Add solutions for problems 9-12.
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.*.swp
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*~
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*.o
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*.hi
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Problem[0-9]
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{-# LANGUAGE BangPatterns, ScopedTypeVariables, FlexibleContexts #-}
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module Euler
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( whenM
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, unlessM
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, primesTo
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, primes
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, zipArraysWith
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, RangeIx(..)
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) where
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import Control.Applicative
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import Control.Monad
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import Control.Monad.ST
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import Control.Monad.Writer
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import Data.Array.ST
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import Data.Array.Unboxed
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import Data.Word
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import qualified Control.Monad.ST.Lazy as LST
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whenM, unlessM :: Monad m => m Bool -> m () -> m ()
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whenM mc m = mc >>= (\c -> when c m)
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unlessM mc m = mc >>= (\c -> unless c m)
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primesTo n = LST.runST $ do
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isPrime <- LST.strictToLazyST (newArray (2, n) 1 :: ST s (STUArray s Integer Word8))
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let primesFrom m = if m > n then return [] else do
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p <- LST.strictToLazyST (readArray isPrime m)
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if p == 0 then primesFrom (m+1) else do
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LST.strictToLazyST $ forM_ [2*m,3*m..n] $ \i -> writeArray isPrime i 0
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(m:) <$> primesFrom (m+1)
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primesFrom 2
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primes :: [Integer]
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primes = let go (!p:xs) = p : go [ x | x <- xs, x `mod` p /= 0 ] in go [2..]
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class Ix a => RangeIx a where
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intersectBounds :: (a, a) -> (a, a) -> (a, a)
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instance RangeIx Int where
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intersectBounds (al, au) (bl, bu) = (max al bl, min au bu)
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instance (RangeIx a, RangeIx b) => RangeIx (a, b) where
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intersectBounds ((al,bl),(au,bu)) ((cl,dl),(cu,du)) =
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((max al cl, max bl dl), (min au cu, min bu du))
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zipArraysWith :: (IArray arrA a, IArray arrB b, IArray arrC c, RangeIx i)
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=> (a -> b -> c) -> arrA i a -> arrB i b -> arrC i c
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zipArraysWith f as bs = array newRange $ [ (i, f (as!i) (bs!i)) | i <- range newRange ]
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where newRange = intersectBounds (bounds as) (bounds bs)
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-- Find the sum of all the primes below two million.
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import Euler
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main = print $ sum $ primesTo 1999999
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{-# LANGUAGE FlexibleInstances, UndecidableInstances #-}
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import Data.Array.Unboxed
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import Euler
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-- What is the greatest product of four adjacent numbers in the same direction
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-- (up, down, left, right, or diagonally) in the 20×20 grid?
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--
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grid :: UArray (Int, Int) Int
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grid = listArray ((1,1),(20,20)) $
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[ 08, 02, 22, 97, 38, 15, 00, 40, 00, 75, 04, 05, 07, 78, 52, 12, 50, 77, 91, 08
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, 49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 04, 56, 62, 00
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, 81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 03, 49, 13, 36, 65
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, 52, 70, 95, 23, 04, 60, 11, 42, 69, 24, 68, 56, 01, 32, 56, 71, 37, 02, 36, 91
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, 22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80
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, 24, 47, 32, 60, 99, 03, 45, 02, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50
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, 32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70
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, 67, 26, 20, 68, 02, 62, 12, 20, 95, 63, 94, 39, 63, 08, 40, 91, 66, 49, 94, 21
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, 24, 55, 58, 05, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72
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, 21, 36, 23, 09, 75, 00, 76, 44, 20, 45, 35, 14, 00, 61, 33, 97, 34, 31, 33, 95
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, 78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 03, 80, 04, 62, 16, 14, 09, 53, 56, 92
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, 16, 39, 05, 42, 96, 35, 31, 47, 55, 58, 88, 24, 00, 17, 54, 24, 36, 29, 85, 57
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, 86, 56, 00, 48, 35, 71, 89, 07, 05, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58
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, 19, 80, 81, 68, 05, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 04, 89, 55, 40
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, 04, 52, 08, 83, 97, 35, 99, 16, 07, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66
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, 88, 36, 68, 87, 57, 62, 20, 72, 03, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69
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, 04, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 08, 46, 29, 32, 40, 62, 76, 36
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, 20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 04, 36, 16
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, 20, 73, 35, 29, 78, 31, 90, 01, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 05, 54
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, 01, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 01, 89, 19, 67, 48
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]
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times :: (IArray a e, RangeIx i, Num e) => a i e -> a i e -> a i e
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a `times` b = zipArraysWith (*) a b
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infixl 7 `times`
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across n = ixmap ((1,1),( 20 ,20-n)) (\(a,b) -> ( a ,b+n)) grid
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down n = ixmap ((1,1),(20-n, 20 )) (\(a,b) -> (a+n, b )) grid
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diag1 n = ixmap ((1,1),(20-n,20-n)) (\(a,b) -> (a+n,b+n)) grid
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diag2 n = ixmap ((1,1+n),(20-n,20)) (\(a,b) -> (a+n,b-n)) grid
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acrossProducts = grid `times` across 1 `times` across 2 `times` across 3
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downProducts = grid `times` down 1 `times` down 2 `times` down 3
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diagProducts1 = grid `times` diag1 1 `times` diag1 2 `times` diag1 3
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diagProducts2 = grid `times` diag2 1 `times` diag2 2 `times` diag2 3
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main = print $ maximum $ concatMap elems $
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[acrossProducts, downProducts, diagProducts1, diagProducts2]
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-- The sequence of triangle numbers is generated by adding the natural numbers.
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-- So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. ...
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-- What is the value of the first triangle number to have over five hundred divisors?
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import Data.List
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triangles = scanl1 (+) [1..] :: [Int]
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divisors n = concat [ [m, q] | m <- takeWhile (\x -> x^2 <= n) [1..], let (q, r) = n `divMod` m, r == 0 ]
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main = print $ head $ [ n | n <- triangles, length (divisors n) > 500 ]
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11
Problem3.hs
11
Problem3.hs
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-- What is the largest prime factor of the number 600851475143 ?
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n `divides` m = m `mod` n == 0
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primes = go [2..] where go (p:ps) = p : go (filter (\n -> not (p `divides` n)) ps)
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import Euler
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factors n = go primes n
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where go (p:ps) n | n < p = []
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| p `divides` n = p : go (p:ps) (n `div` p)
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| otherwise = go ps n
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factors n = go (primes ()) n
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where go (p:ps) n | n < p = []
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| n `mod` p == 0 = p : go (p:ps) (n `div` p)
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| otherwise = go ps n
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main = print $ last $ factors 600851475143
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-- What is the 10 001st prime number?
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primes :: [Int]
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primes = let go (p:ps) = p : go [ n | n <- ps, n `mod` p /= 0 ] in go [2..]
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main = print $ primes !! 10000
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import Euler
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main = print $ primesTo 1000000 !! 10000
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-- A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
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--
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-- a^2 + b^2 = c^2
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--
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-- For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
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--
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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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main = print $ head [ a*b*c | a <- [1..1000]
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, b <- [a+1..1000-a]
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, let c = 1000 - (a + b)
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, a^2 + b^2 == c^2
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]
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