module Problems001to010 where

import Data.Char
import Data.List

import Util


-- 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.
problem001 :: String
problem001 = show . sum $ multiplesof3or5upto1000
    where
        multiplesof3or5upto1000 = [x | x <- [1..999], isMultiple x]
        isMultiple x = x `mod` 3 == 0 || x `mod ` 5 == 0
   
       
-- 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.
problem002 :: String
problem002 = show . sum $ evenFibNumbersBelow4Mio
    where
        evenFibNumbersBelow4Mio = filter even fibBelow4Mio
        fibBelow4Mio = takeWhile under4Mio fibonacci
        under4Mio n = n < 4000000
        
       
-- The prime factors of 13195 are 5, 7, 13 and 29.
-- What is the largest prime factor of the number 600851475143 ?
problem003 :: String
problem003 = show . last $ primeFactors 600851475143


-- A palindromic number reads the same both ways. 
-- The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.
-- Find the largest palindrome made from the product of two 3-digit numbers.
problem004 :: String
problem004 = show . maximum $ palindromes
    where
        palindromes = [n | x <- [100..999], y <- [100..999], let n = x*y, isPalindrome n]       
        isPalindrome number = let s = show number in s == reverse s
        

-- 2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
-- What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
problem005 :: String
problem005 = show $ foldl lcm 1 [11..20] 
        

-- The sum of the squares of the first ten natural numbers is,
-- 1^2 + 2^2 + ... + 10^2 = 385
-- The square of the sum of the first ten natural numbers is,
-- (1 + 2 + ... + 10)^2 = 55^2 = 3025
-- Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 - 385 = 2640.
-- Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.
problem006 :: String
problem006 = show (squareOfSum numbers - sumOfSquares numbers) 
    where 
        numbers = [1..100]
        sumOfSquares ns = sum (map square ns)
        squareOfSum ns = square . sum $ ns
        square x = x ^ 2


-- By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
-- What is the 10 001st prime number?
problem007 :: String
problem007 = show $ primes [2..] !! 10000


-- Find the greatest product of five consecutive digits in the 1000-digit number.
-- 73167176531330624919225119674426574742355349194934
-- 96983520312774506326239578318016984801869478851843
-- 85861560789112949495459501737958331952853208805511
-- 12540698747158523863050715693290963295227443043557
-- 66896648950445244523161731856403098711121722383113
-- 62229893423380308135336276614282806444486645238749
-- 30358907296290491560440772390713810515859307960866
-- 70172427121883998797908792274921901699720888093776
-- 65727333001053367881220235421809751254540594752243
-- 52584907711670556013604839586446706324415722155397
-- 53697817977846174064955149290862569321978468622482
-- 83972241375657056057490261407972968652414535100474
-- 82166370484403199890008895243450658541227588666881
-- 16427171479924442928230863465674813919123162824586
-- 17866458359124566529476545682848912883142607690042
-- 24219022671055626321111109370544217506941658960408
-- 07198403850962455444362981230987879927244284909188
-- 84580156166097919133875499200524063689912560717606
-- 05886116467109405077541002256983155200055935729725
-- 71636269561882670428252483600823257530420752963450
problem008 :: String
problem008 = show . maximum $ products
    where
        products = map (product . convert . take 5) extract
        convert = map digitToInt 
        extract = tails dataString
        dataString = 
              "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843"
         ++ "8586156078911294949545950173795833195285320880551112540698747158523863050715693290963295227443043557"
         ++ "6689664895044524452316173185640309871112172238311362229893423380308135336276614282806444486645238749"
         ++ "3035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776"
         ++ "6572733300105336788122023542180975125454059475224352584907711670556013604839586446706324415722155397"
         ++ "5369781797784617406495514929086256932197846862248283972241375657056057490261407972968652414535100474"
         ++ "8216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586"
         ++ "1786645835912456652947654568284891288314260769004224219022671055626321111109370544217506941658960408"
         ++ "0719840385096245544436298123098787992724428490918884580156166097919133875499200524063689912560717606"
         ++ "0588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450"


-- A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
-- a^2 + b^2 = c^2
-- For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
-- There exists exactly one Pythagorean triplet for which a + b + c = 1000.
-- Find the product abc. 
problem009 :: String
problem009 = show . head $ [a*b*c | a<-[1..333], b<-[1..500], let c = 1000 - a - b, a*a + b*b == c*c]


-- The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
-- Find the sum of all the primes below two million.
problem010 :: String
problem010 = show . sum $ primesUpTo 2000000













