Comments on: Project Euler: Problem 13 http://www.geekality.net/2009/10/04/project-euler-problem-13/ With a hint of Social Ineptitude Tue, 07 Feb 2012 09:05:01 +0000 hourly 1 http://wordpress.org/?v=3.3.1 By: Ed http://www.geekality.net/2009/10/04/project-euler-problem-13/#comment-1401 Ed Sat, 09 Oct 2010 12:40:57 +0000 http://www.geekality.net/?p=612#comment-1401 He hasn't missed the point in this case. The idea of ProjectEuler.Net is to solve the problems programmatically using the power of a computer to your advantage. Whilst methods that save time in terms of computational cycles are better, the method you mention would be more suited to solving the problem by hand. A modern PC is capable of handling massive numbers extremely fast. I solved this problem in a similar fashion to the method show above but without the need for an external library and the code ran in 7ms: private static string Solution13() { List numbers = new List { double.Parse("37107287533902102798797998220837590246510135740250"), double.Parse("46376937677490009712648124896970078050417018260538"), double.Parse("74324986199524741059474233309513058123726617309629"), double.Parse("91942213363574161572522430563301811072406154908250"), double.Parse("23067588207539346171171980310421047513778063246676"), double.Parse("89261670696623633820136378418383684178734361726757"), double.Parse("28112879812849979408065481931592621691275889832738"), double.Parse("44274228917432520321923589422876796487670272189318"), double.Parse("47451445736001306439091167216856844588711603153276"), double.Parse("70386486105843025439939619828917593665686757934951"), double.Parse("62176457141856560629502157223196586755079324193331"), double.Parse("64906352462741904929101432445813822663347944758178"), double.Parse("92575867718337217661963751590579239728245598838407"), double.Parse("58203565325359399008402633568948830189458628227828"), double.Parse("80181199384826282014278194139940567587151170094390"), double.Parse("35398664372827112653829987240784473053190104293586"), double.Parse("86515506006295864861532075273371959191420517255829"), double.Parse("71693888707715466499115593487603532921714970056938"), double.Parse("54370070576826684624621495650076471787294438377604"), double.Parse("53282654108756828443191190634694037855217779295145"), double.Parse("36123272525000296071075082563815656710885258350721"), double.Parse("45876576172410976447339110607218265236877223636045"), double.Parse("17423706905851860660448207621209813287860733969412"), double.Parse("81142660418086830619328460811191061556940512689692"), double.Parse("51934325451728388641918047049293215058642563049483"), double.Parse("62467221648435076201727918039944693004732956340691"), double.Parse("15732444386908125794514089057706229429197107928209"), double.Parse("55037687525678773091862540744969844508330393682126"), double.Parse("18336384825330154686196124348767681297534375946515"), double.Parse("80386287592878490201521685554828717201219257766954"), double.Parse("78182833757993103614740356856449095527097864797581"), double.Parse("16726320100436897842553539920931837441497806860984"), double.Parse("48403098129077791799088218795327364475675590848030"), double.Parse("87086987551392711854517078544161852424320693150332"), double.Parse("59959406895756536782107074926966537676326235447210"), double.Parse("69793950679652694742597709739166693763042633987085"), double.Parse("41052684708299085211399427365734116182760315001271"), double.Parse("65378607361501080857009149939512557028198746004375"), double.Parse("35829035317434717326932123578154982629742552737307"), double.Parse("94953759765105305946966067683156574377167401875275"), double.Parse("88902802571733229619176668713819931811048770190271"), double.Parse("25267680276078003013678680992525463401061632866526"), double.Parse("36270218540497705585629946580636237993140746255962"), double.Parse("24074486908231174977792365466257246923322810917141"), double.Parse("91430288197103288597806669760892938638285025333403"), double.Parse("34413065578016127815921815005561868836468420090470"), double.Parse("23053081172816430487623791969842487255036638784583"), double.Parse("11487696932154902810424020138335124462181441773470"), double.Parse("63783299490636259666498587618221225225512486764533"), double.Parse("67720186971698544312419572409913959008952310058822"), double.Parse("95548255300263520781532296796249481641953868218774"), double.Parse("76085327132285723110424803456124867697064507995236"), double.Parse("37774242535411291684276865538926205024910326572967"), double.Parse("23701913275725675285653248258265463092207058596522"), double.Parse("29798860272258331913126375147341994889534765745501"), double.Parse("18495701454879288984856827726077713721403798879715"), double.Parse("38298203783031473527721580348144513491373226651381"), double.Parse("34829543829199918180278916522431027392251122869539"), double.Parse("40957953066405232632538044100059654939159879593635"), double.Parse("29746152185502371307642255121183693803580388584903"), double.Parse("41698116222072977186158236678424689157993532961922"), double.Parse("62467957194401269043877107275048102390895523597457"), double.Parse("23189706772547915061505504953922979530901129967519"), double.Parse("86188088225875314529584099251203829009407770775672"), double.Parse("11306739708304724483816533873502340845647058077308"), double.Parse("82959174767140363198008187129011875491310547126581"), double.Parse("97623331044818386269515456334926366572897563400500"), double.Parse("42846280183517070527831839425882145521227251250327"), double.Parse("55121603546981200581762165212827652751691296897789"), double.Parse("32238195734329339946437501907836945765883352399886"), double.Parse("75506164965184775180738168837861091527357929701337"), double.Parse("62177842752192623401942399639168044983993173312731"), double.Parse("32924185707147349566916674687634660915035914677504"), double.Parse("99518671430235219628894890102423325116913619626622"), double.Parse("73267460800591547471830798392868535206946944540724"), double.Parse("76841822524674417161514036427982273348055556214818"), double.Parse("97142617910342598647204516893989422179826088076852"), double.Parse("87783646182799346313767754307809363333018982642090"), double.Parse("10848802521674670883215120185883543223812876952786"), double.Parse("71329612474782464538636993009049310363619763878039"), double.Parse("62184073572399794223406235393808339651327408011116"), double.Parse("66627891981488087797941876876144230030984490851411"), double.Parse("60661826293682836764744779239180335110989069790714"), double.Parse("85786944089552990653640447425576083659976645795096"), double.Parse("66024396409905389607120198219976047599490197230297"), double.Parse("64913982680032973156037120041377903785566085089252"), double.Parse("16730939319872750275468906903707539413042652315011"), double.Parse("94809377245048795150954100921645863754710598436791"), double.Parse("78639167021187492431995700641917969777599028300699"), double.Parse("15368713711936614952811305876380278410754449733078"), double.Parse("40789923115535562561142322423255033685442488917353"), double.Parse("44889911501440648020369068063960672322193204149535"), double.Parse("41503128880339536053299340368006977710650566631954"), double.Parse("81234880673210146739058568557934581403627822703280"), double.Parse("82616570773948327592232845941706525094512325230608"), double.Parse("22918802058777319719839450180888072429661980811197"), double.Parse("77158542502016545090413245809786882778948721859617"), double.Parse("72107838435069186155435662884062257473692284509516"), double.Parse("20849603980134001723930671666823555245252804609722"), double.Parse("53503534226472524250874054075591789781264330331690") }; double result = numbers.Aggregate((x, y) => x + y); return result.ToString().Substring(0, 11).Replace(".", string.Empty); } He hasn’t missed the point in this case. The idea of ProjectEuler.Net is to solve the problems programmatically using the power of a computer to your advantage. Whilst methods that save time in terms of computational cycles are better, the method you mention would be more suited to solving the problem by hand. A modern PC is capable of handling massive numbers extremely fast. I solved this problem in a similar fashion to the method show above but without the need for an external library and the code ran in 7ms:

private static string Solution13()
{
List numbers = new List
