R - plot overlapping time intervals

Question

I have a list of people and their working start and end times during a day. I want to plot a curve showing the total of people working at any given minute in the day. What I could do is just add 1440 additional conditional boolean variables for each minute of the day and sum them up, but that seems very inelegant. I'm wondering if there a better way to do it (integrals?).

Here's the code to generate a df with my sample data:

sample_wt <- function() {

    require(lubridate)

    set.seed(10)

    worktime <- data.frame(
            ID = c(1:100),
            start = now()+abs(rnorm(100,4800,2400))
            )

    worktime$end <- worktime$start + abs(rnorm(100,20000,10000))

    worktime$length <- difftime(worktime$end, worktime$start, units="mins")

    worktime
}

To create a sample data , you can do something like:

DF <- sample_wt() 

Answer 1

Here one option using IRanges package from Bioconductor.

library(IRanges)
## generate sample
DF <- sample_wt()
## create the range from the sample data
rangesA <- IRanges(as.numeric(DF$start), as.numeric(DF$end))
## create one minute range 
xx = seq(min(DF$start),max(DF$end),60)
rangesB <- IRanges(as.numeric(xx),as.numeric(xx+60))
## count the overlaps
ov <- countOverlaps(rangesB, rangesA, type="within")
## plot the result
plot(xx,ov,type='l')

Answer 2

I don't have lubridate installed, so I produced the data.frame through Sys.time instead of now (guess they should be similar). This could make the trick:

    minutes<-seq(as.POSIXct(paste(sep="",Sys.Date()," 00:00:00")),by="min",length.out=24*60)
    rowSums(outer(minutes,worktime$start,">") & outer(minutes,worktime$end,"<"))

Answer 3

Surely it can be improved, but this seems to do it:

time_range <- seq(min(DF$start), max(DF$end), 60)
result <- integer(length(time_range))
for (t in seq_along(time_range)) {
  result[t] <- sum(DF$start <= time_range[t] & DF$end >= time_range[t])
}