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Project Euler problems
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| --Problem 1 | |
| {- | |
| If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. | |
| The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000. | |
| -} | |
| sumMults :: Integral a => a -> a | |
| sumMults n = sum $ filter (\x -> mod x 3 == 0 || mod x 5 == 0) [1..(n-1)] | |
| sumMults2 n = sum [x | x <- [1..(n-1)], (\x -> mod x 3 == 0 || mod x 5 == 0) x] | |
| --Problem 2 | |
| {- | |
| Each new term in the Fibonacci sequence is generated by adding the previous two terms. | |
| By starting with 1 and 2, the first 10 terms will be: | |
| 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... | |
| By considering the terms in the Fibonacci sequence whose values do not exceed four million, | |
| find the sum of the even-valued terms. | |
| -} | |
| fibs :: Num b => [b] | |
| fibs = map fst $ iterate (\(a,b) -> (b,a+b)) (0,1) | |
| fibSum :: Integral a => a -> a | |
| fibSum n = sum $ filter even $ takeWhile (< n) fibs | |
| --Problem 3 | |
| {- | |
| The prime factors of 13195 are 5, 7, 13 and 29. | |
| What is the largest prime factor of the number 600851475143 ? | |
| -} | |
| primeFactors :: Integral a => a -> [a] | |
| primeFactors n = | |
| case factors of | |
| [] -> [n] | |
| _ -> factors ++ primeFactors (n `div` (head factors)) | |
| where factors = take 1 $ filter (\x -> (n `mod` x) == 0) [2 .. n-1] | |
| largestPF :: Integral a => a -> a | |
| largestPF n = head $ reverse $ primeFactors n |
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