samskivert: Euler 013

16 January 2008

Problem 013:

object Euler13 extends Application {
  val data = 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");

  def toList (number :String) :List[Int] = {
    number.toList.map((c) => (c - '0'));
  }

  def toNumber (list :List[Int]) :Long = {
    list.foldLeft(0L)((a :Long, b :Int) => a*10 + b)
  }

  def sumTens (numbers :List[List[Int]]) :List[Int] = {
    var sum = 0;
    for (number <- numbers) {
      if (number.length > 0) {
        sum = sum + number.last;
      }
    }
    return toList(sum.toString());
  }

  def rightShift (numbers :List[List[Int]]) :List[List[Int]] = {
    numbers.map((list) => list.slice(0, list.length-1))
  }

  def sum (numbers :List[List[Int]]) :Long = {
    if (numbers.last.length < 9) {
      numbers.foldLeft(0L)((a :Long, b :List[Int]) => a + toNumber(b))
    } else {
      sum(rightShift(sumTens(numbers) :: numbers));
    }
  }

  println(sum(data.map((n) => toList(n))));
}

For this one, I simply summed the tens column of all the numbers and then tacked that sum onto the list of numbers and lopped off the tens column of all the numbers in the list. When I got down to 8 digit numbers, I simply summed them to get the final result.

©1999–2015 Michael Bayne