49 lines
1.1 KiB
R
49 lines
1.1 KiB
R
|
library(numbers)
|
||
|
|
library(microbenchmark)
|
||
|
|
|
||
|
|
####
|
||
|
|
# limit: Obere Grenze für die Summe der Primzahltripel
|
||
|
|
#
|
||
|
|
# Gibt die Anzahl der einmaligen Primzahltripel
|
||
|
|
# bis zu einer oberen Grenze zurück.
|
||
|
|
####
|
||
|
|
simple87 <- function(limit) {
|
||
|
|
primes <- Primes(1, ceiling(limit^(1/2)))
|
||
|
|
|
||
|
|
x2 <- primes^2
|
||
|
|
x3 <- primes^3
|
||
|
|
x4 <- primes^4
|
||
|
|
x2 <- x2[x2 < limit]
|
||
|
|
x3 <- x3[x3 < limit]
|
||
|
|
x4 <- x4[x4 < limit]
|
||
|
|
|
||
|
|
x <- expand.grid(x2, x3, x4)
|
||
|
|
xSums <- rowSums(x)
|
||
|
|
length(unique(xSums[xSums < limit]))
|
||
|
|
}
|
||
|
|
|
||
|
|
# Wir erzeugen die Kombinationen selbst und
|
||
|
|
# generieren eine Matrix über cbind()
|
||
|
|
# Dadurch spart man sich die matrix <-> data.frame Konvertierung
|
||
|
|
faster87<-function(limit) {
|
||
|
|
primes <- Primes(1, ceiling(sqrt(limit)))
|
||
|
|
|
||
|
|
x2 <- primes^2
|
||
|
|
x3 <- primes^3
|
||
|
|
x4 <- primes^4
|
||
|
|
x2 <- x2[x2 < limit]
|
||
|
|
x3 <- x3[x3 < limit]
|
||
|
|
x4 <- x4[x4 < limit]
|
||
|
|
|
||
|
|
x <- cbind(rep(x2, each=length(x3)*length(x4)),
|
||
|
|
rep(x3, times=length(x2)*length(x4)),
|
||
|
|
rep(x4, times=length(x2)*length(x3))
|
||
|
|
)
|
||
|
|
|
||
|
|
xSums <- rowSums(x)
|
||
|
|
length(unique(xSums[xSums < limit]))
|
||
|
|
}
|
||
|
|
|
||
|
|
ress <- microbenchmark(simple87(5e7), faster87(5e7), times=500L)
|
||
|
|
|