Euler13.scala

// https://projecteuler.net/problem=13
/*
Work out the first ten digits of the sum of the following one-hundred 50-digit numbers.

37107287533902102798797998220837590246510135740250
...
53503534226472524250874054075591789781264330331690
*/

/*
Most of these digits are irrelevant. Which is good, because there is a way to squeeze most of the processing into the Int data type,
and make this a trivial problem of adding a couple-hundred integers, casting to Long, and dividing by the correct multiple of 10.
*/
import scala.math.BigDecimal

object Euler13 {

	// timer function at the top of every solution: http://biercoff.com/easily-measuring-code-execution-time-in-scala/
	def time[R](block: => R): R = {
		val t0 = System.nanoTime()
		val result = block
		val t1 = System.nanoTime()
		println("Elapsed time: " + ((t1 - t0) / 1000000.0) + "ms")
		result
	}


	def solution1(): Long = {
		val inputString = formatInputString()
			// Even if every number is 9,999,999 -- 100 of these added together still fits in Int type
		val first7Nums: Array[Int] = inputString.split(",").map(x => x.substring(0,7).toInt)
		val second7Nums: Array[Int] = inputString.split(",").map(x => x.substring(7,14).toInt)
		val first7Sum: Int = first7Nums.sum
		val second7Sum: Int = second7Nums.sum
		// println(first7Sum)
		// println(second7Sum)
			// second7Sum should account for anything that could possibly affect 10th digit, and first7Sum gives left side of the number.
			// this assumes first7Sum will be a 9 digit number, which is pretty safe if you take a 100 7-digit numbers and add them.
		((first7Sum * 100000L) + second7Sum) // / 10000
		
		// this is actually wrong, but I wanna save it and try for right answer in solution2
	}
	
	def solution2(): Long = {
		val inputString = formatInputString()
			// Even if every number is 9,999,999 -- 100 of these added together still fits in Int type
		val first7Nums: Array[Int] = inputString.split(",").map(x => x.substring(0,7).toInt)
		val second7Nums: Array[Int] = inputString.split(",").map(x => x.substring(7,14).toInt)
		val third7Nums: Array[Int] = inputString.split(",").map(x => x.substring(14,21).toInt)
		val first7Sum: Int = first7Nums.sum
		val second7Sum: Int = second7Nums.sum
		val third7Sum: Int = third7Nums.sum / 1000
		// println(first7Nums.length)
		// println(second7Sum)
		// println(third7Sum)
			// second7Sum should account for anything that could possibly affect 10th digit, and first7Sum gives left side of the number.
			// this assumes first7Sum will be a 9 digit number, which is pretty safe if you take a 100 7-digit numbers and add them.
		((first7Sum * 1000000000L) + (second7Sum * 10000L) + third7Sum) // / 10000
		
		// same answer as Solution 1. What am I missing?
	}
	
	def solution3(): BigDecimal = {
		// intuition here is, instead of dealing with massive integers, convert to BigDecimal with massive precision level, and turn it into a two-liner that way.
		val inputString = formatInputString()
		inputString.split(",").map(x => BigDecimal("." + x)).sum
	}


	def main(args: Array[String]) {
	
		time{ println(solution2()) }
			// Elapsed time: 12.069451ms
		time{ println(solution2()) }
			// Elapsed time: 2.624538ms
			// both return 5537424779, both wrong
		
		time{ println(solution3()) }
			// Elapsed time: 7.666191ms
			// This does return a slightly different number, for reasons I need to understand. But it's correct.
			// So somehow, I made a bad assumption that only the first 14 digits or so were relevant. Apparently the fractions much further to the right make a difference...
				// when you add 100 of them. And on top of that it's a much more elegant solution with comparable performance.
	}


	def formatInputString(): String = {
		"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"
	}
}