[R] Union/Intersect two continuous sets

Hans W Borchers hwborchers at googlemail.com
Thu Dec 22 16:50:11 CET 2011

谢一鸣 <cutexym <at> gmail.com> writes:

> Dear All,
> It is my first time using this mail list to post a question. And I
> sincerely hope that this will not bother any subscribers.
> So far as I know, there are functions like union( ), which can help to
> combine two sets of discrete data. But what if the data sets are with
> continuous data. For instance, I got three sets like [2, 4], [5, 6], [3.4,
> 5.5]. I wonder if there is a quick solution to recognize their union is [2,
> 6], and return the size of this union 6-2=4 to me. The similar demand is
> for the intersection operation.
> If you get any idea, please inform me. Thanks in advance!
> Xie

I got interested in your request as I could use it myself (not for intervals,
but a similar kind of problem).
I assume, you represent your set of intervals as a matrix M with two columns,
first column the left endpoints, second the right ones.

Intersection is easy, as it is the interval from the maximum of left end
points to the minimum of the right end points (or NULL if the maximum is
greater than the minimum).

For the union I didn't see a simple, i.e. one or two lines, solution ahead,
so here is my dumb, looped version. Surely there are more elegant solutions

    # Mnew the union of intervals in M, an (nx2)-matrix with n > 1:
    o <- order(M[, 1], M[, 2])
    L <- M[o, 1]; R <- M[o, 2]
    k <- 1
    Mnew <- matrix(c(L[k], R[k]), 1, 2)
    for (i in 2:nrow(M)) {
        if (L[i] <= Mnew[k, 2]) {
            Mnew[k, 2] <- max(R[i], Mnew[k, 2])
        } else {
            k <- k+1
            Mnew <- rbind(Mnew, c(L[i], R[i]))

    # Inew the intersection of intervals in M, an (nx2)-matrix with n > 1:
    L <- max(M[, 1]); R <- min(M[, 2])
    Inew <- if (L <= R) c(L, R) else c()

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