Question

Is there a way to encode increasing integer sequences in R, analogous to encoding run lengths using run length encoding (rle)?

I’ll illustrate with an example:

Analogy: Run length encoding

r <- c(rep(1, 4), 2, 3, 4, rep(5, 5))
rle(r)
Run Length Encoding
  lengths: int [1:5] 4 1 1 1 5
  values : num [1:5] 1 2 3 4 5

Desired: sequence length encoding

s <- c(1:4, rep(5, 4), 6:9)
s
[1] 1 2 3 4 5 5 5 5 6 7 8 9

somefunction(s)
Sequence lengths
  lengths: int [1:4] 5 1 1 5
  value1 : num [1:4] 1 5 5 5

Edit 1

Thus, somefunction(1:10) will give the result:

Sequence lengths
  lengths: int [1:1] 10
  value1 : num [1:1] 1 

This results means that there is an integer sequence of length 10 with starting value of 1, i.e. seq(1, 10)

Note that there isn’t a mistake in my example result. The vector in fact ends in the sequence 5:9, not 6:9 which was used to construct it.

My use case is that I am working with survey data in an SPSS export file. Each subquestion in a grid of questions will have a name of the pattern paste("q", 1:5), but sometimes there is an “other” category which will be marked q_99, q_other or something else. I wish to find a way of identifying the sequences.

Edit 2

In a way, my desired function is the inverse of the base function sequence, with the start value, value1 in my example, added.

lengths <- c(5, 1, 1, 5)
value1 <- c(1, 5, 5, 5)

s
[1] 1 2 3 4 5 5 5 5 6 7 8 9
sequence(lengths) + rep(value1-1, lengths) 
[1] 1 2 3 4 5 5 5 5 6 7 8 9

Edit 3

I should have stated that for my purposes a sequence is defined as increasing integer sequences as opposed to monotonically increasing sequences, e.g. c(4,5,6,7) but not c(2,4,6,8) nor c(5,4,3,2,1). However, any other integer can appear between sequences.

This means a solution should be able to cope with this test case:

somefunction(c(2, 4, 1:4, 5, 5))
    Sequence lengths
      lengths: int [1:4] 1 1 5 1
      value1 : num [1:4] 2 4 1 5 

In the ideal case, the solution can also cope with the use case suggested originally, which would include characters in the vector, e.g.

somefunction(c(2, 4, 1:4, 5, "other"))
    Sequence lengths
      lengths: int [1:5] 1 1 5 1 1
      value1 : num [1:5] 2 4 1 5 "other"

Answer 1

EDIT : added control to do the character vectors as well.

Based on rle, I come to following solution :

somefunction <- function(x){

    if(!is.numeric(x)) x <- as.numeric(x)
    n <- length(x)
    y <- x[-1L] != x[-n] + 1L
    i <- c(which(y|is.na(y)),n)

    list(
      lengths = diff(c(0L,i)),
      values = x[head(c(0L,i)+1L,-1L)]
    )

}

> s <- c(2,4,1:4, rep(5, 4), 6:9,4,4,4)

    > somefunction(s)
    $lengths
    [1] 1 1 5 1 1 5 1 1 1

    $values
    [1] 2 4 1 5 5 5 4 4 4

This one works on every test case I tried and uses vectorized values without ifelse clauses. Should run faster. It converts strings to NA, so you keep a numeric output.

> S <- c(4,2,1:5,5, "other" , "other",4:6,2)

> somefunction(S)
$lengths
[1] 1 1 5 1 1 1 3 1

$values
[1]  4  2  1  5 NA NA  4  2

Warning message:
In somefunction(S) : NAs introduced by coercion