R: Project Euler 10-19

problem10.R

library(pracma)
sum(primes(2e6))

problem11.R

n <-
"08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48"

n <- t(matrix(as.numeric(strsplit(n, "( |\n *)")[[1]]), 20))

value <- function(x,y) if (x > 20 || x < 1 || y > 20 || y < 1) 0 else n[x,y]

maxProd <- function(x,y) max(
	prod(mapply(value, x:(x-3), y)),
	prod(mapply(value, x:(x-3), y:(y+3))),
	prod(mapply(value, x, y:(y+3))),
	prod(mapply(value, x:(x+3), y:(y+3)))
)

f <- function(x,y) mapply(maxProd, x, y)

max(outer(1:20, 1:20, f))

problem12.R

library(memoise)
library(numbers)

s <- memoise(function(n) sigma(n,0))
f <- function(n) if (n%%2==0) s(n/2)*s(n+1) else s(n)*s((n+1)/2)
n <- 1
while (f(n) <= 500) n <- n+1
n*(n+1)/2

problem13.R

library(gmp)

s <- c(
"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")

n <- sum(as.bigz(s))
n %/% 10^(floor(log10(n))-9)

problem14.R

limit <- 1e6-1

steps <- numeric(limit); steps[1] <- 1

for (n in 2:limit) {
	if (steps[n] > 0) next
	s <- numeric(0)
	repeat {
		if (n <= limit && steps[n] > 0) {
			x <- steps[n] + length(s)
			for (i in s) {
				if (i <= limit) steps[i] <- x
				x <- x-1
			}
			break
		}
		s <- c(s, n)
		if (n %% 2 == 0) n <- n %/% 2
		else             n <- 3*n + 1
	}
}

which.max(steps)

problem15.R

choose(40,20)

problem16.R

library(gmp)

n <- pow.bigz(2,1000)
sum(n %/% pow.bigz(10, floor(log10(n)):0) %% 10)

problem17.R

s0 <- c(
	"", "One", "Two", "Three", "Four", "Five",
	"Six", "Seven", "Eight", "Nine", "Ten",
	"Eleven", "Twelve", "Thirteen", "Fourteen", "Fifteen",
	"Sixteen", "Seventeen", "Eighteen", "Nineteen"
)
s1 <- c(
	"", "", "Twenty", "Thirty", "Forty", "Fifty",
	"Sixty", "Seventy", "Eighty", "Ninety"
)

spell <- function(n) {
	s <- ""
	repeat {
		if (n < 20) return(paste(s, s0[n+1], sep=""))
		if (n < 100) return(paste(s, s1[n%/%10+1], s0[n%%10+1], sep=""))
		if (n == 1000) return("OneThousand")
		if (n %% 100 == 0) return(paste(s0[n%/%100+1], "Hundred", sep=""))
		s <- paste(s0[n%/%100+1], "HundredAnd", sep="")
		n <- n %% 100
	}
}

sum(nchar(sapply(1:1000, spell)))

problem18.R

s <- c(
	"75",
	"95 64",
	"17 47 82",
	"18 35 87 10",
	"20 04 82 47 65",
	"19 01 23 75 03 34",
	"88 02 77 73 07 63 67",
	"99 65 04 28 06 16 70 92",
	"41 41 26 56 83 40 80 70 33",
	"41 48 72 33 47 32 37 16 94 29",
	"53 71 44 65 25 43 91 52 97 51 14",
	"70 11 33 28 77 73 17 78 39 68 17 57",
	"91 71 52 38 17 14 91 43 58 50 27 29 48",
	"63 66 04 68 89 53 67 30 73 16 69 87 40 31",
	"04 62 98 27 23 09 70 98 73 93 38 53 60 04 23"
)

x <- sapply(mapply(strsplit, s, " "), as.numeric)

join <- function(x, y) {
	sapply(1:length(y), function(i) y[[i]] + max(x[[i]], x[[i+1]]))
}

Reduce(join, rev(x))[[1]]

problem19.R

d <- weekdays(seq(as.Date("1901/1/1"), as.Date("2000/12/31"), "month"))
length(d[d == "日曜日"])