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

Method: Set all max values to -Inf, then find the indices of the max. No sorting required.

X <- runif(1e7)
system.time(
{
  X[X == max(X)] <- -Inf
  which(X == max(X))
})

Works with ties and is very fast.

If you can guarantee no ties, then an even faster version is

system.time(
{
  X[which.max(X)] <- -Inf
  which.max(X)
})

EDIT: As Joris mentioned, this method doesn't scale that well for finding third, fourth, etc., highest values.

which_nth_highest_richie <- function(x, n)
{
  for(i in seq_len(n - 1L)) x[x == max(x)] <- -Inf
  which(x == max(x))
}

which_nth_highest_joris <- function(x, n)
{
  ux <- unique(x)
  nux <- length(ux)
  which(x == sort(ux, partial = nux - n + 1)[nux - n + 1])
}

Using x <- runif(1e7) and n = 2, Richie wins

system.time(which_nth_highest_richie(x, 2))   #about half a second
system.time(which_nth_highest_joris(x, 2))    #about 2 seconds

For n = 100, Joris wins

system.time(which_nth_highest_richie(x, 100)) #about 20 seconds, ouch! 
system.time(which_nth_highest_joris(x, 100))  #still about 2 seconds

The balance point, where they take the same length of time, is about n = 10.