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-- https://projecteuler.net/problem=1 | ||
-- Add all the natural numbers below one thousand that are multiples of 3 or 5. | ||
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getMultiples = [x | x <- [0..999], x `mod` 3 == 0 || x `mod` 5 == 0] | ||
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answer = sum getMultiples |
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--https://projecteuler.net/problem=2 | ||
--By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms. | ||
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fibs = 0 : 1 : zipWith (+) fibs (tail fibs) | ||
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evenfibs = [x | x <- fibs, mod x 2 == 0] | ||
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answer = sum $ takeWhile(<=4000000) evenfibs |
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--https://projecteuler.net/problem=3 | ||
--What is the largest prime factor of the number 600851475143 ? | ||
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primeFactors :: Integer -> [Integer] | ||
primeFactors 1 = [] | ||
primeFactors n = let prime = head $ dropWhile ((/= 0) . mod n) [2 .. n] | ||
in (prime :) $ primeFactors $ div n prime | ||
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answer = last $ primeFactors 600851475143 |
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-- https://projecteuler.net/problem=4 | ||
-- Find the largest palindrome made from the product of two 3-digit numbers. | ||
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products = [x*y | x <- [100..999], y <- [100..999]] | ||
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palindromes :: (Integral a) => [a] -> [a] | ||
palindromes [] = [] | ||
palindromes (x:xs) | ||
| (show x) == reverse (show x) = x : palindromes xs | ||
| otherwise = palindromes xs | ||
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answer = maximum (palindromes products) | ||
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-- https://projecteuler.net/problem=5 | ||
-- What is the smallest number divisible by each of the numbers 1 to 20? | ||
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divisible :: (Integral a) => a -> Bool | ||
divisible n = all (==0) $ map (mod n) [1..20] | ||
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answer = head [x | x <- [1..] , divisible x] |
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-- https://projecteuler.net/problem=6 | ||
-- What is the difference between the sum of the squares and the square of the sums? | ||
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sumOfSquares = sum $ map (^2) [1..100] | ||
squareOfSum = (^2) $ sum [1..100] | ||
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answer = squareOfSum - sumOfSquares |
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-- https://projecteuler.net/problem=7 | ||
-- Find the 10001st prime. | ||
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isPrime :: (Integral a) => a -> Bool | ||
isPrime n | ||
| n <= 1 = False | ||
| otherwise = 0 `notElem` map (mod n) [2..n-1] | ||
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primes = [x | x <- [2..] , isPrime x] | ||
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answer = last $ take 10001 primes |
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-- https://projecteuler.net/problem=9 | ||
-- Find the only Pythagorean triplet, {a, b, c}, for which a + b + c = 1000. | ||
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set = [0..1000] | ||
triplets = [(a,b,c) | a <- set, b <- set, c <- set, a + b + c == 1000, a < b, b < c] | ||
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answer = [(a,b,c) | (a,b,c) <- triplets, (a^2) + (b^2) == (c^2)] |
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-- https://projecteuler.net/problem=10 | ||
-- Calculate the sum of all the primes below two million. | ||
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isPrime :: (Integral a) => a -> Bool | ||
isPrime n | ||
| n <= 1 = False | ||
| otherwise = 0 `notElem` map (mod n) [2..n-1] | ||
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primes = [x | x <- [2..2000000] , isPrime x] | ||
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answer = sum primes |
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import Data.List | ||
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triangleNumber :: (Integral a) => a -> a | ||
triangleNumber n = foldl (+) 0 [1..n] | ||
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primeFactors :: Integer -> [Integer] | ||
primeFactors 1 = [] | ||
primeFactors n = let prime = head $ dropWhile ((/= 0) . mod n) [2 .. n] | ||
in (prime :) $ primeFactors $ div n prime | ||
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factorCount :: Integer -> Int | ||
factorCount n = foldl (*) 1 $ map (1+) $ map (length) $ group $ primeFactors n | ||
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answer :: Integer -> Integer | ||
answer n | ||
| (factorCount $ triangleNumber n) > 500 = n | ||
| otherwise = answer n |
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-- https://projecteuler.net/problem=13 | ||
-- Find the first ten digits of the sum of one-hundred 50-digit numbers. (Given in input.txt) | ||
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import System.IO | ||
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main = do | ||
handle <- openFile "input.txt" ReadMode | ||
contents <- hGetContents handle | ||
let bigNumbers = map read (lines contents)::[Integer] | ||
let bigSum = sum bigNumbers | ||
let answer = take 10 (show bigSum) | ||
putStr answer | ||
hClose handle |