{
double.Parse(“37107287533902102798797998220837590246510135740250″),
double.Parse(“46376937677490009712648124896970078050417018260538″),
double.Parse(“74324986199524741059474233309513058123726617309629″),
double.Parse(“91942213363574161572522430563301811072406154908250″),
double.Parse(“23067588207539346171171980310421047513778063246676″),
double.Parse(“89261670696623633820136378418383684178734361726757″),
double.Parse(“28112879812849979408065481931592621691275889832738″),
double.Parse(“44274228917432520321923589422876796487670272189318″),
double.Parse(“47451445736001306439091167216856844588711603153276″),
double.Parse(“70386486105843025439939619828917593665686757934951″),
double.Parse(“62176457141856560629502157223196586755079324193331″),
double.Parse(“64906352462741904929101432445813822663347944758178″),
double.Parse(“92575867718337217661963751590579239728245598838407″),
double.Parse(“58203565325359399008402633568948830189458628227828″),
double.Parse(“80181199384826282014278194139940567587151170094390″),
double.Parse(“35398664372827112653829987240784473053190104293586″),
double.Parse(“86515506006295864861532075273371959191420517255829″),
double.Parse(“71693888707715466499115593487603532921714970056938″),
double.Parse(“54370070576826684624621495650076471787294438377604″),
double.Parse(“53282654108756828443191190634694037855217779295145″),
double.Parse(“36123272525000296071075082563815656710885258350721″),
double.Parse(“45876576172410976447339110607218265236877223636045″),
double.Parse(“17423706905851860660448207621209813287860733969412″),
double.Parse(“81142660418086830619328460811191061556940512689692″),
double.Parse(“51934325451728388641918047049293215058642563049483″),
double.Parse(“62467221648435076201727918039944693004732956340691″),
double.Parse(“15732444386908125794514089057706229429197107928209″),
double.Parse(“55037687525678773091862540744969844508330393682126″),
double.Parse(“18336384825330154686196124348767681297534375946515″),
double.Parse(“80386287592878490201521685554828717201219257766954″),
double.Parse(“78182833757993103614740356856449095527097864797581″),
double.Parse(“16726320100436897842553539920931837441497806860984″),
double.Parse(“48403098129077791799088218795327364475675590848030″),
double.Parse(“87086987551392711854517078544161852424320693150332″),
double.Parse(“59959406895756536782107074926966537676326235447210″),
double.Parse(“69793950679652694742597709739166693763042633987085″),
double.Parse(“41052684708299085211399427365734116182760315001271″),
double.Parse(“65378607361501080857009149939512557028198746004375″),
double.Parse(“35829035317434717326932123578154982629742552737307″),
double.Parse(“94953759765105305946966067683156574377167401875275″),
double.Parse(“88902802571733229619176668713819931811048770190271″),
double.Parse(“25267680276078003013678680992525463401061632866526″),
double.Parse(“36270218540497705585629946580636237993140746255962″),
double.Parse(“24074486908231174977792365466257246923322810917141″),
double.Parse(“91430288197103288597806669760892938638285025333403″),
double.Parse(“34413065578016127815921815005561868836468420090470″),
double.Parse(“23053081172816430487623791969842487255036638784583″),
double.Parse(“11487696932154902810424020138335124462181441773470″),
double.Parse(“63783299490636259666498587618221225225512486764533″),
double.Parse(“67720186971698544312419572409913959008952310058822″),
double.Parse(“95548255300263520781532296796249481641953868218774″),
double.Parse(“76085327132285723110424803456124867697064507995236″),
double.Parse(“37774242535411291684276865538926205024910326572967″),
double.Parse(“23701913275725675285653248258265463092207058596522″),
double.Parse(“29798860272258331913126375147341994889534765745501″),
double.Parse(“18495701454879288984856827726077713721403798879715″),
double.Parse(“38298203783031473527721580348144513491373226651381″),
double.Parse(“34829543829199918180278916522431027392251122869539″),
double.Parse(“40957953066405232632538044100059654939159879593635″),
double.Parse(“29746152185502371307642255121183693803580388584903″),
double.Parse(“41698116222072977186158236678424689157993532961922″),
double.Parse(“62467957194401269043877107275048102390895523597457″),
