How to find the number of runs?

Question

How to find the number of runs in the following

1. aaaabbabbbaabba

2. bbaaaaaabbbbaaaaaaa

Answer 1

If you want do this in R, check out the rle function.

For example:

> ext <- function(x) {strsplit(x, "")[[1]]}
> x <- ext("aaaabbabbbaabba")
> y <- ext("bbaaaaaabbbbaaaaaaa")
> length(rle(x)$lengths)
[1] 7
> length(rle(y)$lengths)
[1] 4

See also this related question on Stack Overflow on counting runs in R

Answer 2

Quoting http://en.wikipedia.org/wiki/Wald-Wolfowitz_runs_test:

A "run" of a sequence is a maximal non-empty segment of the sequence consisting of adjacent equal elements. For example, the sequence "++++−−−+++−−++++++−−−−" consists of six runs, three of which consist of +'s and the others of −'s.

In your case

1) aaaabbabbbaabba      2) bbaaaaaabbbbaaaaaaa
   1   2 34  5 6 7         1 2     3   4