「HaskellでProject Euler(Problem 13～15)」ブログ用

euler13.hs

main = print $ sumHead 10

sumHead :: (Read a, Num a) => Int -> a
sumHead n = read $ take n $ show $ sum nums

nums = [
 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]

euler14-1.hs

import Data.Ord (comparing)
import Data.List (maximumBy)

main = print $ maxCollatz 999999

maxCollatz :: Integral a => a -> a
maxCollatz n = last $ maximumBy (comparing length) $ map collatz [n,(n-1)..1]

-- nからはじまるコラッツ数列(逆順)
collatz :: Integral a => a -> [a]
collatz n = collatz' n [n]
  where
    collatz' 1 ns = ns
    collatz' n ns = collatz' next $ next:ns
      where next | even n    = n `div` 2
                 | otherwise = 3 * n + 1

euler14-2.hs

import Data.Ord (comparing)
import Data.List (maximumBy)

main = print $ maxCollatz 999999

maxCollatz :: Integral a => a -> a
maxCollatz n = last $ maxCollatz' [] n
  where
    maxCollatz' m current
      | current <= 0 = m
      | processed    = maxCollatz' m next
      | otherwise    = maxCollatz' (maximumBy (comparing length) [m, collatz current]) next
        where
          -- 2倍した値が n 以下であれば、すでにcurrentを含むコラッツ数列を作成済みであり、
          -- currentから始まるコラッツ数列がmより長くは成り得ないため処理を省く
          processed = current * 2 <= n
          next = current - 1

-- nから始まるコラッツ数列(逆順)
collatz :: Integral a => a -> [a]
collatz n = collatz' n [n]
  where
    collatz' 1 ns = ns
    collatz' n ns = collatz' next $ next:ns
      where next | even n    = n `div` 2
                 | otherwise = 3 * n + 1

euler14-3.hs

main = print $ maxCollatz 999999

maxCollatz :: Integral a => a -> a
maxCollatz n = snd $ foldl process (0, 0) [n, n-1..1]
  where
    process m n' | processed = m
                 | otherwise = max m (collatz n', n')
      where
        -- 2倍した値が n 以下であれば、すでにn'を含むコラッツ数列を作成済みであり、
        -- n'から始まるコラッツ数列がmより長くは成り得ないため処理を省く
        processed = n' * 2 <= n

-- nからはじまるコラッツ数列の長さを返す
collatz :: (Integral a, Enum b, Num b) => a -> b
collatz n = collatz' n 0
  where
    collatz' 1 l = succ l
    collatz' n l = collatz' next $ succ l
      where next | even n    = n `div` 2
                 | otherwise = 3 * n + 1

euler15-1.hs

import Data.List (groupBy)
import Data.Maybe (catMaybes)

main = print $ route 20 20

route :: (Num a, Num b, Num c, Ord a, Ord b) => a -> b -> c
route row line = route' [(1, (0, 0))]
  where
    route' [(n, p)] | p == (row, line) = n
    route' rs =
          let rs' = catMaybes $ concat $ map (\(n, (r, l)) -> [(proceed n (r+1) l), (proceed n r (l+1))]) rs
          in route' $ summarize rs'
    proceed n r l | (r <= row) && (l <= line) = Just (n, (r, l))
                  | otherwise                 = Nothing

summarize :: (Num a, Eq b) => [(a, b)] -> [(a, b)]
summarize rs = map (foldl1 (\(n1, p) (n2, _) -> (n1+n2, p))) $ groupBy (\(_, p1) (_, p2) -> p1 == p2) rs

euler15-2.hs

main = print $ route 20 20

-- 二項係数を用いて格子経路を算出
route :: Integral a => a -> a -> a
route x y = fact (x + y) `div` ((fact x) * (fact y))

fact :: (Eq a, Num a) => a -> a
fact 0 = 1
fact n = n * fact (n - 1)