Fastest way to find *the index* of the second (third…) highest/lowest value in vector or column

Question

Fastest way to find the index of the second (third...) highest/lowest value in vector or column ?

i.e. what

sort(x,partial=n-1)[n-1]
         


        

Answer 1

EDIT 2 :

As Joshua pointed out, none of the given solutions actually performs correct when you have a tie on the maxima, so :

X <- c(11:19,19)

n <- length(unique(X))
which(X == sort(unique(X),partial=n-1)[n-1])

fastest way of doing it correctly then. I deleted the order way, as that one doesn't work and is a lot slower, so not a good answer according to OP.

To point to the issue we ran into :

> X <- c(11:19,19)    
> n <- length(X)
> which(X == sort(X,partial=n-1)[n-1])
[1]  9 10 #which is the indices of the double maximum 19

> n <- length(unique(X))
> which(X == sort(unique(X),partial=n-1)[n-1])
[1] 8 # which is the correct index of 18

The timings of the valid solutions :

> x <- runif(1000000)

> ind <- 2

> n <- length(unique(x))

> system.time(which(x == sort(unique(x),partial=n-ind+1)[n-ind+1]))
   user  system elapsed 
   0.11    0.00    0.11 

> system.time(sapply(sort(unique(x), index.return=TRUE), `[`, n-ind+1))
   user  system elapsed 
   0.69    0.00    0.69