Sum of intervals lengths from an integer vector

Question

Let's say I have this integer vector:

> int.vec
 [1]  1  2  3  5  6  7 10 11 12 13

(created from int.vec <- c(1:3,5:7,10:13))

I'm looking for a function that will return the sum of the lengths of all intervals in this vector.

So basically for int.vec this function will return:

3+3+4 = 10

Answer 1

length(int.vec)
# 10

Your intervals are sequences of numbers, x1:xn, x1:xm, x1:xp, where the length of each vector (or interval in this case) is n, m, and p respectively.

The length of the whole vector is length(x1:xn) + length(x1:xm) + length(x1:xp), which is the same as length(n + m + p).

---

Now, if we really are interested in the length of each individual vector of sequences, we can do

int.vec <- c(1:3,5:7,10:13)

## use run-length-encoding (rle) to find sequences where the difference == 1
v <- rle(diff(int.vec) == 1)[[1]]
v[v!=1] + 1
# [1] 3 3 4

And, as pointed out by @AHandcartAndMohair, if you're working with a list you can use lengths

int.list <- list(c(1:3), c(5:7), c(10:13))
lengths(int.list)
# [1] 3 3 4