double.Parse(“23189706772547915061505504953922979530901129967519″),
double.Parse(“86188088225875314529584099251203829009407770775672″),
double.Parse(“11306739708304724483816533873502340845647058077308″),
double.Parse(“82959174767140363198008187129011875491310547126581″),
double.Parse(“97623331044818386269515456334926366572897563400500″),
double.Parse(“42846280183517070527831839425882145521227251250327″),
double.Parse(“55121603546981200581762165212827652751691296897789″),
double.Parse(“32238195734329339946437501907836945765883352399886″),
double.Parse(“75506164965184775180738168837861091527357929701337″),
double.Parse(“62177842752192623401942399639168044983993173312731″),
double.Parse(“32924185707147349566916674687634660915035914677504″),
double.Parse(“99518671430235219628894890102423325116913619626622″),
double.Parse(“73267460800591547471830798392868535206946944540724″),
double.Parse(“76841822524674417161514036427982273348055556214818″),
double.Parse(“97142617910342598647204516893989422179826088076852″),
double.Parse(“87783646182799346313767754307809363333018982642090″),
double.Parse(“10848802521674670883215120185883543223812876952786″),
double.Parse(“71329612474782464538636993009049310363619763878039″),
double.Parse(“62184073572399794223406235393808339651327408011116″),
double.Parse(“66627891981488087797941876876144230030984490851411″),
double.Parse(“60661826293682836764744779239180335110989069790714″),
double.Parse(“85786944089552990653640447425576083659976645795096″),
double.Parse(“66024396409905389607120198219976047599490197230297″),
double.Parse(“64913982680032973156037120041377903785566085089252″),
double.Parse(“16730939319872750275468906903707539413042652315011″),
double.Parse(“94809377245048795150954100921645863754710598436791″),
double.Parse(“78639167021187492431995700641917969777599028300699″),
double.Parse(“15368713711936614952811305876380278410754449733078″),
double.Parse(“40789923115535562561142322423255033685442488917353″),
double.Parse(“44889911501440648020369068063960672322193204149535″),
double.Parse(“41503128880339536053299340368006977710650566631954″),
double.Parse(“81234880673210146739058568557934581403627822703280″),
double.Parse(“82616570773948327592232845941706525094512325230608″),
double.Parse(“22918802058777319719839450180888072429661980811197″),
double.Parse(“77158542502016545090413245809786882778948721859617″),
double.Parse(“72107838435069186155435662884062257473692284509516″),
double.Parse(“20849603980134001723930671666823555245252804609722″),
double.Parse(“53503534226472524250874054075591789781264330331690″)
};
double result = numbers.Aggregate((x, y) => x + y);
return result.ToString().Substring(0, 11).Replace(“.”, string.Empty);
}

]]> By: Torleif http://www.geekality.net/2009/10/04/project-euler-problem-13/#comment-286 Torleif Tue, 20 Apr 2010 06:04:31 +0000 http://www.geekality.net/?p=612#comment-286 Interesting. Do you have an example? Interesting. Do you have an example?

]]> By: John C http://www.geekality.net/2009/10/04/project-euler-problem-13/#comment-240 John C Mon, 29 Mar 2010 15:03:43 +0000 http://www.geekality.net/?p=612#comment-240 Nice brute force solution, but I think you're really missing the point of the exercise. The idea is that when you are adding n decimal numbers, there is an upper bound on the number of digits that can be carried over. for example 999*100 = 99900 Do you notice how only 2 extra digits were introduced? Thus, if you only need the first 10 digits, how many characters can you truncate from each string? You can safely truncate the numbers because any potential carry-over digits can only reach "so far" from the end Nice brute force solution, but I think you’re really missing the point of the exercise. The idea is that when you are adding n decimal numbers, there is an upper bound on the number of digits that can be carried over.

for example
999*100 = 99900
Do you notice how only 2 extra digits were introduced?

Thus, if you only need the first 10 digits, how many characters can you truncate from each string? You can safely truncate the numbers because any potential carry-over digits can only reach “so far” from the end

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