[R] Fastest way to find the last index k such that x[k] < y in a sorted vector x?

[Göran Broström]

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"

How about 

> k <- max(which(x < y))

Haven't done any benchmarking, though.

Göran

> 
> 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. 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.
> 
> Best
> 
> Henrik Bengtsson
> 
> Dept. of Mathematical Statistics @ Centre for Mathematical Sciences
> Lund Institute of Technology/Lund University, Sweden (+2h UTC)
> Office: P316, +46 46 222 9611 (phone), +46 46 222 4623 (fax)
> h b @ m a t h s . l t h . s e, http://www.maths.lth.se/bioinformatics/
> 
> 
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-- 
 Göran Broström                      tel: +46 90 786 5223
 professor                           fax: +46 90 786 6614
 Department of Statistics            http://www.stat.umu.se/egna/gb/
 Umeå University
 SE-90187 Umeå, Sweden             e-mail: gb at stat.umu.se

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