- -- and list expansion continue.
- lsc :: Integral t => [t] -> t -> t
- lsc pl cn =
- if length pl < 10001
- then pcc pl pl cn
- else last pl
- main :: IO ()
- main = print $ lsc [2] 3
- -- 104743
- -- real 0m15,728s
- -- user 0m15,596s
- -- sys 0m0,077s
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