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Add comments to solution functions in SolutionsTo50.hs #4

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24 changes: 24 additions & 0 deletions src/SolutionsTo50.hs
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Original file line number Diff line number Diff line change
Expand Up @@ -29,12 +29,21 @@ solutionsTo50_ n = case n of
18 -> solution18
_ -> putStrLn "Solution not present in program"

-- | Solves Project Euler Problem 1:
-- Find the sum of all the multiples of 3 or 5 below 1000.
-- This is solved by taking the union of multiples of 3 and 5 and summing them.
solution1 :: Integer
solution1 = sum $ union [3,6..999] [5,10..999]

-- | Solves Project Euler 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.
solution2 :: Integer
solution2 = sum . filter even $ takeWhile (<= 4000000) fibs

-- | Solves Project Euler Problem 3:
-- Find the largest prime factor of the number 600851475143.
-- This is solved by generating prime factors and finding the maximum.
solution3 :: Integer
solution3 = let primes = 2 : filter (null . tail . primeFactors) [3,5..]
primeFactors n = factor n primes
Expand All @@ -44,27 +53,42 @@ solution3 = let primes = 2 : filter (null . tail . primeFactors) [3,5..]
| otherwise = factor n ps
in maximum $ primeFactors 600851475143

-- | Solves Project Euler Problem 4:
-- Find the largest palindrome made from the product of two 3-digit numbers.
-- This is solved by iterating through products of 3-digit numbers and checking for palindromes.
solution4 :: Integer
solution4 = maximum [x | y<-[999,998..100], z<-[999,998..y], let x = y*z, isPalindromic x]

-- | Solves Project Euler Problem 5:
-- What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
-- This is solved by finding the least common multiple (LCM) of numbers from 1 to 20.
solution5 :: Integer
solution5 = foldr1 lcm [1..20]

-- | Solves Project Euler Problem 6:
-- Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.
solution6 :: Integer
solution6 = sumSquare - squareSums
where squareSums = sum $ map (^2) [1..100]
sumSquare = (^2) $ sum [1..100]

-- | Solves Project Euler Problem 8:
-- Find the thirteen adjacent digits in the 1000-digit number that have the greatest product.
solution8 :: Integer
solution8 = maximum . map product . takeWhile (\l -> length l >= 13) . map (take 13) . tails $ digitArr
where digitArr = map digitToInt digitString

-- | Solves Project Euler Problem 13:
-- Work out the first ten digits of the sum of the following one hundred 50-digit numbers
-- (stored in p13numbers.txt).
solution13 = do
numbers <- fmap ( map read . lines ) (readFile "p13numbers.txt")
putStrLn . take 10 . show . sum $ numbers



-- | Solves Project Euler Problem 18:
-- Find the maximum total from top to bottom of the triangle (stored in triangle.txt).
solution18 = do
a <- answer
putStrLn $ show a
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