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Bill Ewanick 2023-09-28 16:13:48 -04:00
parent d4cf6b25c8
commit 6bee470b8a
4 changed files with 80 additions and 0 deletions

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"concat", "concat",
"coprime", "coprime",
"elems", "elems",
"Factorisation",
"factorise",
"foldl" "foldl"
] ]
} }

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{-
https://projecteuler.net/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.
-}
module Main where
main :: IO ()
main = print ans
ans :: Integer
ans = sum $ allNumbersUnder 1000
isMultipleOf :: Integral a => a -> a -> Bool
isMultipleOf n x = x `rem` n == 0
all3sUnder :: Integral a => a -> [a]
all3sUnder n = filter (isMultipleOf 3) [1..n-1]
all5sUnder :: Integral a => a -> [a]
all5sUnder n = filter (isMultipleOf 5) [1..n-1]
allXsUnderN :: Integral a => a -> a -> [a]
allXsUnderN x n = filter (isMultipleOf x) [1..n-1]
allNumbersUnder :: Integral a => a -> [a]
allNumbersUnder l = allXsUnderN 3 l <> allXsUnderN 5 l

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{-
https://projecteuler.net/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.
-}
module Main where
main :: IO ()
main = print ans
ans = sum $ filter even $ takeWhile(< 4_000_000) fibs
fibs = 1 : 2 : zipWith (+) fibs (tail fibs)

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{-
https://projecteuler.net/problem=3
The prime factors of 13195 are 5, 7, 13, and 29.
What is the largest prime factor of the number 600851475143?
-}
module Main where
import Math.NumberTheory.Primes (Prime (unPrime),
UniqueFactorisation (factorise),
primes)
main :: IO ()
main = print ans
ans :: Int
ans = last $ filter (isFactor bigNum) primes'
primes' :: [Int]
primes' = takeWhile (< sqrt') $ map unPrime primes
where
sqrt' = floor $ sqrt (toEnum bigNum)
bigNum :: Int
bigNum = 600851475143
isFactor :: Int -> Int -> Bool
isFactor x n = x `rem` n == 0
ans' :: [Int]
ans' = map (unPrime . fst) $ factorise (fromEnum bigNum)
-- [(Prime 71,1),(Prime 839,1),(Prime 1471,1),(Prime 6857,1)]
-- [71,839,1471,6857]