# Project Euler: Problem 13

Published: Tue 22 May 2012

In blog.

Problem thirteen from Project Euler is one of those problems that's so simple, I don't understand why it's in the double digits section. The problem reads:

 ```1 2``` ```Work out the first ten digits of the sum of the following one-hundred 50-digit numbers. ```

It then proceeds to list 100 long numbers. I'm not going to paste them here because they are in the code solutions below and I don't want to clog up the “tubez” with more redundant information than I'm about to.

Enough of my jibber-jabber. Here is my Haskell solution first (trying to change things up here):

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105``` ```module Main where main :: IO() main = do print . take 10 . show \$ sum big_number where big_number = [ 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 ] ```

followed by my Python solution:

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113``` ```#!/usr/bin/python """ code solution for project euler's problem #13 in python. """ from __future__ import print_function def print_10(number): print(str(number)[0:10]) if __name__ == "__main__": big_number = [ 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] print_10(sum(big_number)) ```

Scala:

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110``` ```import BigInt._ object problem_13 { def main (args : Array[String]){ val big_number = List("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") map {BigInt(_)} val sums = big_number sum val su = sums toString val su10 = su take 10 println(su10) } } ```

Some of you may be wondering, “Why a Scala solution?” To which I respond, “Why not?” Because that's a little short, I'll add that it has something to do with Scala starting to gain traction in the industry and me seeing if I would like to get paid to program in it.

The solution, in all three languages, is pretty simple. The recipe essentially says, “Put all numbers into a list. Get the sum of that list, turn that number into a string, and get the first 10 characters of that string.”

Times:

Haskell (compiled) : real 0m0.004s

Haskell (runghc) : real 0m0.314s

Python : real 0m0.059s

Scala (compiled) : real 0m0.757s

For the most part it's pretty standard in these tests to see performance times such that Haskell (compiled) < Python < Haskell (runghc). Java and Perl usually fall somewhere between the Haskell (compiled) and Python, in that order. To see Scala be 2x slower than Haskell (runghc) was a shocker. The only thing that makes sense to me for the slowdown is having to use the BigInt library. That is probably the biggest thing I took away from these time tests - if I want to do REALLY large number crunching and performance DOES matter, JVM-based languages might not be the best option.

A few thoughts on Scala: