[R] Fastest way to find the last index k such that x[k] < y in a sorted vector x?
Thomas Lumley
tlumley at u.washington.edu
Thu Jun 27 18:47:48 CEST 2002
On Thu, 27 Jun 2002, Henrik Bengtsson wrote:
> Hi, I am trying to find the fastest way to
>
> "find the last index k such that x[k] < y in a *sorted* vector x"
>
> These are my two alternatives:
>
> x <- sort(rnorm(1e4))
> y <- 0.2
>
> # Alt 1
> k <- max(1, sum(x < y))
>
> # Alt 2 "divide and conquer"
> lastIndexLessThan <- function(x, y) {
> k0 <- 1; k1 <- length(x)
> while ((dk <- (k1 - k0)) > 1) {
> k <- k0 + dk %/% 2
> if (x[k] < y) k0 <- k else k1 <- k
> }
> k0
> }
> k <- lastIndexLessThan(x, y)
>
> Simple benchmarking shows that alternative 1 is faster for short vectors and
> alternative 2 is faster for long vectors. I believe this is because alt 1 is
> implemented internally.
Yes.
> Is there an internal function of alternative 2 that
> I don't know about? It would be great because then it would probably be the
> fastest one on both short and long vectors.
You can use uniroot, eg.
uniroot(function(i) (x[i]>y)-i/N,c(1,length(x)))$root-1
where N>length(x)
On the other hand, I had to go to vectors of length 10^5 to get any
reproducible difference between this and
max(which(x<y))
-thomas
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