-- (C) Copyright Collin Doering 2014 -- -- This program is free software: you can redistribute it and/or modify -- it under the terms of the GNU General Public License as published by -- the Free Software Foundation, either version 3 of the License, or -- (at your option) any later version. -- -- This program is distributed in the hope that it will be useful, -- but WITHOUT ANY WARRANTY; without even the implied warranty of -- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -- GNU General Public License for more details. -- -- You should have received a copy of the GNU General Public License -- along with this program. If not, see . -- File: ProjectEuler.hs -- Author: Collin J. Doering -- Date: May 18, 2014 ----------------------------------------------------------------------------------------------- -- Problem 4: Largest palindrome product -- ----------------------------------------------------------------------------------------------- isPalindrome :: (Eq a) => [a] -> Bool isPalindrome x | mod len 2 == 0 && take (div len 2) x == reverse (drop (div len 2) x) = True | otherwise = False where len = length x largestPalidromeOfSize :: Int -> Int largestPalidromeOfSize n = foldr max 0 . map (uncurry (*)) . filter (isPalindrome . show . uncurry (*)) $ [ (x,y) | x <- [s,s-1..t], y <- [s,s-1..t] ] where s = (10 ^ n) - 1 t = s `quot` 2 ----------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------- -- Problem 5: Smallest multiple -- ----------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------- -- Problem 7: 10001 prime -- ----------------------------------------------------------------------------------------------- isPrime :: Integral b => b -> Bool isPrime n = all (not . (== 0) . (n `mod`)) [2..quot n 2] nthPrime :: Integral a => Int -> a nthPrime n = [ x | x <- [2..], isPrime x] !! n ----------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------- -- Problem 8: Largest product in a series -- ----------------------------------------------------------------------------------------------- p8Series :: Integer p8Series = read . concat $ [ "73167176531330624919225119674426574742355349194934" , "96983520312774506326239578318016984801869478851843" , "85861560789112949495459501737958331952853208805511" , "12540698747158523863050715693290963295227443043557" , "66896648950445244523161731856403098711121722383113" , "62229893423380308135336276614282806444486645238749" , "30358907296290491560440772390713810515859307960866" , "70172427121883998797908792274921901699720888093776" , "65727333001053367881220235421809751254540594752243" , "52584907711670556013604839586446706324415722155397" , "53697817977846174064955149290862569321978468622482" , "83972241375657056057490261407972968652414535100474" , "82166370484403199890008895243450658541227588666881" , "16427171479924442928230863465674813919123162824586" , "17866458359124566529476545682848912883142607690042" , "24219022671055626321111109370544217506941658960408" , "07198403850962455444362981230987879927244284909188" , "84580156166097919133875499200524063689912560717606" , "05886116467109405077541002256983155200055935729725" , "71636269561882670428252483600823257530420752963450" ] largestProduct :: Integer -> Integer largestProduct n = foldr max 0 . flip fiveProducts [] $ [ read [x] | x <- show n] fiveProducts :: Num a => [a] -> [a] -> [a] fiveProducts [] acc = acc fiveProducts (a:b:c:d:e:f:g:h:i:j:k:l:m:xs) acc = fiveProducts (b:c:d:e:f:g:h:i:j:k:l:m:xs) (a * b * c * d * e * f * g * h * i * j * k * l * m : acc) fiveProducts _ acc = acc ----------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------- -- Problem 13: Large Sum -- ----------------------------------------------------------------------------------------------- numsToSum = [ 37107287533902102798797998220837590246510135740250 , 46376937677490009712648124896970078050417018260538 , 74324986199524741059474233309513058123726617309629 , 91942213363574161572522430563301811072406154908250 , 23067588207539346171171980310421047513778063246676 , 89261670696623633820136378418383684178734361726757 , 28112879812849979408065481931592621691275889832738 , 44274228917432520321923589422876796487670272189318 , 47451445736001306439091167216856844588711603153276 , 70386486105843025439939619828917593665686757934951 , 62176457141856560629502157223196586755079324193331 , 64906352462741904929101432445813822663347944758178 , 92575867718337217661963751590579239728245598838407 , 58203565325359399008402633568948830189458628227828 , 80181199384826282014278194139940567587151170094390 , 35398664372827112653829987240784473053190104293586 , 86515506006295864861532075273371959191420517255829 , 71693888707715466499115593487603532921714970056938 , 54370070576826684624621495650076471787294438377604 , 53282654108756828443191190634694037855217779295145 , 36123272525000296071075082563815656710885258350721 , 45876576172410976447339110607218265236877223636045 , 17423706905851860660448207621209813287860733969412 , 81142660418086830619328460811191061556940512689692 , 51934325451728388641918047049293215058642563049483 , 62467221648435076201727918039944693004732956340691 , 15732444386908125794514089057706229429197107928209 , 55037687525678773091862540744969844508330393682126 , 18336384825330154686196124348767681297534375946515 , 80386287592878490201521685554828717201219257766954 , 78182833757993103614740356856449095527097864797581 , 16726320100436897842553539920931837441497806860984 , 48403098129077791799088218795327364475675590848030 , 87086987551392711854517078544161852424320693150332 , 59959406895756536782107074926966537676326235447210 , 69793950679652694742597709739166693763042633987085 , 41052684708299085211399427365734116182760315001271 , 65378607361501080857009149939512557028198746004375 , 35829035317434717326932123578154982629742552737307 , 94953759765105305946966067683156574377167401875275 , 88902802571733229619176668713819931811048770190271 , 25267680276078003013678680992525463401061632866526 , 36270218540497705585629946580636237993140746255962 , 24074486908231174977792365466257246923322810917141 , 91430288197103288597806669760892938638285025333403 , 34413065578016127815921815005561868836468420090470 , 23053081172816430487623791969842487255036638784583 , 11487696932154902810424020138335124462181441773470 , 63783299490636259666498587618221225225512486764533 , 67720186971698544312419572409913959008952310058822 , 95548255300263520781532296796249481641953868218774 , 76085327132285723110424803456124867697064507995236 , 37774242535411291684276865538926205024910326572967 , 23701913275725675285653248258265463092207058596522 , 29798860272258331913126375147341994889534765745501 , 18495701454879288984856827726077713721403798879715 , 38298203783031473527721580348144513491373226651381 , 34829543829199918180278916522431027392251122869539 , 40957953066405232632538044100059654939159879593635 , 29746152185502371307642255121183693803580388584903 , 41698116222072977186158236678424689157993532961922 , 62467957194401269043877107275048102390895523597457 , 23189706772547915061505504953922979530901129967519 , 86188088225875314529584099251203829009407770775672 , 11306739708304724483816533873502340845647058077308 , 82959174767140363198008187129011875491310547126581 , 97623331044818386269515456334926366572897563400500 , 42846280183517070527831839425882145521227251250327 , 55121603546981200581762165212827652751691296897789 , 32238195734329339946437501907836945765883352399886 , 75506164965184775180738168837861091527357929701337 , 62177842752192623401942399639168044983993173312731 , 32924185707147349566916674687634660915035914677504 , 99518671430235219628894890102423325116913619626622 , 73267460800591547471830798392868535206946944540724 , 76841822524674417161514036427982273348055556214818 , 97142617910342598647204516893989422179826088076852 , 87783646182799346313767754307809363333018982642090 , 10848802521674670883215120185883543223812876952786 , 71329612474782464538636993009049310363619763878039 , 62184073572399794223406235393808339651327408011116 , 66627891981488087797941876876144230030984490851411 , 60661826293682836764744779239180335110989069790714 , 85786944089552990653640447425576083659976645795096 , 66024396409905389607120198219976047599490197230297 , 64913982680032973156037120041377903785566085089252 , 16730939319872750275468906903707539413042652315011 , 94809377245048795150954100921645863754710598436791 , 78639167021187492431995700641917969777599028300699 , 15368713711936614952811305876380278410754449733078 , 40789923115535562561142322423255033685442488917353 , 44889911501440648020369068063960672322193204149535 , 41503128880339536053299340368006977710650566631954 , 81234880673210146739058568557934581403627822703280 , 82616570773948327592232845941706525094512325230608 , 22918802058777319719839450180888072429661980811197 , 77158542502016545090413245809786882778948721859617 , 72107838435069186155435662884062257473692284509516 , 20849603980134001723930671666823555245252804609722 , 53503534226472524250874054075591789781264330331690 ] first10DigitsOfSum :: [Integer] -> Integer first10DigitsOfSum = read . take 10 . show . sum 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