R: Project Euler 40-49

problem41.R

library(pracma)
 
xs <- colSums(t(perms(1:7)) * (10^(6:0)))
for (x in xs) if(isprime(x)) {answer <- x; break} else next
answer

problem42.R

words <- scan("words.txt", what="character", sep=",", na.strings="")
words <- strsplit(words, "")

f <- function(x, y) x + which(LETTERS %in% y)
nums <- Vectorize(function(c) Reduce(f, c, 0))(words)

tri <- 1:(ceiling(sqrt(max(nums)*2)))
tri <- (tri*(tri+1))%/%2

length(nums[nums %in% tri])

problem43.R

candidate <- function(d) {
	len <- length(d)
	if (len <  4)  return(TRUE)
	if (len == 4)  return((100*d[2]+10*d[3]+d[4])  %% 2  == 0)
	if (len == 5)  return((100*d[3]+10*d[4]+d[5])  %% 3  == 0)
	if (len == 6)  return((100*d[4]+10*d[5]+d[6])  %% 5  == 0)
	if (len == 7)  return((100*d[5]+10*d[6]+d[7])  %% 7  == 0)
	if (len == 8)  return((100*d[6]+10*d[7]+d[8])  %% 11 == 0)
	if (len == 9)  return((100*d[7]+10*d[8]+d[9])  %% 13 == 0)
	if (len == 10) return((100*d[8]+10*d[9]+d[10]) %% 17 == 0)
}

nexts <- function(d) {
	n <- (n <- (0:9))[!n %in% d]
	sapply(n, function(n) list(c(d, n)))
}

res <- numeric(0)
s <- sapply(1:9, list)
while (length(s) > 0) {
	top <- s[[1]]; s <- s[-1]
	if (!candidate(top)) next
	if (length(top) == 10) {res <- c(res, list(top)); next}
	s <- c(nexts(top), s)
}

sum(sapply(res, function(d) sum(d*10^((length(d)-1):0))))

problem45.R

m <- 165; n <- 143; p <- (h <- 40755)
while (p != h || p == 40755) {
	if (p < h) {m <- m+1; p <- m*(3*m-1)%/%2}
	else       {n <- n+1; h <- n*(2*n-1)}
}
p

problem46.R

library(pracma)

primes <- 3
isAnswer <- function(n) {
	x <- 1:(sqrt(n/2))
	x <- n-(2*x*x)
	!any(x %in% primes)
}

n <- 3
repeat {
	n <- n+2
	if (isprime(n)) {primes <- c(primes, n); next}
	if (isAnswer(n)) break
}
n

problem47.R

max <- 1e6
x <- numeric(max)
n <- 2
repeat {
	if (n > max) break
	if (x[n] == 0) {
		m <- n * 2:(max %/% n)
		x[m] <- x[m] + 1
	}
	if (n > 4 && all(x[(n-3):n] == 4)) {answer <- n-3; break}
	n <- n+1
}
answer

problem48.R

library(gmp)
sum(pow.bigz(1:1000,1:1000))%%1e10

problem49.R

library(pracma)
library(hash)

p <- (p <- primes(9999))[p > 1000]

digits <- apply(t(matrix(
	c(p%/%1000, p%/%100%%10, p%/%10%%10, p%%10), nr=length(p)
)), 2, sort)
d <- colSums(digits * (10^(3:0)))

f <- function(xs) {
	for (x in xs) {
		if (x == 1487) next
		y <- (y <- xs[xs > x])[(2*y-x) %in% y]
		if (length(y) > 0) return(c(x, y, 2*y-x))
	}
}

h <- invert(hash(p,d))

for (k in keys(h)) {
	v <- strtoi(h[[k]])
	if (length(v) < 3) next
	if (length(x <- f(v)) > 0) {answer <- x; break}
}
answer