haskell: add [p12, p17]

Signed-off-by: Amneesh Singh <natto@weirdnatto.in>

haskell/Lib.hs

@@ -1,19 +1,39 @@
-module Lib (fib, primes, primeFactors) where
+module Lib
+  ( factors,
+    fib,
+    primes,
+    primeFactors,
+    sumOfDigits,
+  )
+where
+
+import Data.List (nub)
+
+factors :: Integral a => a -> [a]
+factors n = concat [if mod n f == 0 then nub [f, div n f] else [] | f <- [1 .. flsqrt n]]
 
 fib :: [Integer]
 fib = 1 : 2 : zipWith (+) fib (tail fib)
 
-isPrime :: Integer -> Bool
-isPrime n = n > 1 && null [[] | k <- [2 .. (floor $ sqrt $ fromIntegral n)], mod n k == 0]
+flsqrt :: Integral a => a -> a
+flsqrt n = floor $ sqrt $ fromIntegral n
+
+isPrime :: Integral a => a -> Bool
+isPrime n = n > 1 && null [[] | k <- [2 .. flsqrt n], mod n k == 0]
 
 primes :: [Integer]
 primes = 2 : filter isPrime [3, 4 ..]
 
-primeFactors :: Integer -> [Integer]
+primeFactors :: Integral a => a -> [a]
 primeFactors n = genPrimeFactors n 2
   where
-    genPrimeFactors :: Integer -> Integer -> [Integer]
+    genPrimeFactors :: Integral a => a -> a -> [a]
     genPrimeFactors n c
       | c * c > n = [n]
       | mod n c /= 0 = genPrimeFactors n (c + 1)
       | otherwise = c : genPrimeFactors (div n c) c
+
+sumOfDigits :: Integral a => a -> a
+sumOfDigits n
+  | n == 0 = 0
+  | otherwise = mod n 10 + sumOfDigits (div n 10)

haskell/p12.hs

@@ -0,0 +1,10 @@
+import Lib (factors)
+
+main :: IO ()
+main = putStr $ show $ solve 500
+
+solve :: Int -> Integer
+solve n = head [tn | i <- [1 ..], let tn = triangleNumber i, (length . factors) tn > n]
+
+triangleNumber :: Int -> Integer
+triangleNumber n = toInteger $ div (n * (n + 1)) 2

haskell/p13.hs

@@ -0,0 +1,106 @@
+main :: IO ()
+main = putStr $ take 10 $ show $ sum nums
+
+nums :: [Integer]
+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
+  ]

haskell/p14.hs

@@ -0,0 +1,15 @@
+import Data.Ord (comparing)
+import Data.List (maximumBy)
+
+main :: IO ()
+main = putStr $ show $ fst $ maximumBy (comparing snd) $ zip range $ map collatz range
+  where
+    range :: [ Int ]
+    range = [1 .. 10 ^ 6 - 1]
+
+-- eh 12s isn't much
+collatz :: Int -> Int
+collatz n
+  | n == 1 = 1
+  | even n = 1 + collatz (div n 2)
+  | otherwise = 1 + collatz (3 * n + 1)

haskell/p15.hs

@@ -0,0 +1,3 @@
+-- formula based approach i.e, 40C20
+main :: IO ()
+main = putStr $ show $ div (product [21..40]) (product [1..20])

haskell/p16.hs

@@ -0,0 +1,4 @@
+import Lib (sumOfDigits)
+
+main :: IO ()
+main = putStr $ show $ sumOfDigits (2^1000 :: Integer)

haskell/p17.hs

@@ -0,0 +1,22 @@
+--The answer is written for numbers <= 1000
+
+main :: IO ()
+main = putStr $ show $ solve 1000
+
+solve :: Int -> Int
+solve n = sum $ map (length . numWord) [1 .. n]
+
+numWord :: Int -> [Char]
+numWord n
+  | n == 0 = ""
+  | n == 1000 = "onethousand"
+  | n < 20 = ones !! (n - 1)
+  | n < 100 = tens !! (div n 10 - 2) ++ numWord (mod n 10)
+  | mod n 100 == 0 = numWord (div n 100) ++ "hundred"
+  | otherwise = numWord (div n 100) ++ "hundredand" ++ numWord (mod n 100)
+  where
+    tens :: [[Char]]
+    tens = ["twenty", "thirty", "forty", "fifty", "sixty", "seventy", "eighty", "ninety"]
+
+    ones :: [[Char]]
+    ones = ["one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten", "eleven", "twelve", "thirteen", "fourteen", "fifteen", "sixteen", "seventeen", "eighteen", "nineteen"]