Add Haskell solutions for Problems 13, 14, 16, 20

Haskell/p013.hs

@@ -0,0 +1,212 @@
+-- Work out the first ten digits of the sum of the following one-hundred 50-digit numbers.
+--
+-- 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
+
+--firstDigitsSum :: (Show a, Read a, Integral a) => Int -> [a] -> a
+firstDigitsSum :: Int -> [Integer] -> Integer
+firstDigitsSum n xs = read $ take n $ show $ sum xs
+
+main = do
+    let result = firstDigitsSum 10 [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
+                                   ]
+
+    putStrLn $ "Project Euler, Problem 13\n"
+        ++ "Answer: " ++ (show result)

Haskell/p014.hs

@@ -0,0 +1,29 @@
+-- The following iterative sequence is defined for the set of positive integers:
+--
+-- n → n/2 (n is even)
+-- n → 3n + 1 (n is odd)
+--
+-- Using the rule above and starting with 13, we generate the following sequence:
+--
+-- 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
+--
+-- It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem),
+-- it is thought that all starting numbers finish at 1.
+--
+-- Which starting number, under one million, produces the longest chain?
+--
+-- NOTE: Once the chain starts the terms are allowed to go above one million.
+
+collatz :: (Integral a) => a -> [a]
+collatz n
+    | n == 1 = [1]
+    | n `mod` 2 == 0 = n:(collatz $ n `div` 2)
+    | otherwise = n:(collatz $ 3 * n + 1)
+
+maxCollatzLength :: Int -> Int
+maxCollatzLength n = snd $ maximum $ zip [ length (collatz x) | x <- [1..n-1] ] [1..n-1]
+
+main = do
+    let result = maxCollatzLength 1000000
+    putStrLn $ "Project Euler, Problem 14\n"
+        ++ "Answer: " ++ (show result)

Haskell/p016.hs

@@ -0,0 +1,10 @@
+-- 2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.
+--
+-- What is the sum of the digits of the number 2^1000?
+
+import ProjectEuler (digitSum)
+
+main = do
+    let result = digitSum $ 2 ^ 1000
+    putStrLn $ "Project Euler, Problem 10\n"
+        ++ "Answer: " ++ (show result)

Haskell/p020.hs

@@ -0,0 +1,17 @@
+-- n! means n × (n − 1) × ... × 3 × 2 × 1
+--
+-- For example, 10! = 10 × 9 × ... × 3 × 2 × 1 = 3628800,
+-- and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.
+--
+-- Find the sum of the digits in the number 100!
+
+import ProjectEuler (digitSum)
+
+factorial :: (Integral a) => a -> a
+factorial 0 = 1
+factorial n = n * factorial (n - 1)
+
+main = do
+    let result = digitSum $ factorial 100
+    putStrLn $ "Porject Euler, Problem 20\n"
+        ++ "Answer: " ++ (show result)